text: File:Team1's Coupled pendulums revised.png


text:
User:Egm6321.f11.team1.steele.m/Report3

R*3.7 Question from meeting 15, page 2: Use IFM to show that the solution of (2) below is (3) underneath. $$\dot x(t)= ax(t) + bu(t)$$ $$x(t)=[\exp\{a(t-t_0)\}]x(t_0)+\int^t_{t_0}[\exp\{a(t-\tau)\}]\,b \,u(\tau)\, d \tau$$ From lecture notes [[media:pea1.f11.mtg15.djvu|Mtg 15]]

Solution
The solution requires an understanding of how the Euler Integrating Factor Method (IFM) is based on the 1st and 2nd exactness conditions. Please note that the equations below for the Euler IFM were derived in a previous homework assignment and noted again for clarity. The derivation builds to the solution. First Exactness Condition of N1-ODEs If an N1-ODE is exact then it has a particular form of M(x,y) + N(x,y)y' = 0 where $$ y' = \frac{dy}{dx}$$ The appended derivations to this point are from meeting 8 Second Exactness Condition of N1-ODEs Now, we must derive the 2nd exactness condition. A general ND-ODE is exact if for G the following relations exist: $$\frac{d\phi}{dx} = G$$ $$\phi(x,y) = k$$ $$\frac{d\phi(x,y(x))}{dx} = G(y',y,x) = 0$$ Let $$\phi(x,y)$$ be a smooth function, then for the 2nd exactness condition we have $$M_y(x,y) = \frac {\partial^2\phi(x,y)}{\partial x\partial y} = N_x(x,y) = \frac{\partial^2\phi(x,y)}{\partial y\partial x}$$ The appended derivations to this point are from meeting 9 If an N1-ODE satisfies the 1st exactness condition but not the 2nd, then the N1-ODE can be transformed by using the Euler Integrating Factor Method (IFM). Assume the conditions below. $$M(x,y) + N(x,y)y' = 0 \And M_y(x,y) \ne N_x(x,y)$$ The transformation of the given N1-ODE to a form that fulfills both exactness conditions begins by finding an integrating factor h(x,y). For condition 1, the substitution of h gives $$(hM) + (hN)y' = \bar{M} + \bar{N}y' = 0$$ The key is to derive a solution using $$\bar{M} = hM \And \bar{N} = hN$$ The derivations are as follows: $$\bar{M}_y = h_yM + hM_y = \bar{N}_x = h_xN + hN_x$$ So the Euler IFM gives the following solution using h(x,y) as the transformation. $$h_xN - h_yM + h(N_x - M_y) = 0 $$ The cumulative derivations to this point are from meetings 10-11 But in our case of this problem, the following equation is the direct basis for the derivation. The inhomogeneous form of this equation has a solution based on meeting 11. So the IFM takes a different derivation path. The updated solution process begins here for report 3. $$\underbrace{-a \,x}_{\displaystyle\color{blue}{M(t,x)}} + \underbrace{\color{blue}{1}}_{\displaystyle\color{blue}{N(t,x)}} \cdot dx/dt = bu(t) $$ The 1st order linear differential equation is a function of t with two variables x(t) and u(t). So let us rewrite the equation as $$-ax + x' = bu = M + Nx'$$ Note that M = -ax and N = 1, so that $$\frac{h_t}{h} = \frac{1}{\N}(N_t - M_x) = (0 - a) = n(s)$$ $$\int_{t_0}^t\frac{h_t}{h} = \int_{t_0}^t(-a)$$ The equation reduces to $$\ln h = -a(t-t_0)$$ Which can be exponentiated to give the integrating factor $$ h = \exp ({\ln h}) = \exp -a(t-t_0)$$ Once the integrating factor is found, the following identity is used to integrate for hx. $$\frac{h_t}{h} = -a$$ So rearrangement gives $$h_t = ha = \dot {h}$$ The substitution into the 1st exactness condition for the inhomogenous condition gives $$h\dot {x} + \dot {h} x = \dot{hx} = hbu$$ Integrate both sides and get $$\int_{t_0}^t{\dot {hx}} = \int_{t_0}^t{b*u}*dt$$ The use of the dummy variable tau and rearrangement with respect to the integration constant gives $$x(t)=[\exp\{a(t-t_0)\}]x(t_0)+\int^t_{t_0}[\exp\{a(t-\tau)\}]\,b \,u(\tau)\, d \tau$$ The first term on the left is the homogeneous solution, and the 2nd term on the right is the particular solution.

References for R3.7 Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 9) [[media:pea1.f11.mtg9.djvu|Mtg 9]] 8 Sep 2011. Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 10) [[media:pea1.f11.mtg10.djvu|Mtg 10]] 8 Sep 2011. Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 11) [[media:pea1.f11.mtg11.djvu|Mtg 11]] 13 Sep 2011. Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 15) [[media:pea1.f11.mtg15.djvu|Mtg 15]] 22 Sep 2011

R*3.8 Question from meeting 15, page 4: Generalize (2) p. 15-2 to the case of linear time-variant system (1) p. 14-4. See (1) p. 15-2. Verify that your expression is indeed the solution for (1) p.14-4. $$\mathbf{x}(t) = \left[\exp \{\mathbf{A}(t-t_0) \} \right] \, \mathbf{x}(t_0) + \int^t_{t_0} \left[\exp \{ \mathbf{A} (t-\tau) \} \right] \mathbf{B} \, \mathbf{u}(\tau) \, d\tau$$ $$\mathbf{\dot[x]}(t) = \mathbf{A}(t) \,\mathbf{x}(t) + \mathbf{B}(t)\, \mathbf{u}(t)$$ From lecture notes [[media:pea1.f11.mtg15.djvu|Mtg 15]]

Solution
The equation (2) from p. 15-2 was for the case of n = 1. But the solution can be generalized for all n by simply applying the same derivation to the equation in matrix form. $$\mathbf{\dot[x]}(t) = \mathbf{A}(t) \,\mathbf{x}(t) + \mathbf{B}(t)\, \mathbf{u}(t)$$

The derivation path is similar since the solution of a scalar linear 1st order differential equation is the same for a system of such equations.

The 1st order linear differential equation is a function of t with two matrices x(t) and u(t) and two varying coefficient matrices a(t) and b(t). So let us rewrite the equation as $$-\mathbf{A}\mathbf{X} + \mathbf{X}' = \mathbf{B}\mathbf{U} = \mathbf{M} + \mathbf{N}\mathbf{X}'$$ $$\frac{\mathbf{h_t}}{\mathbf{h}} = \frac{1}{\mathbf{N}}(\mathbf{N_t} - \mathbf{M_x}) = (0 - \mathbf{A}) = \mathbf{n(s)}$$ So rearrangement gives $$ x(t) = \left[\exp\int^t_(t_0)\mathbf{A}(\mathbf{\tau}d\tau\right]\mathbf{x}(t_0) + \int^t_{t_0}\left[exp \int^t_{\tau}\mathbf{A}(s)ds \right]\mathbf{b}(\mathbf{\tau})\mathbf{u(\tau)}\, d\tau $$

References for R3.8 Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 11) [[media:pea1.f11.mtg11.djvu|Mtg 11]] 13 Sep 2011. Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 14) [[media:pea1.f11.mtg14.djvu|Mtg 14]] 20 Sep 2011. Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 15) [[media:pea1.f11.mtg15.djvu|Mtg 15]] 22 Sep 2011.

R*3.9 Question from meeting 15, page 5: Verify that (1) satisfies (2)-(3). The equations (1) to (3) are shown from top to bottom below. $$\mathbf{\Phi}(t,t_0) = \exp \{\mathbf{A}(t-t_0) \}$$ $$\displaystyle\frac{d}{dt} \mathbf{\Phi}(t,t_0) = \mathbf{A} \, \mathbf{\Phi}(t,t_0)$$ $$\mathbf \Phi (t_0,t_0) = \mathbf I$$ From lecture notes [[media:pea1.f11.mtg15.djvu|Mtg 15]]

Solution
The derivation of a matrix is a direct derivation of a linear system. So it follows the general rules of derivation and matrix algebra. The derivative of an exponential function as a scalar is the same as that for a linear system in matrix algebraic notation. Therefore, the simple rules of derivation apply to prove that (1) satisfies (2) $$\frac {d}{dt} {\mathbf{\Phi}(t,t_0)} = \frac {d}{dt} \exp \{\mathbf{A}(t-t_0) \}$$ $$\frac {d}{dt} {\mathbf{\Phi}(t,t_0)} = \frac {d}{dt} [\mathbf{A}(t-t_0)] * \exp \{\mathbf{A} (t-t_0) \}$$ This simply reduces to show that (1) satisfies (2). $$\displaystyle\frac{d}{dt} \mathbf{\Phi}(t,t_0) = \mathbf{A} \, \mathbf{\Phi}(t,t_0)$$ In addition, the identity matrix is derived from general matrix algebra. $${\mathbf{\Phi}(t_0,t_0)} = \exp \{\mathbf{A}(t_0-t_0) \} = \exp \{\mathbf{A}(0) \} $$ $${\mathbf{\Phi}(t_0,t_0)} = \exp {\begin{bmatrix} 1     & \cdots & 0      \\ \vdots & \ddots & \vdots \\ 0     & \cdots & 1 \end{bmatrix}} $$ Therefore, the substitutions give the identity matrix, which is a matrix with values of 1 along the diagonal and 0 elsewhere.

References for R3.9 King, A.C., J. Billingham, and S.R. Otto. Differential Equations: Linear, Nonlinear, Ordinary, Partial. New York: Cambridge University Press, 2003. Oulia, Masoud and David E. Stevens. Fundamentals of Engineering Exam, 2nd Edition. Boston: Barron's Educational Services Inc., 2008. Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 15) [[media:pea1.f11.mtg15.djvu|Mtg 15]] 22 Sep 2011.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Egm6321.f11.team1.steele.m/Report3


text:
Literature/1903/Pavlov

Russian title: "Eksperimental’naiia psikhologiia i psikhopatologiia na zhivotnykh."

Reprints

 * Pavlov, Ivan P. Lectures on Conditioned Reflexes. Translated by Horsley Gantt. New York: International Publishers, 1928. Volume 1, pages 47-60. The translation of the extract in the text was provided by Gregory Razran.
 * See also
 * Pavlov, I. P. Conditioned Reflexes: An Investigation of the Physiological Activity of the Cerebral Cortex. Translated and Edited by G. V. Anrep. London: Oxford University Press, 1927.

Wikimedia

 * Ivan Pavlov
 * Conditioned reflex

 * Experimental psychology

 * Behaviorism

Chronology

 * Razran, Gregory (1965). "Russian physiologists' psychology and American experimental psychology: A historical and a systematic collation and a look into the future." Psychological Bulletin, vol. 63 no. 1 (Jan 1965): 42-64. Abstract

Reviews

 * In this paper the definition of conditioned and other reflexes was given and it was shown that a conditioned reflex should be regarded as an elementary psychological phenomenon, which at the same time is a physiological one. It followed from this that the conditioned reflex was a clue to the mechanism of the most highly developed forms of reaction in animals and humans to their environment and it made an objective study of their psychic activity possible. -- From "Pavlov," nobelprize.org, 1904

title: Literature/1903/Pavlov


text:
User:Leighblackall/CV

Leigh lives in Melbourne Australia with his beautiful wife Sunshine, their baby Eve, and their dog Lego. Leigh enjoys outdoor recreation with a passion for back country telemark skiing, and fond memories of rock climbing and cycle touring. He also enjoys tinkering with permaculture design and ideas for post industrial living.

Leigh’s professional interest is in educational development, focused on open and networked learning and research, using social media and community engagement. Leigh currently works with the Centre for School Leadership, Learning and Development at Charles Darwin University.

Sunshine wants Leigh to find a small block of land by a river, free them from wage slavery, and go back to being an artist, growing vegies, running goats, and raising a baby - Leigh whole heartedly agrees. In the meantime, slave on...

=Contact=
 * eMail: leighblackallATgmailDOTcom
 * Phone: +610404561009
 * Site: http://about.me/leighblackall

=Presentations=
 * Open Education and Research at the University of Canberra A presentation delivered with James Neill at the 2010 Annual Conference of Knowledge Commercialisation Australasia

 * Open PhD: Connecting Sharing Developing - A 10 minute presentation to the University of Canberra, PhD Students Induction Day, 4 Feb 2010

 * Deconstructing Behaviorism within Social Constructivism Guest speaker to Ascilite and Desire2Learn in Wellington

 * Popular Internet in Teaching And Research - Introductory presentation to the Faculty of Health, University of Canberra. References and image credits at delicious.com/leighblackall/uchealth

 * The Disconnect Between Learning And Education - Slides for Skills Tasmania Conference, 2008

 * Open Educational Resources and Practices - In this article I take a look at what constitutes an open educational resource and consider the issues and benefits to an educational institution. An institution which is moving to participate in open educational resource development and adopt more open educational practices. There is a description of the initial steps being made by the Educational Development Centre at Otago Polytechnic - a tertiary education and vocational training institution in Southern New Zealand.

 * Networked Learning - Continuing on Knowledge Sharing by Sean FitzGerald and Leigh Blackall, http://networkedlearning.wikispaces.org/knowledge sharing Networked Learning attempts to simplify the concepts and stimulate wider audiences. Backing music by Melissa Welch http://www.archive.org/details/camomille076

 * Teaching is Dead, Long Live Learning - A presentation for Education Au’s Global Summit. http://leighblackall.wikispaces.com/Global+Summit

=Publications=
 * 1) Feedback on Leigh's work
 * 2) Open Education Practices: A User Guide for Organisations - A user guide for the Regional Hub of Ako Aotearoa
 * 3) Sci-fi learning - The power of POV Co authored with Simon Brown and Vicki Marchant for the Australian education journal Knowledge Tree, edition 19, 2009
 * 4) Models for Open Education - A talk given to the seventh annual Open Education Conference held in Vancouver 2009. Presentation notes here.
 * 5) Sustainability considerations relating to the use of Second Life for education - A scoping document to add to a literature review for the NZ research project Second Life in Education New Zealand (SLENZ)
 * 6) Virtual Classroom Project - Using Second Life to conceive an ideal learning space.
 * 7) Socially constructed media and communications - A keynote for the Desire2Learn and Ascilite round table discussion in Wellington on the evening of 18 June 2008
 * 8) The Disconnect Between Education and Learning - Keynote presentation to Skills Tasmania 2008 Conference Business in the 21st Century: Growth through skills and Innovation
 * 9) Educational Development at Otago Polytechnic - An article for PennState University's web journal Terra Ingognita.
 * 10) Open educational resources and practices. Keynote presentation with audio and article made for WIAOC 2007, George Siemens Future of Education, Paper published in the Italian e-Learning Association Journal - Je-LKS (n.2 2007), and republished by TESL-EJ Volume 11, Number 4.
 * 11) The Future of Learning in a Networked World - Book of compiled articles from the Future of Learning in a Networked World conference.
 * 12) Teaching is Dead, Long Live Learning - A keynote presentation to Global Summit 2006
 * 13) Learn Online blog - Articles, opinion and ideas to do with online learning, networked learning and flexible learning.
 * 14) Teach and Learn Online 2005 book - A collection of articles, ideas, opinion and instructions for teaching and learning online, published through Lulu.com
 * 15) Digital literacy and how it affects teaching and learning - A critique for the Australian education Journal Knowledge Tree republished in the December 2005 edition of the International Journal of Instructional Technology and Distance Learning
 * 16) Networked Learning Continuing on Knowledge Sharing by Sean FitzGerald and Leigh Blackall, Networked Learning attempts to simplify the concepts and stimulate wider audiences.
 * 17) Knowledge Sharing with Distributed Networking Tools - A presentation for the Networks September 12–14 2005 Mini-online Event - Cool Results: Engaging Clients in E-learning hosted by LearningTimes Australia
 * 18) Networked Learning in Action - An interactive session for the 2005 AUSTAFE Conference. Thursday 28 July 2005, Sydney Olympic Park.
 * 19) Using Free and Open Source Software to Create Free and Open Courseware - a resource for the Australian Flexible Learning Framework Community

=Teaching=
 * Facilitating Online
 * Composing educational resources
 * Flexible learning
 * Networked Learning
 * Social Media
 * Learning 4 Content Wikieducator workshops

=Educational media=
 * 1) Wikiversity projects including: Networked Learning, Facilitating Online, Social Media], Composing educational resources, and Open academia in practice. More>>>
 * 2) Wikibooks include: Consultation on the Anatomy and Physiology of Animals, work on Permaculture Design], project management of Sustainable Business].
 * 3) Otago Polytechnic - various open educational resource developments on a MediaWiki platform with staff at Otago Polytechnic
 * 4) Screencasting - a series of video, audio and print format demonstrations on the use and how to for a range of software, web services and netowked learning techniques.
 * 5) Construction Modules - Interactive video using Flash for the TAFE Connect, Horticulture Online project. The construction modules include: Concrete and Masonry Drainage Timber and Metal Paths and Paving all feature timelapse video, animation, and a vast number of short audio visual demonstrations recorded from an actual construction job and developed into these sharable object based educational resources.
 * 6) History and visual arts in Australia - My first online media development for a year 8 class. Looks at the paintings of Sidney Nolan and their relationship to Australian history, in particular, Ned Kelly.
 * 7) Political Posters - Carol Wells from the Centre for the Study of Political Graphics came to Newcastle TAFE to give a talk on political posters and the women of Juarez, Mexico. I was called in to record the presentation and make this resource for future design students.
 * 8) Building Online Communities - I recorded this presentation by Rolf Kleef while in Johannesburg South Africa in 2001. Later I did the best I could with the poor quality sound to create this resource for the Association of Progressive Communications.
 * 9) BlendedChocolate.com - An interactive audio visual resource about chocolate preparation in the baking trade.
 * 10) Surf Life Saving Australia - An interactive audio visual resource to assist lifesavers in learning for the Bronze Medallion.
 * 11) People - 10 lesson plans for visual art students aged 12 - 14 interested in people. Plans are to the Australian NSW secondary visual arts syllabus.

=Home Movies=

I like to make home movies. I record on a phone, and edit in a single sitting, using free copyright music. They're rough, sometimes a bit too conceptual, but I like them. They've been loaded to Archive, Blip.tv and YouTube.
 * 1) Outback Australia - A series of short home videos about skiing outback in Australia
 * 2) Back Country New Zealand - A series of short videos about back country skiing in New Zealand. The objective was to record with pocket cameras, and finish a video to free music within a day or 2 of getting back from the trip.
 * 3) Black Bulga Range - In the spring of 2002, The Black Bulga Range was scheduled to be logged.
 * 4) Taiwan A series of short videos about my life in Taiwan 1999-2001
 * 5) The Snow - In the winter of 2002 I went back country skiing with Miriam, Theo and Clare.
 * 6) There's a Light in My Eyes - Shot over 2 runs down the Corker Trail, There's a Light in my Eyes is a dramatic account of the incredible 35Km down hill bike run from Carey's Peak, Barington Tops National Park.
 * 7) Stencil Graffiti at Mullum High - During my second 4 week prac session while studying to be a teacher in 2002, I ran a class in stencil graffiti. Staff from the school tell me that new kids still ask if they're going to do stencil graffiti!
 * 8) Urban Planning - In 2001, the Newcastle City Council ran a conference on urban planning. We ended up doing a performance art piece, this video was the back drop.
 * 9) Dancing to Architecture - I directed this 25 minute open source documentary/motion picture about the 2002 This is Not Art (TINA) media festival.
 * 10) Association of Progressive Communication - Uraguay Conference 2001 - I did a brief stint working with the Melbourne, Australia group Community Communications Online (C2O) and represented them at the AGM of the Association of Progressive Communications (APC) in Uraguay, South America in 2001.

=Educational record= 2004 - Certificate 4 in Small Business - Hunter Business and Enterprise Centre 2003 - Certificate 4 in Workplace Training and Assessment - Hunter Institute of TAFE NSW 2002 - Diploma in Education, secondary school visual arts - University of Newcastle 1998 - Bachelor of Arts/Visual Arts - University of Newcastle 1994 - Associate Diploma in Fine Arts - Northern Sydney Institute of TAFE NSW 1994 - Initial Employment Training - Australian Army Reserve, Infantry

=Work history=

2012
Full time with the Faculty of Health Science at La Trobe University, Australia. Educational Designer. Onging...

Full time with the Centre for School Leadership, Learning and Development at Charles Darwin University, Australia. Director of eLearning. Evaluated online learning capabilities, document handling procedures and workflow management issues. Implemented a transition to Google Docs, and the use of Blogger, Youtube, Docs and Drive for the delivery of online courses. Established a professional development plan, centred around informal and work based learning. Conducted research. Worked on a PhD about networked learning.

2011
Full time with University of Canberra, Australia. Learning Commons Coordinator in Sport Studies and the Faculty of Health. Working with staff in developing social media and Internet skills useful to their teaching and research work. Also responsible for the development and maintenance of the Faculty website. Presentations and papers. Working on a PhD about networked learning.

 * Panelist at Critical Animals, This is Not Art, discussing the role of archive and museum in preserving online cultural heritage
 * Developed and taught The Business and Politics of Sport, a third and fourth year Bachelor of Sport Management unit. Unit was made fully flexible, online, and assessment based.
 * Committee member on the University of Canberra's key theme group planning educational practices around Greater Access, Choice and Flexibility.
 * Developed a cross disciplinary unit of study on Social Media
 * Managed the The History of the Australian Paralympic Movement, where the project is establishing a working group for the development of Wikipedia entries on Australian athletes and participation at games, add photos and media to Wikimedia Commons, and write an historical text on Wikibooks
 * Progressed an Open-PhD on networked learning and the relationship educational institutions might have to such practices

2010
Full time with University of Canberra, Australia. Learning Commons Coordinator in Sport Studies and the Faculty of Health. Working with staff in developing social media and Internet skills useful to their teaching and research work. Also responsible for the development and maintenance of the Faculty website. Presentations and papers.

 * Panelist at Athabasca University's Conference Making Sense of Social Media in Education, Government, and the Enterprise.
 * Open PhD: Connecting and Sharing - A presentation made to University of Canberra researchers.
 * Sustainable Business Text Book - Project manager and editor of a text book for Otago Polytechnic and the New Zealand Ministry for the Environment's Sustainable Management Fund
 * Open Education Practices: A User Guide for Organisations - Author, project manager, researcher.
 * UC IP - Convened a mini conference for the University of Canberra's policy review for intellectual property
 * Proposed IP Policy - Submission to the University of Canberra Intellectual Property Policy Review

2009
Full time with Otago Polytechnic in Dunedin, New Zealand, working in educational research, development and implementation up until October 2009. Full time with the University of Canberra, Australia. Learning Commons Coordinator in Sport Studies and the Faculty of Health. Working with staff in developing social media and Internet skills useful to their teaching and research work. Also responsible for the development and maintenance of the Faculty website. Presentations and papers.

 * Popular Internet in teaching and research - A presentation made to the Faculty of Health's Teaching Showcase event at the University of Canberra.
 * Models for Open Education - A talk given to the seventh annual Open Education Conference held in Vancouver 2009. Presentation notes here.

2008
Full time with Otago Polytechnic in Dunedin, New Zealand, working in educational research, development and implementation. Research and consultancy with various other educational institutions. Presentations and papers.

 * EduPOV - A talk given to NSW TAFE about social media and educational approaches to it.
 * Elected to Wikieducator Council
 * Key note speaker at eFest2008
 * Elected to the DEANZ Council
 * Presentation to the DEANZ 2008 conference on Educational Development in Otago Polytechnic
 * Guest speaker to Ascilite and Desire2Learn in Wellington: Deconstructing Behaviorism within Social Constructivism
 * Keynote presentation to Skills Tasmania 2008 Conference Business in the 21st Century: Growth through skills and Innovation - The Disconnect Between Education and Learning

2007
Full time with Otago Polytechnic in Dunedin, New Zealand, working in educational research, development and implementation. Research and consultancy with various other educational institutions. Presentations and papers.

 * Keynote presentation to Webstock Mini in Wellington NZ about SecondLife and Virtual Worlds in society and Education.
 * Keynote presentation for WIAOC 2007 - Open Educational Resources and Practices.
 * Attended the Commonweath of Learning's Techtonic Shift Thinktank meeting in Vancouver to discuss the future of Wikieducator and free educational content.
 * Assisted in the drafting of a new Intellectual Property and Copyright policy for Otago Polytechnic that utilises the Creative Commons Attribution license.

2006
Full time with Otago Polytechnic in Dunedin, New Zealand, working in educational research, development and implementation. Research and consultancy with various other educational institutions. Presentations and papers.

 * Key note presentation to Education.au's Global Summit.
 * Facilitation of the Future of Learning an a Networked World international open-space conference tour across New Zealand.
 * Presentation to KnowledgeBank on [networkedlearning:digital literacy and how it affects teaching and learning practices Digital literacy and how it affects teaching and learning].

2005
In business offering educational resource design and consultation services. Part time teaching at the Western Sydney Institute of TAFE.

 * Presentation: Networked Learning to KnowTips conference Canada. March 2006.
 * Full time Educational Development for Otago Polytechnic - research into new practices and development of learning programmes.
 * Presentation: Networked Learning to the Tasmanian Learnscope Showcase 2005
 * Teaching: Hadleighs Ways. Introducing a group of men in the Blue Mountains to computers and the Internet.
 * Teaching: BlacktownYoof. Introducing digital photography and editing to a group of young kids having troubles in school.
 * Event Coordination: [talo:taloswapmeet05 Coordinated the TALO Swap/Meet 2005 conference]. Hosted by the Western Sydney Institute of TAFE NSW.
 * Writing: Critique for eLearning Journal, Knowledge Tree. Looking at digital literacies in Australian education.
 * Consultation: [networkedlearning:knowledge sharing Online Presentation for Networks, Cool Results]. A presentation delivered with Sean FitzGerald over Elluminate, hosted by Learning Time Australia.
 * Consultation: Learnscope project training 14 individuals from private training organisations around NSW about the Internet and tools that may help them in offering online training.
 * Resource design and development: Blended Learning teacher training resource development initiated for the Western Sydney Institute of TAFE NSW to support workshops on using free, easy and open source software in online teaching pratices.
 * Consultation: [hypar:home Presentation to the Helping Young People at Risk (HYPAR) Conference] on the use of blogs, RSS. audio and mobile devices in education.
 * Consultation: [payitforwardlearning:home Presentation to the NSW TAFE Outreach Exchange project] of an idea to use wikis in Outreach programs.
 * Consultation: Presentation to the Australian Flexible Learning Framework - eLearning event on using free and open source software to create free and open courseware.
 * Consultation and development: Maintaining the Teach and Learn Online weblog and email list, providing ongoing support, information and training resources to teachers and trainers around Australia.
 * Teaching: Introduction to animation. A 9 week class looking at some of the concepts. tools and techiques behind animated and sequential art.
 * Consultation: [networkedlearning:Integrating technologies Integrating Technologies to Support Learning] - A full day workshop with Marty Cielens for Learnscope 2005 teams.
 * Consultation: [networkedlearning:knowledge sharing Knowledge Sharing with Distributed Networking Tools]. A presentation with Sean Fitzgerald to the "Cool Results" Online conference.
 * Consultation: Numerous workshops and presentions to various projects in TAFE NSW, including NSW Outreach, Illawarra IT, Western Sydney and South Western Sydney Institutes Professional Development Units, and the Australian Institute of Sport.

2004
In business offering educational resource design and consultation services. Part time project management for the Hunter Institute Teaching and Learning Innovations Centre. Part time mentoring for the Hunter Institute Outreach program.

 * Resource design and development: Designed, developed and produced the Surf Life Saving Australia CDROM for training the Bronze Medallion. Resource included interactive videos and extensive Flash development. See portfolio for screen grabs and more information.
 * Resource design and development: Designed, developed and produced BlendedChocolate.com, a multi media resource used by the Baking Section of the Hunter Institute of TAFE NSW.
 * Consultation: Wrote a paper for the Australian Flexible Learning Framework entitled Using Free and Open Source Software to Create Free and Open Courseware. Full text version here
 * Project Management: Worked part time for the Hunter Institute of TAFE NSW in their Institute Teaching and Learning Innovations Centre (ITALIC) managing staff and resource development projects.
 * Resource Design: Co wrote a learning object script for the Learning Federation and their Innovation, Enterprise and Creativity brief.
 * Mentored a group of 'youth at risk' for the Hunter Institute Outreach program.

2003
In business offering educational resource design and consultation services. Part time project management for the Hunter Institute Teaching and Learning Innovations Centre. Mentored for the Newcastle Youth Venue. Casual teaching in high schools.

 * Resource design and development: Designed, developed and produced interactive videos and flash movies for the Horticulture Online project as part of the TAFE Connect initiative. See portfolio for screen grabs and more information.
 * Project Management: Worked part time for the Hunter Institute of TAFE NSW in their Institute Teaching and Learning Innovations Centre (ITALIC) managing staff and resource development projects.
 * Film Direction: Directed the documentary film Dancing to Architecture, an open source documentary about the This Is Not Art (TINA) festivals in Newcastle that year.
 * Mentored individuals from the Newcastle Youth Venue who had an interest in multi media for the web.

2002
Studying full time the Diploma in Education at the University of Newcastle. Tree planting.

 * Part time tree planter for Greening Australia

2001
Full time public servant in Taiwan. Part time artist and film maker. Representative

 * Full time project officer for the Public Relations and Cultural Affairs Unit of the Australian Commerce and Industry Office in Taipei.
 * Art: Solo exhibition of the installation Room For Rent including the publishing of the zeen What's in the Brown Paper Bag 5 at Brian's Place Gallery, Taipei.
 * Film Making: A series of short music films about Taiwan.
 * Art: Attended the residency Solar Circut on Maria Island, Tasmania - producing a series of new media artworks and performances based on the human history of Maria Island.
 * Representative for Community Communications Online to the Association of Progressive Communication AGM Montevideo - Uruguay, and development meeting in Johannesburg - South Africa.

2000
Full time public servant in Taiwan.

 * Full time project officer for the Public Relations and Cultural Affairs Unit of the Australian Commerce and Industry Office in Taipei.

1999
English Teaching in Taiwan.

 * Taught English at the Kid Castle Primary School in Taipei
 * Taught English at Li An Elementary High School in Taipei
 * Taught English private tuition around Taipei

1998
Bachelor of Arts degree. Part time sales assistant. Events management.

 * Part time sales assistant for MacCleans Book Sellers Hamilton.
 * Set up and managed The Warehouse, a venue for events and art exhibitions in Newcastle.
 * President of the Arts Club of the Newcastle University Students Association.

1997
Bachelor of Arts Degree. Part time sales assistant. Environmental campaigner.

 * Part time sales assistant for MacCleans Book Sellers Hamilton.
 * Part time environmental campaigner for the Newcastle Wilderness Society.

1996
Bachelor of Arts Degree. Environmental campaigner. Builder's Labourer.

 * Part time environmental campaigner for the Newcastle Wilderness Society.
 * Part time labourer for Bernie Hockings.

1995
Bachelor of Arts Degree. Reserve infantryman.
 * Part time infantryman with the 1 Commando Regiment.

1994
Associate Diploma in Fine Arts. Reserve infantryman.
 * Part time infantryman with the 1 Commando Regiment.

title: User:Leighblackall/CV


text:
Engineering Projects/Bridges/Howard Community College/fall2011/501 DAS/Week 3 (Oct. 03 - Oct. 07, 2011)

The information in this link will be updated for the designated week as we move forward with the project as we discussed.

Let's remember to add more details and do a better job at documenting our work visually(pictures) and verbally


text:
Literature/1931/Russell

2nd edition

 * Preface : By David Papineau

Wikimedia

 * Bertrand Russell

 * Scientific method

 * Philosophy of science

title: Literature/1931/Russell


text:
User:Sahit87

Trying to do a course in WikiUniversity

title: User:Sahit87


text:
Literature/1948/Skinner

 * http://books.google.com/books?id=KEiYzfCVzv4C

Excerpts

 * Science in general emerged from a competitive culture. Most scientists are still inspired by competition or at least supported by those who are. But when you come to apply the methods of science to the special study of human behavior, the competitive spirit commits suicide. It discovers the extraordinary fact that in order to survive, we must in the last analysis not compete.

Wikimedia

 * Walden Two

 * B. F. Skinner

 * Utopia

 * Walden

title: Literature/1948/Skinner


text:
Literature/1971/Skinner

 * http://books.google.com/books?id=CtF6FDfUcQoC

Excerpts

 * 1 A Technology of Behavior
 * The speaker does not feel the grammatical rules he is said to apply in composing sentences, and men spoke grammatically for thousands of years before anyone knew there were rules.
 * In the traditional view, a person is free. He is autonomous in the sense that his behavior is uncaused. He can therefore be held responsible for what he does and justly punished if he offends. That view, together with its associated practices, must be re-examined when a scientific analysis reveals unsuspected controlling relations between behavior and environment.
 * 2 Freedom

 * 3 Dignity

 * 4 Punishment

 * 5 Alternatives to Punishment

 * 6 Values

 * 7 The Evolution of a Culture

 * 8 The Design of a Culture

 * 9 What is Man?

Wikimedia

 * Beyond Freedom and Dignity

 * B. F. Skinner

 * Walden Two
 * Walden

 * Utopia

title: Literature/1971/Skinner


text:
Motivation and emotion/Book/2011/Empathy

Empathy
Humans are naturally social beings. We seek the company of others for a variety of reasons: love, support, encouragement, friendship, intimacy, guidance and understanding. Being able to support another person, whether in a time of need or a time of happiness, is an opportunity to share the things that we seek for ourselves. Empathy is a unique way of developing our personal characteristics while maintaining relationships and contributing to our own social awareness.

The beginnings of empathy: It's child's play!

The emotional and physical development of children are the main two focuses for parental teaching, with emotional growth being nurtured through the communication of empathy and thoughtfulness (Therrien, 1979). To expand on this concept, a study was undertaken by Knafo, Zahn-Waxler, Hulle, Robinson and Rhee (2008) involving infant boys and girls aged between 14-36 months. Also included in the study were the infants' mothers and a third person who had no significance to the infant. In one scenario, the mother of the infant was instructed to act injured in front of the child while in another instance the unrelated person feigned injury. Results showed infants across all age groups responded more empathetically toward the injured mother than to the person who held no importance to them. This may be due to early parental influences witnessed by the infant including the mother expressing concern for another family member or comforting a distressed child or sibling. These responses and interactions between parent and child assist in the development of caring actions in the infant (Miklikowska, Duriez, & Soenens, 2011).

Expanding on this, toddlers develop a sense of self and realise that other children are separate from themselves (Miklikowska, Duriez, & Soenens, 2011). The child is no longer preoccupied with their own being but has become alert to the needs of others and resultantly, the youngster is willing to put another's needs alongside their own. The child's realisation of self-concept enables him/her to experience empathy for another. This in turn eventuates into prosocial behaviours such as helping and expressing concern for others, and while the foundations are laid in infancy, development continues across the lifespan.

 Here are some examples of everyday interactions with others. Take a moment to look at the images, read the captions and consider Who do you turn to...?

Did you find that comfort and closeness were attributed to your mother or a mother figure? Or that solving problems and learning were characteristics you contributed to your father or other close male? In a 2011 study, Chao found that mothers were likely to be more forthcoming with showing emotion and encouraging affection with their child, while fathers had a more prominent role in sharing information and knowledge with their child. Other gender influences were also apparent in the relationship between children and parents, with the study indicating a stronger link to personal and emotional closeness was evident between children and mothers when compared with the relationship type of a child and their father. This was partially due to the social expectation of the female to assume the traditional role of the primary carer, while the male partner was expected to go out to work to maintain the home and provide for the family unit. Furthermore, gender differences were apparent in the display of empathy with females showing more empathetic behaviour than males. This was attributed to mothers tendency to be more affectionate and empathic toward their daughters than their sons.

Empathy and sympathy
What is the difference between empathy and sympathy?

Empathy = aural
Listening to another individual, hearing them and understanding their experience, without evaluating or judging the individual or the event (Maltby, Day, & Macaskill, 2007).

Sympathy = heart
Giving support to another person for an upsetting or bad incident while claiming knowledge of the other persons experience (Maltby, Day, & Macaskill, 2007).

Consider the list of working professionals in the table below. Based on the above definitions, think about whether you would categorise them as an empathic or sympathetic occupation and why you would you classify them as such. Think about whether you are basing your decision on personal experience and whether that has affected your assessment of people in that occupation.

Research by de Wied et al., (2007) provided expressive examples of differences between empathy and sympathy. The example provided involved individuals seeing a child who was crying.

While both examples are similar in phrasing, on deeper consideration they are quite different reactions. Empathy shows the individual displaying understanding of the child's situation, while retaining a personal boundary. [[Suggestion for inclusion: to walk alongside them.}} Sympathy assumes the emotion of the child and leaves no distance between the individual and the child. Furthermore, empathy allows the individual to be caring and express concern, while sympathy is overwhelmed with mirrored feelings which may be detrimental and inhibit the support the child needs.

'How do you think you would reaction in this situation? Would you act differently knowing the differences between empathy and sympathy?'

The following short video compares empathy and sympathy. Dr Alessandra prompts the viewer to consider whether we accept ourselves and acknowledge our own feelings and emotions as this may have some effect on how we act and react to other individuals.

|Dr Tony Alessandra - Empathy vs Sympathy

Empathy and motivation
Is empathy driven by motivation? Or are people motivated to be empathic? For example, do we show empathy to someone if we think we can gain something from doing so (egocentric), or do we act selflessly thinking only of another persons welfare (altruistic)? It has been indicated that individuals whose primary motivation is to help increase another person's well-being think differently to those who help others for the benefit of themselves (Graziano et al., 2007).

As individuals continue to develop and mature, environmental factors begin to play a role in exercising empathy. A link between empathy and prosocial behaviour has been found and partially contributed to environmental factors including social gatherings and interactions and responses from peers (Knafo et al., 2008). Motivation is considered to be a vital aspect to understanding prosocial behaviour, with Reeve (2009) noting that intrinsic motivation develops through personal interest and is often due to an individual's need [[and add hyperlink:https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2020/Basic_psychological_need_theory}} for nurture and support. This engages some level of satisfaction for the individual when providing assistance or support to another person.

A working example of intrinsic motivation is volunteering. It would appear the majority of volunteers are driven to help others because they want to make a difference and are acting on altruistic reasoning. Volunteers expect little or no reward and are often overutilised due to their unassuming and hard working attitude. Volunteers provide an invaluable service to local and national communities and are a true representative of empathy by offering support, understanding and respect for others.

Dimensions of empathy
What influence does oxytocin have in the display of empathy? Oxytocin is a neuropeptide which is associated with maternal bonding and social attachments allowing individuals to act in a helping manner and engage in prosocial activity. Oxytocin affects the activation of the amygdala which is located within the limbic system of the brain and is responsible for memory, behaviour and emotions.

TEDtalk - Paul Zak - oxytocin

Empathy consists of two main factors – cognitive and affective (Miklikowska, Duriez, & Soenens, 2011). The cognitive aspect reflects perspective taking, understanding and comprehension of the situation or issues. The affective component represents the emotional response to another person. Showing concern is the motivator exhibited to engage in helping an individual who is in an unhappy state.

Mirror neurons are found in the premotor cortex and become activated when we witness others who are acting in a focused manner. Ginot (2009) showed that an individual's mirror neuron system fires when s/he sees another individual experiencing discomfort or pain. Research has shown that the observing individual will often unconsciously adopt the same behaviour or emotion the other person in feeling. It is suggested that this adoption is required learning in order for us to understand how to interact and comprehend the feelings and experiencing of those around us.

Personal comparison quiz
(As this quiz is for use as a reflective tool only, it does not require submission)

How empathetic are you? Complete this quiz on three separate occasions when you are in different moods:
 * feeling sad or down
 * feeling tired
 * feeling happy or satisfied.

This will provide an interesting comparison of results to see when you are feeling more empathetic to others and will help determine if hormones and moods influence the individuals willingness to empathise. Note: There are no right or wrong answers to the questions as answers are based purely on individual interpretation.

{Which word best describes your current mood? + Happy + Tired + Sad
 * type="[]"}

{Listen to the following music (FurElise by Beethoven) and determine the influence on your current mood. + Calming + Unresponsive + Irritating
 * type="[]"}

{Considering your current mood, which word most closely reflects your feelings when looking at this picture? + Compassionate + Indifferent + Distressed
 * type="[]"}

Did you find there were different answers for questions depending on your mood at the time of taking the quiz?

Or were you reasonably consistent with your responses?

Interest has been taken in the effects of mood and the role it plays in our emotions and our reactivity toward others. A study conducted by Singer et al., (2008) investigated the possibility of oxytocin (OT) influencing our behaviour in a social setting as well as having an effect on our capacity to empathise. The authors hypothesised that manufactured (group 1) and placebo (group 2) administered oxytocin would enhance prosocial behaviour and increase empathic activity. Interestingly, results in both groups indicated no enhancement was evident for empathy based interactions or prosocial activity. However, an effect was found when group individuals experienced personal pain, but no difference was found when the same individual empathised with another persons pain. Additionally, increased amygdala activity was exhibited if the individual was suffering anxiety.

Peer pressure
Imagine you are a group member listening to someone tell a story. The story is quite heartfelt and has clearly affected the other members in your group who respond by empathising with the storyteller. You don't really know the person or their situation and the story hasn't really affected you, but you do know the others in the group. Do you act with compliance and also show empathy just to fit in with the group?

Earned empathy
The social aspect of empathy was investigated in a 2006 study undertaken by Singer et al. The study indicated that individuals observing a person receiving pain were more likely to show empathy to that person if they had previously witnessed that person treating others in a fair manner. This was in direct contrast to individuals showing little or no empathy to persons experiencing pain if they had witnessed them treating others unfairly.

Expected empathy
If an individual has a reputation for displaying empathy, other persons will seek them out when they need someone to talk to. Consequently, the empathetic individual feels an expectation to show empathy and offer support, and by doing so, provides reinforcement that they are empathetic toward others (Reeve, 2009).

A study by Graziano, Habashi, Tobin and Sheese (2007) found that adults were more likely to assist a close relative in need than they were to offer support to a distantly related person. However, when circumstances of life and death occurred, people were more willing to assist another individual irrespective of the presence or absence of a personal relationship.

When discussing the Big 5 personality traits of agreeableness, conscientiousness, openness (to experience), extraversion and neuroticism, agreeableness is considered to be one of the more important aspects of personality as it provides links to prosocial behaviour, motivation and empathy. In a study by Graziano et al. (2007), individuals high in agreeableness were found to be more likely to help a stranger in need and more likely to offer help to family and friends in both low personal cost and high personal cost circumstances. This may suggest that an individual who is high in agreeableness is more sensitive and more receptive toward needs in their peers. Additionally, an interesting comparison was noted between a person with high agreeableness and an individual with low agreeableness. When presented with a life and death scenario, most people were willing to assist regardless of whether the person was known or unknown to them. This was in direct contrast to situations involving everyday helping exercises, where individuals low in agreeableness would not necessarily be responsive to assisting others including family or friends.

 * BFI - Big Five Inventory
 * Take the link [| Big 5 Personality Test] to complete a version of the Big 5 Personality Inventory. Your results will indicate whether you are low, average or high in each of the 5 traits. You can also choose to have your results (anonymously) submitted and used for data analysis.

Empathy and therapy
Psychotherapists, psychologists and counsellors frequently display empathy during sessions with clients. This may be conveyed through the effective use of attentive silence (Ladany, Hill, Thompson, & O’Brien, 2004) or via empathetic responses to the client. The table below captures the sense of understanding conveyed by the therapist to the client during a session.

Clients are to be treated individually. Therefore, adaptations of this wording is essential to ensure the personal situation of the client is understood and respected.

Empathy is a vital component in building a trusting relationship between therapist and client, and aims to provide a sense of safety for the client (Elliott, Bohard, Watson, & Greenberg, 2011). Importantly, an empathic approach requires the professional to not only listen to what the client is saying, but to indeed hear what is not being said (Crenshaw & Hardy, 2007). Additionally, Therrien (1979) advises therapists who provide empathetic responses during client sessions promote a more positive outlook for change amongst their clients. However, empathy in client sessions will only prove successful it if is displayed in a genuine manner (Elliott & Freire, 2007).

The person-centred approach to client therapy developed by Carl Rogers in 1957 (cited in Elliott & Freire, 2007) has proven effective for persons with anxiety related issues. While it may take several sessions for the client to feel confident and ready to open up fully to the therapist, a comforting and relaxed environment provides a setting where the client feels safe. When these situational aspects are accompanied by an open minded therapist, the session is more likely to produce a positive outcome for the client (Elliott, Bohard, Watson, & Greenberg, 2011).

Mindfulness also has value in the therapeutic setting. Mindfulness is a form of self awareness meditation which allows the practitioner to be aware and accepting of themselves, and in turn enables him/her to be fully present when facilitating a client session (Bruce, Manber, Shapiro, & Constantino, 2010). The combination of empathy and mindfulness allows the therapist to engage with the client and be receptive to the experience of the client while not absorbing the experience as their own. As maintaining personal distance is a continuing factor in the client therapist relationship, the integration of different approaches provides an alternative for gaining a positive session outcome for the client.

Watch the mindfulness relaxation video. While therapists can benefit from taking time to think about themselves in order to be a better practitioner, so we can all afford to take some time to get to know ourselves better. This in turn helps us become more aware of others and how we can respond appropriately to them.

Do

 * Listen
 * Maintain eye contact
 * Remain composed
 * Be attentive
 * Show interest
 * Allow the other person to speak
 * Be respectful
 * Sit quietly - hands in lap and feet on floor
 * Nod
 * Ask for clarification
 * Restate what has been said

Do not

 * Fidget or fiddle
 * Roll eyes
 * Text or talk on phone
 * Look around room
 * Fold arms
 * Yawn
 * Look bored
 * Slouch in chair
 * Be judgemental
 * Eat or drink
 * Say "You should/shouldn't..OR I "I know exactly how you feel"

As individuals, we all want to have our feelings and experiences recognised and acknowledged. If we understand our own feelings and emotions, we can make ourselves available to others. Being able to show empathy and provide support to others is an opportunity to contribute to social awareness, engage in personal relationships and enhance our own life.

...and if it seems too hard, remember...

Empathy is child's play!


text:
User:Leighblackall/Business Plan

SB undefined

This is a template for a sustainable business plan. It can be used for planning a new business that is yet to start, or an existing business in need of a business plan. Alternatively, it offers some quick reference guidance in some aspects of the business. Copy it into your own word processor and spread sheet calculator. Use the linked information as a guide for each section. You will find information in the Booklets relating to each section of the business plan.

What is the purpose of the business plan?
Write down why you are writing this business plan. It is important that you have a clear reason. Ensure that you refer to this reason as you complete your plan

=Business profile=
 * The business profile is designed to be an overview of your business and the business plan. It should provide readers with a quick overview of your business, including your values and objectives, so they can get an immediate feel for what you’re doing and where you’re going. Ideally it should be no more than five pages. Comment only on sections relevant to your business.
 * Useful booklets
 * The business profile

Executive summary

 * What is the purpose of your business?
 * Briefly outline the history (if any) of your business
 * Objectives (where do you want to be in five years?)

 * Useful booklets
 * Your reasons for starting a business

Products/services

 * What key products or services are you going to offer?
 * How will you ensure they are delivered in a sustainable manner? Consider how they will be environmentally responsible and contribute positively to the local and wider community. See Examples of sustainable business in the Sustainable Business Practice booklet.
 * List the major requirements you’ll have to comply with, or apply for
 * Where will the business be located?
 * Indicate key people or organisations prepared to help you

 * Useful booklets
 * Sustainable business practice (Section: Case studies - Return to sender eco-coffins)

The market

 * How big is your market? Outline the potential demand
 * Describe the major targets your business will be aiming for
 * What major trends will impact on your business? See sustainable trends in the Sustainable business practice booklet

 * Useful booklets:
 * Is there a market?
 * Sustainable business practice (Section: The market - Sustainable trends)

Achievements so far

 * List your achievements to date. If you have not started your business then list what you’ve done to prepare yourself

 * Useful booklets:
 * The business profile (Section: Relevant business achievements)

Competition

 * List the major competition
 * Are any of your competition competing on sustainability? For instance, for the cafe owner, are any of the other cafes offering organic food, or offering end of day food to the homeless shelter etc?
 * Mention any other topics not covered above that are likely to have an impact on your business:

 * Useful booklets
 * Competitor analysis

Your competitive advantages

 * What are your key competitive advantages?
 * Could sustainability be a competitive advantage for your business?
 * List as many reasons as you can why you are better than your competition:
 * Useful booklets:
 * Competitor analysis (Section: What is your competitive advantage?)

Stakeholder engagement

 * Outline how you intend to communicate with your stakeholders (people or organisations that have the ability to influence your business or who are impacted on by your business, eg customers, neighbours, suppliers) and what type of information you will be sharing with them. See also Stakeholder engagement in the Sustainable business practice booklet
 * Collect information from your customers
 * Useful booklets:
 * Sustainable business practice
 * Marketing

Strengths, weaknesses, opportunities and threats

 * What are the organisations strengths and/or opportunities? Include in your answer, sustainability strengths and opportunities (for instance ability to use environmentally sound materials, ability to create jobs for locals, involvement in community activity, employment of long term unemployed, product safety, employee share ownership scheme)
 * What are the organisations weaknesses and threats? Include in your answer, sustainability weaknesses and threats (for instance, difficulty to source environmental materials, difficulties in accessing skilled labour to develop environmental technology)

 * Useful booklets
 * Is there a market? Section: Identify any opportunities and threats

Sustainable Business Practice
This business plan includes prompts to help you consider how to build a sustainable (in the sense of environmentally and socially responsible) as well as a long-life business.

In addition to the prompts throughout the business plan, complete the questions below. Use the operational sustainability principles (ie Good employer, environmental responsibility, community contribution and fairness, and influencing others) See Operational principles within the Sustainable business practice booklet for a more detailed description of the principle.

For those businesses who are ready to go a step further with sustainable business practice, read the Applying strong sustainability to business practice.
 * What are the main social and environmental negative impacts your business has? To help you assess this, see sustainability impact in the Sustainable Business Practice booklet
 * Where are the greatest opportunities for your business to contribute environmentally and socially?
 * What are your sustainability goals?
 * What can be done to minimise the negative impacts, maximise the opportunities and achieve your sustainability goals? Often there are easy things that can be done that have a significant impact, such as changing a supplier to one who sources environmentally and socially responsible materials
 * How are you integrating sustainability into the organisation? for more about this see Integrating sustainability into your organisation
 * How are you being innovative and considering the long term implications (on future generations) of your business? See Strategic principles section of the Sustainable business practice booklet
 * How are you being transparent about your actions with your stakeholders? ''See Strategic principles section of the Sustainable business practice booklet for more information about this.

 * Useful booklets:
 * Sustainable business practice

Organisational Relationships

 * Who are the people/organisations that have the ability to influence your business? (eg neighbours, media, customers, environmental advocates, employees)
 * What is most important to them about your business?
 * Who are the people/organisations that your business has the ability to influence? (eg suppliers, customers, employees) See also Sustainable business practice: How your business influences
 * What is most important to them about your business?
 * How does your business make it easy for its customers to make sustainable choices? ''See also Sustainable business practice: Make sustainable choices easy
 * How do you contribute make your local community a better place to live and do business?
 * Are there any opportunities to make your wider community a better place to live and do business? ''See also Sustainable business practice: The wider community
 * How do you know if your organisation is operating fairly? Consider the impact both within the supply chain (eg child labour used in the manufacturers business) and within the business directly (such as fairness of remuneration rates)
 * How do you ensure that the business does not put any stakeholders at risk when dealing with uncertainty? ''See also Sustainable business practice: toxic materials

 * Useful booklets:
 * Sustainable business practice (Section: Organisational relationships)

=Marketing=

Your best customers
Who are your best customers?

 * Useful booklets
 * Is there a market? (Section: Profile your ‘ideal’ customer)

Market analysis

 * How is your customer base changing? For example, see Sustainable Trends.
 * What are your competitors currently doing?
 * From the above information, what in your business do you think you should change strategically?
 * Note: Fill out this section for each of the targets you have selected. If you have five targets, then you’ll be repeating this worksheet five times.
 * 1. Select one target for the next 12 months. Describe the target in as much detail as possible
 * 2. Are you going to change any of the following for the selected target? If you are, then state what you intend to do:
 * Price?
 * Product or service?
 * How will you distribute?
 * 3. List the promotional activities you’ll use to attract the target described
 * 4. Estimate the total cost of the ideas generated in Point 3 above. Is this amount of money feasible? Can you still make a profit?

 * Useful booklet
 * Marketing (Section: Market analysis)

Tactical marketing plan timeline

 * Useful booklets
 * Marketing (Section: How to complete a tactical plan)

=Finance=

The financial part of your business plan is where you pull together all of the various elements of your business and express them in a common denominator: dollars. It is the part of the exercise where you see whether all your efforts and plans will result in you making a profit or not.

This is also an opportunity to consider what impact your sustainability commitments have on your financial results. You may consider there will be no cash outlay until the business is paying you a living wage, or you may consider from day one, your business will make financial donations to the local community. You may also join the local Sustainable Business Network (link to www.sustainable.org) or gain some type of environmental certification. Be sure to consider these costs in your financial projections.

See the Plumber's commitment in the Sustainable business practice booklet.

1 Year Profit and Loss Forecast

 * Useful booklet
 * Finance (Section: The profit and loss forecast)

Monthly Profit and Loss Forecast

 * Useful booklet
 * Finance (Section: The profit and loss forecast)

Three Year Profit and Loss Forecast

 * Useful booklet
 * Finance (Section: The profit and loss forecast)

One-year cashflow forecast

 * Useful booklet
 * Finance (Section: Cashflow budget)

Break-even calculations
To calculate the necessary level of sales for your business, use the information developed in your Profit and Loss Forecast

 * Useful booklet
 * Finance (Section: Break-even calculation)

=Business structure, tax and compliance=

 * Useful booklets
 * New Zealand business structure, tax and compliance
 * Managing external factors

=Risk management strategy= List below the top hazards and risks in your business in order of priority, and plan how you will eliminate, isolate, minimise or manage each risk. Dont forget sustainability risks such as public backlash against those who cause environmental damage, or a reduction in the supply of oil, pushing oil prices and potentially material prices up dramatically

 * Useful booklet
 * How to lower the risk

=Planning for the future=

Short-term planning

 * Useful booklets
 * Planning for the future

 * You have now completed the business plan - basic version.

=Additional sections for specific business needs= The following sections can be added to the business plan if applicable. Check the headings below to see whether any of the additional information applies

=Choosing your team=
 * How will you ensure a safe and healthy workplace
 * How do you know if you are paying a living wage (enough for employees and their families to meet their needs)?
 * How do you ensure you are an equal opportunity employer? See also http://www.eeotrust.org.nz/
 * Is there anything else you could do to ensure you are a good employer?

Creating a job description
Job title:

Immediate superior (person to whom reporting):

Responsible for:

Brief description of job:

Major job objectives:

1.

2.

3.

Key tasks:

Resources required to achieve key tasks:

Creating a person specification
1. Physical requirements:

2. Qualifications—level of education and experience:

3. Special aptitudes—numeracy, literacy and computer skills, etc:

4. Personal characteristics—communication and people skills, etc:

5. Specific circumstances—able to travel, etc:

Application form
Position applied for:
 * Personal information

Date:

Full name:

Address:

Contact details:

Phone:

Fax:

Email:

Start with your current or last position
 * Previous experience

1. Job title:

Name of company:

Contact person:

From:

Key Tasks:

2. Job title:

Name of company:

Contact person:

From:

Key Tasks:

3. Job title:

Name of company:

Contact person:

From:

Key Tasks:

Performance appraisal (PA)
Staff member:

Date of PA

PA completed? yes/no

Results of PA

Action taken as result of Performance Appraisal:

 * Useful booklet
 * Choosing your team

=E-Commerce=

Other e-commerce uses
Outline here any other ways not previously covered that your business uses e-commerce

Email and databases
Outline how you use email and your customer databases in your business

Using the internet
Outline here how your business uses the internet to become more efficient, to research markets, to order products and services, to source information and to reduce costs

Permission marketing
Describe here how you use e-commerce to develop permission marketing in your business

Your website
Describe here the functionality and purpose of your website

Encouraging employee innovation
Outline here how you encourage employees to innovate in your business

Developing a culture of innovation
What are you doing to encourage a culture of innovation in your business?

Innovation training
What are you planning to do to ensure that you and your staff can continue to upskill in innovative practices and be exposed to new ideas?

 * Useful booklets
 * E-Commerce

=Raising investment funds=

Raising outside investment
If you’re looking to raise outside investment for your business, where do you expect these funds to come from? If necessary, list multiple sources (for example, cashflow, the bank, a corporate investor)

Your key barriers
What do you think are the key barriers faced by other businesses that might wish to compete against you?

Market size
What is the size of your market in New Zealand dollars?

Identifying key contacts
List here the key people you can contact for assistance. Include their experience, qualifications, history and the relationship they have with you

Exit strategy
Outline how you believe an investor will be able to exit from an investment in your business

Intellectual Property Protection
Describe all the intellectual property protection you have in place for your business

Structuring the deal
Outline how you believe you will structure the deal for any potential investor. Include here also how much your business is worth, and what percentage of your business you intend to sell (if you’re looking for investment capital)

 * Useful booklet
 * Raising investment funds

=Exporting=

Dealing with your customers
How do you intend to deal with people located in another country? By phone? By visiting? By a physical office? By employing staff overseas?

Possible product or services changes
What would you have to change in your product or service to meet the needs of an overseas market?

Coping with a different culture
How will you cope with possible culture and language difficulties?

Market development costs
How do you intend to assess the costs of researching and staying in an overseas market?

Targeted overseas markets
What country or countries have you targeted for export?

What types of people or businesses are you targeting in these countries?

Contacts and sources of assistance
List here all your existing export contacts and sources of assistance that have helped you so far

Distributing
Outline how you intend to distribute your products or services in your targeted country

Branding issues
What brand will you market under in your international markets? Explain why this is suitable

Promoting overseas
How do you intend to promote your business in your targeted international market?

Assessing possible price changes
Do you intend to price your products or services differently internationally? If so, how and why?

Transport issues
Are you going to export the product or sell the right to manufacture the product in another market? If exporting the product, how do you intend to transport your products in a sustainable manner?

How do you intend to transport your products so they reach your markets on time?

 * Useful booklet
 * Exporting

=Manufacturing=

Manufacturing Process
What can you do to ensure that resource use is minimised in the manufacture and use of your materials? What can you do to ensure that waste and pollution (to landfill, water, air) is eliminated or minimised?

Plant requirements
List here your plant requirements

Raw materials
What raw materials and stock are required?

Are you aware of what raw material choices there are to minimise environmental damage (for instance a builder using environmentally preferable glues in the manufacture of plywood?)

 * Useful booklet - Manufacturing

=Industry sector=

 * Useful booklet - Industry sector influences

Key success factors
Identify the key success factors for your business

Key performance indicators
List the key performance indicators for your business. (Get help from an accountant or financial advisor if necessary).

See Measuring sustainable business practice in the Sustainable business practice booklet

title: User:Leighblackall/Business Plan


text:
Literature/1953/Skinner

Abridgements

 * Peter A. Morton. A Historical Introduction to the Philosphy of Mind: Readings With Commentary, 2nd ed. Broadview Press, 2010.

Wikimedia

 * B. F. Skinner

 * Verbal Behavior

 * Beyond Freedom and Dignity
 * Walden Two

title: Literature/1953/Skinner


text:
User talk:RTVP

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Thank you for experimenting with the page How to make a power point presentation on Wikiversity. Your test worked, and it has been reverted or removed. Please use the sandbox for any other tests you want to do. Take a look at the welcome page if you would like to learn more about contributing. Ruy Pugliesi ◥ 11:55, 4 October 2011 (UTC)

title: User talk:RTVP


text: File:DSP HW07.pdf

title: File:DSP HW07.pdf


text:
User:Egm6321.f11.team2.rho/HW3

=R*3.4-Construct a class of N1-ODEs=

Given
A class of N1-ODES of the form is as follows:

Euler Integrating factor method (IFM) is written as

For (3.4.2) to be exact, 2nd exactness condition is applied to find h and (3.4.2) becomes

To solve (3.4.3), 2 cases is considered.

In the cases, the second case is defined as follows:

Case 2:suppose h(x,y), thus h is a function of y only, and then (3.4.3) becomes

Find
Construct a class of N1-ODEs,which is the counterpart of (3.4.1),and satisfies the condition (3.4.4) that an integrating factor h(y) can be found to render it exact.

Solution
Based on (3.4.4), consider:

Thus:

If  $$\displaystyle k_1(y)=d_1 $$ (constant), then (3.4.4) is satisfied as follows:

=R*3.16- Completion of Second Choice=

Given
From (3.16.1) and (3.16.2), we get

For the first choice of the solution, assume that

The process to find $$\displaystyle \phi(x,y,p)$$ is as follows:

Find
Finish the second choice assuming that

Solution
(3.16.10) can be rewritten as follows:

And then the both sides of (3.16.11) are integrated as follows:

The above integration results in

The result is exactly same with (3.16.5).

Thus, the next process and resulted $$\displaystyle \phi(x,y,p)$$ would be same with the above given functions from (3.16.6) to (3.16.9).

=R3.10 Free Vibration of Coupled Pendulums =

Given
The matrix foam of linear time-variant systems is

The solution of generalized SC-L1-ODE-CC is

Coupled pendulums system is shown as follows:

Pendulums:

{| style="width:100%" border="0" $$\displaystyle a=0.3,l=1,k=0.2 $$
 * style="width:95%" |
 * style="width:95%" |

$$\displaystyle m_{1}g=3,m_{2}g=6,g=10$$

No applied forces:

{| style="width:100%" border="0" $$\displaystyle u_{1}=u_{2}=0$$
 * style="width:95%" |
 * style="width:95%" |

Initial conditions:

{| style="width:100%" border="0" $$\displaystyle \theta_{1}(0)=0,\dot\theta_{1}(0)=-2 $$
 * style="width:95%" |
 * style="width:95%" |

$$\displaystyle \theta_{2}(0)=0,\dot\theta_{2}(0)=1$$

Find
1. Use matlab's ode45 command to integrate the system, (3.10.3) and (3.10.4), in matrix form of (3.10.1) for $$\displaystyle t\in[0,7] $$

2. Use (3.10.2) to find the solution at the same time stations as in Q1.

3. Plot $$\displaystyle \theta_{1}(t) $$ and $$\displaystyle \theta_{2}(t) $$ from Q1 and Q2.

Solution
Solved on my own.

(3.10.3) and (3.10.4) are reordered as follows:

Finally we obtain the following matrix:

Mathlab codes and plot from Q1

Mathlab codes and plot from Q2

title: User:Egm6321.f11.team2.rho/HW3


text:
User:Egm6321.f11.team1/report4

= R4.1 Direct Derivation of Alternate Version of RTT =

Given
Another version of the Reynolds Transport Theorem:

 * {| style="width:100%" border="0" align="left"

$$
 * $$\frac{D}{Dt}\int_{\mathcal B_t}f(x,t)\,d\mathcal B_t=\int_{\mathcal B_t}\frac{\partial f}{\partial t}\,d\mathcal B_t+\int_{\partial\mathcal B_t}\mathbf n\cdot(f\mathbf u)\,d(\partial\mathcal B_t)$$
 * $$\displaystyle (Equation\;4.1.1)
 * $$\displaystyle (Equation\;4.1.1)
 * }
 * }

== Find ==

Provide a different and direct derivation of Equation 4.1.1.

Solution
Solution is adapted from Malvern. If $$\displaystyle f(x,t)$$ denotes any property of the material volume $$\displaystyle\mathcal B_t$$, for a spatial volume bounded by a control surface $$\displaystyle\partial\mathcal B_t$$, the following is true:

$$ \begin{bmatrix} \rm Total\,rate\,of\,change\,of\\ \rm{an\,arbitrary\,function} \\ f(x,t)\,\rm in\,region\,\mathcal B_t \end{bmatrix}=\begin{bmatrix} \rm Time\,rate\,of\,change\\ \rm of\,\mathit f(x,t)\,\rm within\,\mathcal B_t\\ \end{bmatrix}+\begin{bmatrix} \rm Flux\,of\,\mathit{f(x,t)}\\ \rm thru\,surface\,\partial\mathcal B_t \end{bmatrix} $$

Now expressing mathematically what is stated above:

= R*4.2 Exactness Verification=

Given
Non-exact L2-ODE-VC

Example: Consider the following ODE:

$$\sqrt{x} \, y'' + 2 x y' +3y=0$$ $$\displaystyle (Equation\;4.2.1) $$

Find
Verify the exactness of Equation 4.2.1

Solution

 * {| style="width:100%" border="0"

 * style="width:95%" |
 * style="width:95%" |

[[media:pea1.f11.mtg21.djvu|Mtg 21 (c,x)]]

To be exact, the equation 4.2.1 must satisfy two conditions.

1st Condition of Exactness

Fist, the equation must be presented in the following format

$$\displaystyle F(x,y,y',y)=g(x,y,y')+f(x,y,y')y$$$$\displaystyle (Equation\;4.2.2) $$

By letting y'=p, the first condition of exactness is satisfied as shown in the following equation:

$$\displaystyle F(x,y,p,y)=\underbrace{2xp+3y}_{g(x,y,p)}+\underbrace{\sqrt{x}}_{f(x,y,p)}y$$$$\displaystyle (Equation\;4.2.3) $$

2nd Condition of Exactness

In order to meet the second condition of exactness, the following equations must be satisfied:

$$\displaystyle f_{xx}+2pf_{xy}+p^2f_{yy}=g_{xp}+pg_{yp}-g_y$$ $$\displaystyle (Equation\;4.2.4) $$

$$\displaystyle f_{xp}+pf_{yp}+2f_y=g_{pp}$$ $$\displaystyle (Equation\;4.2.5) $$

Each element of equationgs 4.2.4 and 4.2.5 are calculated to be the following:

$$\displaystyle f_{xx}=-\frac{1}{4}x^{-\frac{3}{2}}$$

$$\displaystyle f_y=f_{xy}=f_{yy}=f_{xp}=f_{yp}=0$$

$$\displaystyle g_{xp}=g_{pp}=2$$

$$\displaystyle g_y=3$$

$$\displaystyle g_{yp}=0$$

Plugging each relevant element into equation 4.2.4 yields the following:

$$\displaystyle -\frac{1}{4}x^{-\frac{3}{2}}+2p \cdot 0+ p^2 \cdot 0 \neq 2+ p\cdot 0 -3$$

Plugging each relevant element into equation 4.2.5 yields the following:

$$\displaystyle 0+p\cdot 0+2 \cdot 0 \neq 2$$

Equations 4.2.4 and 4.2.5 have not been satisfied, therefore proved equation 4.2.1 is not exact.

 * }

=Problem R*4.3: Find $$\displaystyle m$$ and $$\displaystyle n$$ of the integrating factor $$\displaystyle H(x,y) = x^{m}y^{n} $$ such that the given N2-ODE is exact then solve for $$\displaystyle y(x)$$.=

Given
A function is given by

 * $$\displaystyle x^{m}y^{n} \lbrack \sqrt{x}y''+2xy'+3y \rbrack = 0$$

$$\displaystyle (1) p.21-3 $$

Per Lecture notes: [[media:pea1.f11.mtg21.djvu|Mtg 21 (c)]] where

 * $$\displaystyle h(x,y) = x^{m}y^{n}$$

$$\displaystyle (4.3.1) $$

Find
Part A: Find $$\displaystyle (m,n) $$ such that $$\displaystyle (1) p.21-3 $$ is exact.

Part B: Show that the first integral is a L1-ODE-VC and solve

 * $$\displaystyle \phi(x,y,p) = xp+(2x^{\frac{3}{2}}-1)y = k$$ $$\displaystyle (2)p.21-3

$$

for $$\displaystyle y(x)$$.

Solution

 * {| style="width:100%" border="0"

 * style="width:95%" |
 * style="width:95%" |

Part A:

The first exactness criteria for second order non-liner ODE is
 * $$\displaystyle F(x,y,p) = f(x,y,p)y'' + g(x,y,p) $$

$$\displaystyle (2) p.16-4 $$

where

 * $$\displaystyle p = y'$$

Comparing (1) p.21-3 with the form of (2) p.16-4, the functions $$\displaystyle f $$ and $$\displaystyle g $$ can be defined as

 * $$\displaystyle f(x,y,p)=x^{0.5+m}y^{n}$$$$\displaystyle (4.3.2) $$

 * $$\displaystyle g(x,y,p)=2x^{m+1}y^{n}p+3x^{m}y^{n+1}$$$$\displaystyle (4.3.3) $$

So the form of the 1st exactness condition is met.

For a second order non-liner ODE, the first part of the second exactness condition is
 * $$\displaystyle f_{xx} + 2pf_{xy} + p^2f_{yy} = g_{xp} + pg_{yp} - g_{y} $$$$\displaystyle (1) p.16-5 $$

For a second order non-liner ODE, the second part of the second exactness condition is
 * $$\displaystyle f_{xp} + pf_{yp} + 2f_{y} = g_{pp}$$$$\displaystyle (2) p.16-5 $$

Using the second part of the second exactness condition given above in $$\displaystyle (2) p.16-5 $$ and recognizing the given$$\displaystyle f(x,y,p) $$ from equation $$\displaystyle (4.3.2) $$  is not a function of $$\displaystyle p$$, so the first two terms are zero. Additionally $$\displaystyle g_p$$ is constant wrt. $$\displaystyle p$$ and therefore $$\displaystyle g_{pp}$$ is zero. $$\displaystyle (2) p.16-5 $$ can be simplified as shown below

 * $$\displaystyle 2f_y=g_{pp}=0$$
$$\displaystyle (4.3.4)$$

Taking the derivative .wrt $$\displaystyle y $$ of $$\displaystyle f(x,y,p) = f_y $$ in equation $$\displaystyle (4.3.2) $$ and substituting into $$\displaystyle (4.3.4)$$ yields

 * $$\displaystyle 2\left[x^{0.5+m}ny^{n-1}\right]=0$$
$$\displaystyle (4.3.5) $$

In order for equation $$\displaystyle (4.3.5) $$ to be true $$\displaystyle m=0$$

 * $$\displaystyle n=0$$
$$\displaystyle (4.3.6) $$

For clarity we can now re-write equations $$\displaystyle (4.3.2) $$$$\displaystyle (4.3.3) $$ with $$\displaystyle n=0$$ as shown below:

 * $$\displaystyle f=x^{0.5+m}$$
$$\displaystyle (4.3.7) $$

 * $$\displaystyle g=2x^{m+1}p+3x^{m}y $$
$$\displaystyle (4.3.8) $$

Next, use the first part of the the second exactness condition given in equation $$\displaystyle (1) p.16-5  $$ with the following derivatives of $$\displaystyle f $$ and $$\displaystyle g $$ plugged in.

 * $$\displaystyle {f_{xx} = (m+0.5)(m-0.5)x^{-1.5+n}}$$

 * $$\displaystyle{f_{xy} = 0}$$

 * $$\displaystyle{f_{yy} = 0}$$

 * $$\displaystyle{g_{xp} = 2(m+1)x^{m}}$$

 * $$\displaystyle{g_{yp} = 0}$$

 * $$\displaystyle{g_y=3x^{m}}$$

Which yeilds:
 * $$\displaystyle(m+0.5)(m-0.5)x^{-1.5+m} = 2(m+1)x^{m}-3x^{m}$$
$$\displaystyle (4.3.9) $$

Solving this equation for $$ \displaystyle m $$ yields

 * $$ \displaystyle m = \frac{1}{2}$$
$$\displaystyle (4.3.10)$$

So the integrating factor to make $$\displaystyle (1) p.21-3 $$ exact is

 * $$\displaystyle h(x,y) = x^{0.5} $$
$$\displaystyle (4.3.11) $$

Part B:

So using the integrating factor found above and multiplying through to equation $$\displaystyle (1) p.21-3 $$ to get and exact N2-ODE one can use equation $$\displaystyle (3) p.16-5 $$ to obtain the first integral given in $$\displaystyle (2)p.21-3 $$

Rearranging equation $$\displaystyle (2)p.21-3 $$ and solving for $$\displaystyle y(x)$$ by dividing through by x to put the ODE into the general form:

 * $$ \displaystyle y' + a_0(x)y = b(x) $$
$$\displaystyle (3)p.11-3 $$

Yields:

 * $$ p + (2x^{\frac{1}{2}}-{\frac{1}{x}} )y=k $$

Where:
 * $$ a_o(x)=\frac{(2x^{\frac{3}{2}}-1)}{x}=2x^{\frac{1}{2}}-x^{-1}$$
$$\displaystyle (4.3.12) $$
 * $$ b(x)=\frac{k}{x}$$
$$\displaystyle (4.3.13) $$

The ODE can be solved by finding an integrating factor $$h(x,y)$$ per

 * $$h(x)=exp(\int a_o(x)dx)$$
$$\displaystyle (3)p.11-4 $$

 * $$y(x)= \frac{1}{h(x)}\int h(x)b(x)dx+C_1 $$
$$\displaystyle (1)p.11-5 $$

Substituting in $$h(x)=exp(\int a_o(x)dx)$$ gives:

 * $$y(x)=\frac{\int exp(\int a_0(x)dx)b(x)+C_1}{exp(\int a_0(x)dx)}$$
$$\displaystyle (4.3.14) $$

Integrating $$a_0(x)$$ which is given in $$\displaystyle (4.3.12) $$

 * $$\int a_0(x)dx=\int 2x^{\frac{1}{2}}-x^{-1}=\frac{4}{3}x^{\frac{3}{2}}-ln(x)+C_2$$
$$\displaystyle (4.3.15) $$

Plugging in $$\displaystyle (4.3.15) $$ and $$\displaystyle (4.3.13) $$ into $$\displaystyle (4.3.14) $$ yields:
 * $$y(x)=\frac{\int C_3x^{-1}exp(\frac{4}{3}x^{\frac{3}{2}})\frac{k}{x}+C_1}{ C_3x^{-1}exp(\frac{4}{3}x^{\frac{3}{2}})}$$
$$\displaystyle (4.3.16) $$

where $$C_3 = exp(C_2) $$

Equation $$\displaystyle (4.3.16) $$ is the solution for $$\displaystyle y(x) $$

=R*4.4 Generate a class of exact L2-ODE-VC = Question from meeting 21, pages 5-6: Given (2)-(3) from p. 21-4 $$G = \underbrace{\underbrace{R(x)}_{\displaystyle a_0(x)} y}_{\displaystyle \ne \phi_x} + \underbrace{\underbrace{Q(x)}_{\displaystyle a_1(x)} y'}_{\displaystyle \ne \phi_y} + \underbrace{\underbrace{P(x)}_{\displaystyle a_2(x)} y''}_{\displaystyle = \phi_p}$$
$$\displaystyle (Equation\;4.4.1)$$
$$\phi_x(x,y,p) + \phi_y(x,y,p) \,y' = R(x)y + Q(x)y'$$
$$\displaystyle (Equation\;4.4.2)$$  Find that the solution gives (1) from p. 21-5
$$\phi(x,y,p) = P(x)p + T(x)y + k$$
$$\displaystyle (Equation\;4.4.3)$$

From lecture notes [[media:pea1.f11.mtg21.djvu|Mtg 21]]

Solution
The equations (2) and (3) are within the category of L2-ODE-VC. The key is to use the substitution p = y' for the derivations and p' = y''.The first step is to prove the exactness of the equations below. There are two exactness conditions for the N2-ODE. Note that the functions R and Q are of x but not y. This affects the 2nd exactness condition and subsequent derivations and integrations.

$$G = \underbrace{\underbrace{R(x)}_{\displaystyle a_0(x)} y}_{\displaystyle \ne \phi_x} + \underbrace{\underbrace{Q(x)}_{\displaystyle a_1(x)} y'}_{\displaystyle \ne \phi_y} + \underbrace{\underbrace{P(x)}_{\displaystyle a_2(x)} y''}_{\displaystyle = \phi_p}$$
$$\displaystyle (Equation\;4.4.1)$$

$$g(x,y,p) = \phi_x(x,y,p) + \phi_y(x,y,p) \,y' = R(x)y + Q(x)y'$$
$$\displaystyle (Equation\;4.4.2$$  The function with p=y' can be rearranged.  $$g(x,y,p) = \phi_x(x,p) + \phi_y(x,p) \,y' = R(x)y + Q(x)p$$
$$\displaystyle (Equation\;4.4.3)$$

The equations satisfy the following form of the 1st exactness condition. $$G = \frac{d \phi}{dx} = \phi_x + \phi_y \,y'+ \phi_p \,y'' $$
$$\displaystyle (Equation\;4.4.4)$$ The 2nd exactness condition is derived below. First, assume that
$$f(x,p) := \phi_p(x,p)= P(x)$$ Then the 2nd exactness condition can be applied satisfactorily.
$$f_{xx} + 2pf_{xy} + p^2f_{yy} = g_{xp} + pg_{yp} - g_y$$
$$f_{xp} + pf_{yp} + 2f_y = g_{pp}$$
$$\displaystyle (Equation\;4.4.5)$$ This can be shown by placing the values of R and Q into the equation for 2nd exactness.
$$P_{xx} + 0 + 0 = g_{xp} + pg_{yp} - g_y = Q_{x} - R$$ The next step is to find the integration factor h(x) from the equation below.
$$g(x,yp) := \phi_x + \phi_y \,y' = \phi_x(x,p) + \phi_y(x,p) \,p = R(x)y + Q(x)p$$ Recall that the integration factor in this case is a function of x, so the following equation from meeting 11 can be used.
$$\frac{h_x}{h} = -\frac{1}{N}(N_x - M_y) =: \color{blue}{n(x)}$$ The integration is simple.
$$h(x) = \int \frac{h_x}{h} = -\int \frac{1}{N}(N_x - M_y) = -\int\frac{1}{Q(x)}(Q_x - R)= T(x)y + k$$ Subsequently, the final solution is equated below.
$$\phi(x,y,p) = h(x) + \int(f,x,y,p) \,dp = P(x)p + T(x)y + k$$ References for R4.4 Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 11) [[media:pea1.f11.mtg11.djvu|Mtg 11]] 13 Sep 2011. Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 16) [[media:pea1.f11.mtg16.djvu|Mtg 16]] 22 Sep 2011. Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 21) [[media:pea1.f11.mtg21.djvu|Mtg 21]] 04 Oct 2011.

= R*4.5 Solve a L2-ODE-VC = == Given ==
 * {| style="width:100%" border="0" align="left"

$$
 * $$\displaystyle G=(cosx)y''+(x^2-sinx)y'+2xy=0$$
 *
$$\displaystyle (Equation\;4.5.1)
 *
$$\displaystyle (Equation\;4.5.1)
 * }
 * }

Find
1）Show Equation(4.5.1) is exact. 2）Find $$\displaystyle\, \phi$$ 3）Solve for $$\displaystyle y(x)$$.

Solution
1) The particular form of N2-ODE-VC is $$\displaystyle G(x,y,y',y)=g(x,y,p)+f(x,y,p)y$$ where $$\displaystyle g(x,y,p)=(x^2-sinx)y'+2xy$$ $$\displaystyle f(x,y,p)=cosx$$ This is shown that Equation(4,5,1) satisfies the 1st exactness condition. To verify its exactness, we calculate following terms: $$\displaystyle f_x=-sinx;f_{xx}=-cosx;$$ $$\displaystyle f_{xy}=f_{xp}=0;$$ $$\displaystyle f_y=0;f_{yy}=f_{yp}=0;$$ $$\displaystyle g_x=2xy'-cosx\cdot p+2y;$$ $$\displaystyle g_{xp}=2x-cosx;$$ $$\displaystyle g_y=2x;g_{yp}=0;$$ $$\displaystyle g_p=x^2-sinx;g_{pp}=0.$$ Recall the 2nd exactness condition for L2-ODE-VC:
 * {| style="width:100%" border="0" align="left"

$$
 * $$\displaystyle f_{xx}=2pf_{xy}+p^2f_{yy}=g_{xp}+pg_{yp}-g_y$$
 *
$$\displaystyle (Equation\;4.5.2)
 *
$$\displaystyle (Equation\;4.5.2)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

$$ Substituting those calculated terms into Equation(4,5,2) and Equation(4.5.3). As for Equation(4,5,2) , $$\displaystyle LHS=-cosx+0+0=-cosx$$ $$\displaystyle RHS=2x-cosx+0-2x=-cosx$$ which means $$\displaystyle LHS=RHS$$ As for Equation(4,5,3) , $$\displaystyle LHS=0+0+0=0$$ $$\displaystyle RHS=0$$ which means $$\displaystyle LHS=RHS$$ Therefore, Equation(4,5,1) is exact.
 * $$\displaystyle f_{xp}+pf_{yp}+2f_y=g_{pp}$$
 *
$$\displaystyle (Equation\;4.5.3)
 *
$$\displaystyle (Equation\;4.5.3)
 * }
 * }

2) We find the first integral $$\displaystyle \phi$$ by integrating $$\displaystyle f=\phi_p=cosx$$. $$\displaystyle \phi=h(x,y)+\int fdp$$ $$\displaystyle \phi=h(x,y)+cosx\cdot p$$ Also, $$\displaystyle g=(x^2-sinx)p+2xy=\phi_x+\phi_y p$$ where, $$\displaystyle \phi_x=h_x-sinx\cdot p$$ $$\displaystyle \phi_y=h_y$$. Substituting those partial derivatives of $$\phi$$ into function g. $$\displaystyle (x^2-sinx)p+2xy=(h_y-sinx)p+h_x$$. To solving h(x,y), we assume that $$\displaystyle h_x=2xy $$ Therefore, $$\displaystyle h(x,y)=x^2 y+k_1(y)$$ Partial derivate respect to y, $$\displaystyle h_y=x^2+k_1'(y)-sinx=x^2-sinx$$ We can find that $$\displaystyle k_1'(y)=0$$ which means $$\displaystyle k_1(y)=k_1=constant$$. Therefore, the first integral is $$\displaystyle \phi=x^2y+cosx\cdot p+k_!$$

3) Recall that $$\displaystyle \phi=k_2$$, we obtain a L1-ODE-VC that $$\displaystyle x^2y+cosx\cdot p=k_2 -k_1:=k_3$$. Rewrite it into $$\displaystyle y'+\underbrace{\frac{x^2}{cosx}}_{\displaystyle a_0(x)}y=\underbrace{\frac{k_3}{cosx}}_{\displaystyle b(x)}$$

Therefore, the integration factor is $$\displaystyle h(x)=exp[\int^x a_0'(s)ds]$$ $$\displaystyle =exp[\int^x \frac{s^2}{cos s}ds]$$. The solution is

= R*4.6 Show the equivalence of two forms of 2nd exactness condition of N2-ODE =

Given
$$ \displaystyle g_0 - \frac{d}{dx}g_1+\frac{d^2}{dx^2}g_2=0 $$

$$ \displaystyle g_i:=\frac{\partial G}{\partial y^{(i)}} \, \quad for \ i=0,1,2 $$

Find
It's equal to the 2nd exactness condition in form:

$$ \displaystyle \phi_{xy}=\phi_{yx}\ ,\quad \phi_{px}=\phi_{xp}\ ,\quad \phi_{py}=\phi_{yp} $$

Solution
As defined:

$$ \displaystyle G=\frac{d \phi}{dx} (x,y,p)=0 $$

$$ \displaystyle G=\phi_x+\phi_y \cdot p +\phi_p \cdot q $$

$$ \displaystyle for \quad p=y' \, \ q=y'' $$

$$ \displaystyle g_0 = \frac{\partial G}{\partial y} = \frac{\partial}{\partial y}(\phi_x+\phi_yp+\phi_pq) = \frac{\partial}{\partial y}(\frac{d \phi}{dx}) $$

$$ \displaystyle \frac{d}{dx}g_1 = \frac{d}{dx}(\frac{\partial G}{\partial p}) = \frac{d}{dx}(\phi_{xp}+\phi_{yp}p+\phi_y+\phi_{pp}q) $$

$$ \displaystyle \begin{align} \frac{d^2}{dx^2} g_2& = \frac{d^2}{dx^2}(\frac{\partial G}{\partial q})\\ &=\frac{d^2}{dx^2} [\frac{\partial}{\partial q}(\phi_x + \phi_yp +\phi_pq)] \\ &= \frac{d^2}{dx^2} \phi_p\\ &= \frac{d}{dx}(\phi_{px}+\phi_{py}p+\phi_{pp}q) \end{align} $$

For we have:

$$ \displaystyle g_0-\frac{d}{dx}g_1+\frac{d^2}{dx^2}g_2=0 $$

$$ \displaystyle \frac{\partial}{\partial y}(\frac{d \phi}{dx}) - \frac{d}{dx}(\phi_{xp}+\phi_{yp}p+\phi_y+\phi_{pp}q) + \frac{d}{dx}(\phi_{px}+\phi_{py}p+\phi_{pp}q) = 0 $$

Rearranging:
 * {| style="width:100%" border="0" align="left"

\displaystyle [\frac{\partial}{\partial y} (\frac{d\phi}{dx})-\frac{d}{dx}(\frac{\partial \phi}{\partial y})] + \frac{d}{dx} [(\phi_{px}-\phi_{xp})+(\phi_{py}-\phi_{yp})p+(\phi_{pp}-\phi_{pp})q] = 0 $$ $$
 *
$$\displaystyle (Equation\;4.6.1 )
 * }
 * }

So, both two parts in the left side of equation 4.6.1 are equal to 0 separately:

For first part:

$$ \displaystyle \frac{\partial}{\partial y} (\frac{d\phi}{dx})-\frac{d}{dx}(\frac{\partial \phi}{\partial y})=0 $$

$$ \displaystyle (\phi_{xy}-\phi_{yx})+(\phi_{yy}-\phi_{yy})p+(\phi_{py}-\phi_{yp}q)=0 $$

so:

$$ \displaystyle \phi_{xy}=\phi_{yx} $$

$$ \displaystyle \phi_{py}=\phi_{yp} $$

And, second part:

$$ \displaystyle \frac{d}{dx} [(\phi_{px}-\phi_{xp})+(\phi_{py}-\phi_{yp})p+(\phi_{pp}-\phi_{pp})q] = 0 $$

$$ \displaystyle (\phi_{px}-\phi_{xp})+(\phi_{py}-\phi_{yp})p+(\phi_{pp}-\phi_{pp})q = 0 $$

thus we get:

$$ \displaystyle \phi_{px}=\phi_{xp} $$

= References =

= Team Work Distribution =

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title: User:Egm6321.f11.team1/report4


text:
TESOL/Describing how things are used

At school
These are some things we use at school.

title: TESOL/Describing how things are used


text:
User talk:Jeremy73

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title: User talk:Jeremy73


text:
User talk:Allopoietic

 Hello Allopoietic, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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title: User talk:Allopoietic