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User talk:G-man~enwikiversity

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Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

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title: User talk:G-man~enwikiversity


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User talk:Luisa Nomad

 Hello Luisa Nomad, 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. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --AFriedman 13:54, 21 September 2009 (UTC)

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title: User talk:Luisa Nomad


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User talk:Miiniemiin

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User talk:Sperry Nicholas

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text: User:Vicens

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User talk:Baby Blue

 Hello Baby Blue, 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. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! Jtneill - Talk - c 16:15, 21 September 2009 (UTC)

 Hi , I am Percy. Nice to meet you. I love the beach, swimming, fishing, and I am currently doing some research at Wikiversity on oceanography. I am also learning to play piano. What do you like? Can I be your mascot?

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I blocked this account because it was blanking pages. -- Jtneill - Talk - c 04:39, 5 October 2009 (UTC)

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text:
Digital Libraries/Protocols

 * Older versions of the draft developed by UNC/VT Project Team (2009-10-07 PDF)

Module name
Protocols

Scope
This module addresses the concepts, development and implementation of digital library protocols and covers the roles of protocols in Information retrieval systems (IR) and Service Oriented Architectures (SOA).

Learning objectives:
By the end of this module, the student will be able to:
 * a. Explain the basic concepts and methods related to DL protocols.
 * b. Design and implement a protocol for harvesting metadata from a digital library.
 * c. Design and implement a digital library service based on the principles and guidelines of DL protocols.

5S characteristics of the module:

 * a. Stream: Protocols enable the data in digital libraries to be harvestable. Protocols specify the flows of streams of data.
 * b. Structure: Protocols enable digital libraries to expand and disseminate digital objects and provide various information organization services.
 * c. Spaces: Protocols connect spatially separate digital libraries.
 * d. Scenario: Different protocols implement specific scenarios of communication among digital libraries.
 * e. Society: Different protocols implement and design for different use cases and communities.

Level of effort required:

 * a. Class time: 3 hour
 * b. Student time outside class: 8 hours
 * i. Reading before the class starts: 4 hours
 * ii. Homework assignment: 4 hours

Relationships with other modules:

 * a. 4-b: Metadata: DL protocols are harvesting metadata stored in a digital library. 4-b should be taught before this module.
 * b. 5-a: Architecture overview: This module should be taught around the same time in the semester.
 * c. 5-b: Application software: This module should be taught around the same time in the semester.

Prerequisite knowledge required:

 * a. Knowledge of client-server, P2P, SOA architectures
 * b. Understanding of client request and server response
 * c. Basics of other networking protocols

Introductory remedial instruction:

 * a. Quick overview of software engineering architectures and basics of simple networking protocols.

1. Introduction:

 * This module discusses the following digital library protocols:
 * a. OAI-PMH
 * b. SOA
 * c. P2P
 * d. VIDI
 * e. Z39.50
 * f. DLIOP
 * Later in the module parallel and distributed information retrieval is discussed.

2. Open Archives Initiative Protocol for Metadata Harvesting (OAI-PMH)

 * a. OAI-PMH version history
 * i. It is a protocol developed by the Open Archives Initiative.
 * ii. The Santa Fe Convention led to the first incarnation of the Open Archives Initiative Protocol for Metadata Harvesting (OAI-PMH).
 * iii. OAI-PMH 1.0 introduced the unqualified Dublin Core element set as a baseline for metadata interoperability. OAI-PMH 1.1 was a revision of the 1.0 specification taking account of changes to the emerging XML Schema specification. Both v.1.0 and 1.1 were experimental in nature.
 * iv. OAI-PMH 2.0 is a major revision of the protocol and it is a stable protocol.
 * b. Flexible deployment:
 * i. Multiple service providers can harvest from multiple data providers.
 * ii. Aggregators can sit between data providers and service providers.
 * iii. The harvesting approach can be complemented with searching.
 * c. Main ideas of OAI
 * i. world-wide consolidation of scholarly archives
 * ii. free access to the archives
 * iii. consistent interfaces for archives and service providers
 * iv. low barrier protocol / effortless implementation
 * d. Structure model
 * i. It is a simple protocol based on HTTP and XML.
 * ii. This protocol is carried within HTTP POST or GET methods.
 * e. Protocol details
 * i. Records
 * A record is the metadata of a resource in a specific format. A record has three parts: a header and metadata, both of which are mandatory, and an optional about statement.
 * ii. Datestamps
 * A datestamp is the date of last modification of a metadata record. Datestamp is a mandatory characteristic of every item. It has two possible levels of granularity: YYYY-MM-DD or YYYY-MM-DDThh:mm:ssZ.
 * iii. Metadata schema
 * OAI-PMH supports dissemination of multiple metadata formats from a repository. The properties of metadata formats are:
 * ID string to specify the format (metadataPrefix)
 * metadata schema URL (XML schema to test validity)
 * XML namespace URI (global identifier for metadata format)
 * iv. Sets
 * Sets enable a logical partitioning of repositories. They are optional.
 * v. Request format
 * Requests must be submitted using the GET or POST methods of HTTP, and repositories must support both methods. At least one key=value pair: verb=RequestType must be provided. Additional key=value pairs depend on the request type.
 * vi. Response
 * Responses are formatted as HTTP responses. The content type must be text/xml. HTTP-based status codes, as distinguished from OAI-PMH errors, such as 302 (redirect) and 503 (service not available) may be returned. Compression codes are optional in OAI-PMH, only identity encoding is mandatory. The response format must be well-formed XML with markup
 * vii. Flow control
 * OAI-PMH supports partitioning. Those managing a repository make the decisions on partitioning: whether to partition and how.
 * viii. Errors and exceptions
 * Repositories must indicate OAI-PMH errors by the inclusion of one or more error elements.
 * ix. Request types
 * There are six different request types:
 * Identify
 * ListMetadataFormats
 * ListSets
 * ListIdentifiers
 * ListRecords
 * GetRecord
 * f. Implementing protocol
 * i. Before implementing
 * Data Provider:
 * 1. Which data do you want to deliver?
 * 2. Which Service Providers do you want to provide with data?
 * Service Provider:
 * 1. From which Data Providers do you get the metadata?
 * 2. Which services do you want to provide, and to whom?
 * 3. What kind of metadata do you want to provide through your services?
 * Other things one also needs to consider:
 * 1. Update frequency
 * 2. Metadata format
 * 3. Subject schema
 * ii. Data Provider
 * Requisites:
 * 1. Web server
 * 2. Programming interface / API
 * 3. Archive identifier / base URL
 * 4. Metadata format
 * 5. Datestamps for metadata
 * 6. Unique identifier for each item
 * 7. Logical set hierarchy
 * 8. Flow control
 * Components:
 * 1. Argument Parser validates OAI requests.
 * 2. Error Generator creates XML responses with encoded error messages.
 * 3. Database Query / Local Metadata Extraction retrieves metadata from the repository, according to the required metadata format.
 * 4. XML Generator / Response Creation creates XML responses with encoded metadata information.
 * 5. Flow Control realizes incomplete list sequences for 'larger' repositories. It uses resumption tokens as the control mechanism.
 * iii. Service Provider
 * Requisites:
 * 1. An Internet-connected server
 * 2. A database system on equivalent
 * 3. A programming environment
 * Components and architecture:
 * 1. Archive management involves the selection of repositories to be harvested.
 * 2. Request Component creates HTTP requests and sends them to OAI repositories (Data Provider).
 * 3. Scheduler realizes timed and regular retrieval of the associated archives.
 * 4. Flow Control is implemented via resumption tokens, partitioning of the result list into incomplete sections with a new request to retrieve more results.
 * 5. Update Mechanism realizes the consolidation of metadata which have been harvested earlier (merge old and new data).
 * 6. XML Parser analyses the responses received from the repositories, with validation using the XML schema, and transforms the metadata encoded in XML into the internal data structure.
 * 7. Normaliser transforms data in different metadata formats into a homogenous structure.
 * 8. Database receives the output of the normaliser mapping the XML structure of the metadata into a relational database that will handle multiple values of elements. An alternative is to use an XML database.
 * 9. Duplication Checker merges identical records from different data providers.
 * 10. Service Module provides the actual service to the 'public'. The basis for a service provided is the harvested and stored records of the associated archives.

3. Service Oriented Architecture (SOA) for Digital Library

 * a. Simple definition: SOA provides methods for system development and integration where systems group functionality around business processes and package these as interoperable services
 * b. The development of SOA
 * i. It is an architecture developed with XML and Web Services. It is commonly built using Web Services standards.
 * ii. SOA mostly refer to a platform that could realize the concept of partitioning an enterprise into a series of autonomous services.
 * c. SOA deployment
 * i. Run over standard Web protocols: SOA uses XML and HTTP packaging.
 * ii. Communication: SOA uses SOAP (Simple Object Access Protocol) to exchange information, uses WSDL (Web Service Definition Language) to describe Web Services and uses UDDI (Universal Description Discovery and Integration) to register Web Services.
 * d. SOA for digital library
 * i. Services Technology is widely used in Digital Libraries: Fedora, DSpace and CiteSeer
 * ii. The requirement for mapping a Digital Library application/service into web service:
 * An API interface to that application/service
 * A standard access layer such as SOAP
 * A layer describing the service in a standard fashion encoded using WSDL
 * iii. Role of digital library: Service provider.
 * e. Case Study: Fedora
 * i. Fedora Repository system is a Web Service:
 * Access/Search (API-A) and Management (API-M) use web service
 * Service descriptions use WSDL
 * Fedora uses both SOAP and HTTP bindings
 * Fedora acts as mediator to these services
 * ii. Fedora Repository Service Interfaces
 * Access Service (API-A and API-A-LITE)
 * 1. Search - search repository for objects
 * 2. Object Reflection - what disseminations can the object provide?
 * 3. Object Dissemination - request a view of the object’s content
 * Management Service (API-M)
 * 1. Ingest - XML-encoded object submission
 * 2. Create - interactive object creation via API requests
 * 3. Maintain - interactive object modification via API requests
 * 4. Validate – application of integrity rules to objects
 * 5. Identify - generate unique object identifiers
 * 6. Security - authentication and access control
 * 7. Preserve - automatic content versioning and audit trail
 * 8. Export - XML-encoded object formats

4. Peer-to-Peer Computing (P2P Computing) for Digital Library

 * a. Simple definition:
 * i. Peers act as clients and servers
 * ii. Peers communicate directly
 * b. The development of P2P
 * i. Unstructured P2P (such as Gnutella, Napster) to structured P2P (such as Pastry, Chord)
 * ii. P2P used for provide resources: services, for example, storage services, computational services, streaming media services
 * c. P2P for Digital Library
 * i. Main idea
 * Build Digital Library on the P2P structure, use P2P to store digital objects
 * Use P2P to share and route digital documents
 * ii. Implementation
 * Automatically digital documents can be discovered and routed
 * Uniform client-level metadata query services that are compatible with heterogeneous underlying collections
 * Sharing of digital documents on P2P structure rather than storing the documents on a center server
 * d. Case Study: The ADEPT Digital Library Architecture
 * i. ADEPT (Alexandria Digital Earth Prototype) architecture
 * A framework for building distributed digital libraries of georeferenced information
 * Distributed, heterogeneous, scalable
 * ii. Objects
 * Items: Items are fundamental objects in ADEPT, referring to digital objects. Items only have identity, no other innate properties
 * Collections: Collections are set of items, information about individual items is maintained at the collection level
 * Libraries: Libraries are set of collections, which expose a single standard set of interfaces to the collections
 * iii. ADEPT Collection Discovery Service
 * ADEPT takes unstructured P2P mechanism: Reason: simple, sufficiently manageable and scalable
 * ADEPT uses central CDS server and Register server.
 * Collection registry polls known library CDS server

5. VIDI

 * a. Simple definition: A lightweight protocol between visualization systems and digital libraries.
 * b. VIDI Development
 * i. Extended from OAI Protocol for Metadata Harvesting
 * ii. Based on Digital Library likes MARIAN and Visualization Systems likes Infosphere
 * c. Protocol
 * i. The labels
 * ‘s’ means server-server structure
 * ‘c’ means client-server structure
 * ‘x’ means in this specific scenario, this command is unused
 * ii. Four scenarios from left to right
 * Most commands in server-server structure
 * Least commands in server-server structure
 * Most commands in client-server structure
 * Least commands in client-server structure
 * iii. Most commands in client-server structure scenarios
 * d. VIDI Implementation
 * i. Use of HTTP Request and Response
 * The VIDI protocol requests are expressed as HTTP requests
 * HTTP requests may be expressed using either HTTP GET or POST
 * ii. Protocol Entities Definitions: Metadata Format, Visdata format, Transformer, Result Set, Result Record, Result Set Identifier, Unique Identifier
 * iii. Dates and Times
 * The date used in VIDI protocol is encoded using “Complete date” variant of ISO8601, the format is YYYY-MM-DD
 * The time used in VIDI protocol is encoded using the “complete date plus hours, minutes and seconds” variant of ISO8601, the format is YYYY-MM-DDThh:mm:ssTZD
 * iv. VIDI Commands
 * Identify: Retrieve system information about a DL or VIS
 * ListMetaFormats: Retrieve the metadata format available from a DL
 * ListVisdataFormats: Retrieve the metadata format available from a VIS
 * ListTransformers: Retrieve the transformers that VIS supports in order to transform the metadata format to the visdata format
 * RequestResultSet: Transfer query data

6. Special Protocols: Z39.50

 * a. Introduction:
 * i. A client server protocol for searching and retrieving information from remote computer databases
 * ii. Covered by ANSI/NISO (National Information Standards Organization) standard Z39.50
 * iii. Accepted by ISO (International Standards Organization) as standard 23950
 * iv. The standard is maintained by the Library of Congress (LOC)
 * v. First version of Z39.50 in 1988, Z39.50 – 1992 (version 2), Z39.50 – 1995 (version 3)
 * b. Important components:
 * i. Target: Implements the abstract database and is a ready made server module
 * ii. Gateway: A program that has two interfaces. First, it acts as Origin to a Z39.50 Target. Second, it handles communication with a client application. Client protocol may be HTML, Telnet, Z39.50, etc. Advanced Gateway like the one in the figure below can connect to several Z39.50 targets for parallel search, serial search, merging of results. Advanced Gateways can handle several different protocols on both interfaces SQL, LDAP, HTML, DNS, etc.
 * iii. Origin: Normally part of graphical client which hides complexity from the user. It can access several targets simultaneously. There are clients with a “raw” Origin interface

7. Special Protocols: Stanford’s Digital Library Interoperation Protocol (DLIOP)

 * a. Stanford Digital Library test bed
 * i. Stanford Digital Library test bed was a platform for experimentation with interoperation among online services.
 * ii. The figure 13 shows the InfoBus, central to the architecture of the Stanford test bed. It is based on a hardware bus metaphor to suggest that services, repositories, and clients are 'plugged in', and interoperate by taking advantage of interoperability mechanisms built into the testbed.
 * iii. DLIOP is an asynchronous protocol, providing robustness in the face of network or server outages
 * iv. The approach is to use distributed objects to allow integrated access to heterogeneous service across networks.
 * v. The distributed approach allows the interaction of processes on different machines, with different architectures, implemented in different languages.
 * vi. It uses CORBA to provide communication between remote processes. Xerox PARC’s ILU, a free implementation of a CORBA superset, is used.

 * b. Z39.50 Interoperability Example of InfoBus: Top part of Figure 14 shows how a Z39.50 client communicates with other services (can be Z39.50 or any other Service). Bottom part of Figure 14 shows how non-Z39.50 clients consume services provided by a Z39.50 Service. The rounded rectangles in the figure are parts interfacing with the InfoBus communicating via DLIOP to provide the interoperable framework.

8. Parallel and Distributed Information Retrieval

 * a. Motivation
 * i. Exponential growth in size of online scientific data.
 * ii. Managing the size and growth of data demands scalable and multitasking algorithms.
 * b. Requirements for Distributed IR Protocols
 * i. Enable retrieval of data from digital collections that are geographically separated.
 * ii. Provide methods for linking and accessing heterogeneous collections of scientific data.
 * c. Features of Parallel IR
 * i. Computation model divides the main task into sub-tasks and executes the sub-tasks in parallel.
 * ii. Sub-tasks generally run on homogeneous systems and each system works on the same problem.
 * iii. Parallel IR uses shared memory models.
 * iv. Parallel IR broadcasts every request to every process.
 * v. Main objective is to achieve speed-up.
 * d. Features of Distributed IR
 * i. Like Parallel IR, computation model in Distributed IR divides the main task into sub-tasks and executes the sub-tasks in parallel.
 * ii. Distributed IR sub-tasks are run on different processing units where inter-process communication is via network protocols.
 * iii. Sub-tasks may run on heterogeneous systems.
 * iv. Distributed IR employs a procedure to select a subset of processes to broadcast a request.
 * v. Main objectives in Distributed IR are to achieve scalability and availability and speed, but may not be efficient.
 * e. Case Study on Parallel IR
 * i. Paper on Inverted File Partitioning Schemes in Multiple Disk Systems (IEEE transactions on Parallel and distributed systems, Vol 6, Feb 1995) by Byeong-Soo Jeong and Edward Omiecinski.
 * ii. Paper discusses two schemes for Parallel IR implementation.
 * iii. Goal of the paper is to reduce average response time by partitioning the inverted file.
 * iv. The paper identifies I/O time as a major cost factor in IR system.
 * v. It exploits the potential of I/O parallelism and balances I/O workload for better response time by partitioning and distributing files.
 * vi. The paper discusses two partitioning schemes: based on termid and based on document-id for inverted file systems.
 * f. Case Study on Distributed IR
 * i. Paper on Methodologies for Distributed Information Retrieval (18th international conference on Distributed Computing Systems – 1998) by Alister Moffat, Justin Zobel, Owen De Kretser and Tim Shimmin.
 * ii. This paper discusses three different methodologies for Distributed IR and compares their effectiveness, efficiency and response time.
 * iii. Three different methodologies are defined based on the global information stored at the receptionist.
 * Central Nothing – CN
 * The only global information maintained by the receptionist is a list of librarians.
 * Central Vocabulary – CV
 * Global information stored by the receptionist is the vocabularies of the sub-collections.
 * Central Index – CI
 * Receptionist has full access to the indexes of subcollections.
 * iv. Comparison between three different methodologies for Distributed IR (advantages and disadvantages).

Required readings for students

 * i. Carl Lagoze, Herbert Van de Sompel. The Open Archives Initiative: Building a Low-Barrier Interoperability Framework. JCDL, pp.54-62, First ACM/IEEE-CS Joint Conference on Digital Libraries (JCDL'01), 2001. http://www.openarchives.org/documents/jcdl2001-oai.pdf
 * ii. Byeong-Soo Jeong; Omiecinski, E. Inverted File Partitioning Schemes in Multiple Disk Systems. Parallel and Distributed Systems, IEEE Transactions on Volume 6, Issue 2, Feb. 1995 Page(s):142 - 153 Digital Object Identifier 10.1109/71.342125. http://csdl.computer.org/comp/trans/td/1995/02/l0142abs.htm
 * iii. De Kretser, O.; Moffat, A.; Shimmin, T.; Zobel, J. Methodologies for Distributed Information Retrieval. Distributed Computing Systems, 1998. Proceedings. 18th International Conference on 26-29 May 1998 Page(s):66 – 73. Digital Object Identifier 10.1109/ICDCS.1998.679488. http://csdl.computer.org/comp/proceedings /icdcs/1998/8292/00/82920066abs.htm

Recommended readings for students

 * i. Metadata Preparation for the Gateway to Educational Materials. http://www.thegateway.org/about/documentation/metadata-preparation/metaprep/
 * ii. OAI for beginners – the Open Archives forum online tutorial http://www.oaforum.org/tutorial/english/intro.htm
 * iii. PREMIS Data Dictionary for Preservation Metadata. http://www.loc.gov/standards/premis/v2/premis-2-0.pdf
 * iv. Suleman, H., and Fox, E. A. Beyond Harvesting: Digital Library Components as OAI Extensions, Technical Report, Department of Computer Science, Virginia Tech, 2002. http://eprints.cs.vt.edu:8000/archive/00000625/
 * v. Suleman, H. Open Digital Libraries, Dissertation, Department of Computer Science, Virginia Tech, 2002. http://scholar.lib.vt.edu/theses/available/etd- 11222002-155624/
 * vi. Carl Lagoze, Y Payette, Edwin Shin, Chris Wilper, Fedora: An Architecture for Complex Objects and their Relationships, International Journal on Digital Libraries, Vol. V6, No. 2. (April 2006), pp. 124-138.
 * vii. Yves Petinot, C. Lee Giles, Vivek Bhatnagar, Pradeep B. Teregowda, Hui Han, Isaac Councill, A Service-Oriented Architecture for Digital Libraries (2004), In Proc International Conference on Service Oriented Computing, http://portal.acm.org/citation.cfm?id=1035167.1035205
 * viii. Wang, Jun. VIDI: A Lightweight Protocol Between Visualization Tools and Digital Libraries, Master’s Thesis, Virginia Tech (May 2002). http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.6318
 * ix. B Ahlborn, W Nejdl, W Siberski, OAI-P2P: A Peer-to-Peer Network for Open Archives, 2002 International Conference on Parallel Processing.
 * x. M Bender, S Michel, C Zimmer, G Weikum, Towards Collaborative Search in Digital Libraries Using Peer-to-Peer Technology, In DELOS Workshop: Digital. Library Architectures, pages 61–72, 2004.
 * xi. I Podnar, T Luu, M Rajman, F Klemm, K Aberer, A Peer-to-Peer Architecture for Information Retrieval Across Digital Library Collections, LECTURE NOTES IN COMPUTER SCIENCE, 2006. http://globalcomputing.epfl.ch/alvis/research/publications/2006ECDLPodnar.pdf
 * xii. Greg Janee, James Frew, The ADEPT digital library architecture, Proceedings of the 2nd ACM/IEEE-CS joint conference on Digital libraries, 2002, Pages: 342 – 350. http://portal.acm.org/citation.cfm?id=544220.544306
 * xiii. Gerard Salton and Chris Buckley, Parallel Text Search Methods- paper by Salton and Buckley, Technical Report: TR87-828, 1987. http://portal.acm.org/citation.cfm?id=866232
 * xiv. Robert Kahn, Robert Wilensky, A framework for distributed digital object services, International Journal on Digital Libraries, Volume 6, Issue 2, 2006, Pages: 115 – 123. http://portal.acm.org/citation.cfm?id=1124646.1124650
 * xv. Ray R. Larson, Distributed IR for Digital Libraries, 2003, Pages: 487-498. http://www.springerlink.com/content/eujdc8265v8f55a9/fulltext.pdf
 * xvi. International Standard Maintenance Agency Z39.50 http://www.loc.gov/z3950/agency/
 * xvii. Stanford Digital Library Testbed Development http://dbpubs.stanford.edu:8091/~testbed/
 * xviii. Andreas Paepcke, Summary of Stanford’s Digital Library Testbed Design and Status, 1996. http://www.dlib.org/dlib/july96/stanford/07paepcke.html
 * xix. University of Michigan Digital Library Project http://www.dlib.org/dlib/july96/07atkins.html

Required readings for instructors

 * i. Van de Sompel, H., and Lagoze, C. The Open Archives Initiative Protocol for Metadata Harvesting. Protocol Version 2.0 of 2002-06-14, Document Version 2004/10/12T15:31:00Z http://www.openarchives.org/OAI/2.0/openarchivesprotocol.htm

Concept map
Note: IHMC Cmap Tools is an open source client tool to create concept maps. CmapServer enables the users to collaborate and share concept maps anywhere on the internet. Both software can be downloaded freely for educational purposes from http://cmap.ihmc.us/download/index.php

Homework assignment:

 * a. Form student groups
 * i. Evaluate the interoperability of DL services using the Stanford and University of Michigan Digital Library Testbeds
 * b. Peer-to-Peer architecture is widely used to store digital objects. So, considering a peer-to-peer structure which enables a digital object repository, such as ADEPT, what kind of digital library service should be implemented?

In-class Activities

 * a. In class, break students into groups of 3~4
 * i. Each group discusses what kind of services their digital library should provided. Does the digital library act as data provider or service provider?
 * ii. Discusses what kind of metadata format and subject schema will provide, and what update frequency.
 * iii. Discusses choice of kind of digital library architecture and the components to construct these services.
 * iv. Discusses what kind of protocols will be implemented and why?
 * v. The syntax of the underlying database is abstracted in Z39.50, what are the advantages and disadvantages of that?

Evaluation of learning outcomes

 * In their answers to the discussion questions, students demonstrate an understanding of
 * a. Different DL protocols
 * b. What role does DL protocols acted in DL architecture?
 * c. What the requirement for IR protocols?
 * Evaluate the DL harvesting/providing service which student created.

Glossary

 * a. Dublin Core (DC): A shorthand term for the Dublin Core Metadata Element Set, the primary work of the Dublin Core Metadata Initiative (DCMI); a set of metadata elements intended to be generic and universally useful for object description.
 * b. Interoperability: The ability of two or more systems or components to exchange information and to use the information that has been exchanged.
 * c. Metadata: Data about data; structured description of information objects; used to aid the understanding, administration, and use of information objects.
 * d. Resource discovery: Identifying previously unidentified (to the user) data objects
 * e. CORBA: The Common Object Requesting Broker Architecture is a standard defined by the Object Management Group (OMG) that enables software components written in multiple computer languages and running on multiple computers to work together.

Additional useful links

 * None

Contributors

 * a. Developers:
 * i. Ajeet Singh (Virginia Tech)
 * ii. Yinlin Chen (Virginia Tech)
 * iii. Srinivasa Santhanam (Virginia Tech)
 * iv. Weihua Zhu (Virginia Tech)
 * b. Evaluators:
 * i. Edward A. Fox (Virginia Tech)

title: Digital Libraries/Protocols


text:
User talk:Jewers~enwikiversity

 Hello Jewers, 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. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --AFriedman 16:25, 21 September 2009 (UTC)

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title: User talk:Jewers~enwikiversity


text:
User talk:Stevenaguilar

Hello Former Student!

I'm writing to you because you took a class from me in the past few years at the Art Institute. As of Spring, 2010, I'll not be teaching further classes at AIS for the foreseeable future. (We're parting ways on good terms!) Until now, you've been able to reach my Wikiversity educational resources from my website, but I've decided to delete that link. You can still reach all of those materials here.

If you're interested in what I'm up to in the future (which will include an album in 2010 and a novel in 2011) you can friend my facebook page or drop me an email at info@stevenarntson.info and you'll receive a periodic update about performances, classes, and publications.

If you know any current or former students of mine who might be interested in any of this, please forward this information if you have a moment.

I hope all is well for you.
 * Best! Stevenarntson

 Hello Stevenaguilar, 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. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --AFriedman 16:26, 21 September 2009 (UTC)

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title: User talk:Stevenaguilar


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User talk:Davecormier

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 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
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 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --AFriedman 16:26, 21 September 2009 (UTC)

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Unfortunately, your account clashes with another account also called Davecormier. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Davecormier~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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title: User talk:Davecormier


text:
User:Egm6321.f09.team3.mooney

User:Egm6321.f09.team3.mooney/HW2

User:Egm6321.f09.team3.mooney/HW4

title: User:Egm6321.f09.team3.mooney


text:
User:Egm6321.f09.team3.mooney/HW2

Problem #5
Show that the second exactness condition is satisfied for $$x*y*y' + x*(y')^2 + y*y' =0$$

The second exactness condition is described by the following 2 equations

Equation 1

 * $${f}_{xx} + 2*p*{f}_{xy} + p^2 * {f}_{yy} = {g}_{xp} + p*{g}_{yp}-{g}_{y}$$

Equation 2

 * $${f}_{xp} + p*{f}_{yp} + 2*{f}_{y} = {g}_{pp}$$

solving for the individual components by taking the appropriate partial derivatives gives the following values:
 * $${f}_{xx} = 0$$
 * $${f}_{xy} = 1 $$
 * $${f}_{yy} = 0 $$
 * $${f}_{xp} = 0 $$
 * $${f}_{yp} = 0 $$
 * $${f}_{y} = x  $$
 * $${g}_{xp} = 2p $$
 * $${g}_{yp} = 1 $$
 * $${g}_{pp} = 2x $$
 * $${g}_{y} = p  $$

Therefore to check for exactness we can substitute the calculated values: Equation 1 becomes:
 * $$0 + 2*p*(1) + p^2*(0) = 2*p + p*(1) -p$$ ==> $$2*p = 2*p$$ this satisfies the first part of the condition

Equation 2 becomes:
 * $$0 + p*(0) + 2*x = 2*x$$ ==> $$2*x = 2*x$$ satisfying the second part of the condition

Therefore the equation $$x*y*y' + x*(y')^2 + y*y' =0$$ is exact.

Problem #6
Given $$f = {\phi}_{p}$$ and $$g = {\phi}_{x} + {\phi}_{y}*p$$, derive the second condition of exact through differentiation.

Knowing that partial derivates taken in order provide equal results ($$ {f}_{xy} = {f}_{yx}$$), then we can right the following:

 * $$g = {\phi}_{x} + {\phi}_{y}*p$$

 * $$\frac{\partial g}{\partial p} = {{\phi}_{p}}_{x} + {\phi}_{y} + {\phi}_{yp}*p = {f}_{x} + {\phi}_{y} + {f}_{y}*p$$

 * $$\frac{\partial^2 g}{\partial p^2} = {f}_{xp} + {f}_{y} + {f}_{y} + p*{f}_{yp}$$

 * $${g}_{pp} = {f}_{xp} + p*{f}_{yp} + 2*{f}_{y}$$

The form matches the second criteria of the second exactness illustrated agreement with proposed solution. QED!

Problem #7
Using $${\phi}_{xy} = {\phi}_{yx}$$, $$f = {\phi}_{p}$$ , and $$g = {\phi}_{x} + {\phi}_{yp}$$ derive $${f}_{xx} + 2*p*{f}_{xy} + p^2 * {f}_{yy} = {g}_{xp} + p*{g}_{yp}-{g}_{y}$$

title: User:Egm6321.f09.team3.mooney/HW2


text:
Digital Libraries/Info needs, relevance

 * Older versions of the draft developed by UNC/VT Project Team (2009-10-07 PDF WORD)

Module name
Information Needs/Relevance

Scope
A user's interaction with a DL is often initiated as the result of the user experiencing an information need of some kind. Aspects of that experience and how it might affect the user's interactions with the DL are discussed in this module. In addition, users continuously make decisions about and evaluations of the materials retrieved from a DL, relative to their information needs. Relevance judgments, and their relationship to the user's information needs, are discussed in this module.

Learning objectives:
By the end of this module, the student will be able to:
 * a. Demonstrate an understanding of how people experience a need for information and act on that need;
 * b. Demonstrate an understanding of how people make relevance judgments; and
 * c. Apply this knowledge to the design of systems for formulating a query.

5S characteristics of the module:

 * a. Scenarios: the situations of use of a DL; the information needs and behaviors of the DL users

Level of effort required:

 * a. Class time: 1 1/2 hours (may be longer if multiple learning activities are used)
 * b. Student time outside class:
 * i. Reading before the class starts: 2-3 hours
 * ii. Optional learning activity, 12.d, Out-of-class exercise: Criteria used to make relevance judgments (60 minutes, plus 15 minutes at the beginning of the next class period)
 * iii. Homework assignment: Designing a system to support the expression of information needs: 6-8 hours

Relationships with other modules:

 * Should be taught before or in connection with:
 * a. 6-b: Online info seeking behavior and search strategy
 * b. 9-c: DL evaluation, user studies
 * c. 7-b: Reference services

Prerequisite knowledge required:

 * a. None

Introductory remedial instruction:

 * a. None

Wilson's model of information behaviors
(**Graphic: Wilson, 1997, Figure 1)

 * a. Context of information need
 * i. Person-in-context
 * ii. Situational; supports Dervin's work
 * iii. Types of needs (Weigts et al., 1993)
 * Need for new information
 * Need to clarify information already held
 * Need to confirm information already held
 * Need to clarify beliefs/values held
 * Need to confirm beliefs/values held

 * b. Stress and coping theory precipitate action
 * i. Coping = cognitive and behavioral effects to master, reduce or tolerate the internal and external demands that are created by stressful situations (Folkman & Lazarus, 1985)
 * ii. Perceived stress will lead to coping behaviors, including information seeking

 * c. Intervening variables may be barriers to or instigators of action
 * i. Psychological: cognitive dissonance, attention, avoidance of pain
 * ii .Demographic: educational level, economic status
 * iii. Role-related or interpersonal: attitude of the information provider, presence of others during the information behavior, provider's unwillingness to share information
 * iv. Environmental/situational barriers: lack of time, interruptions, geographic location, power distribution not equitable, cultural norms
 * v. Information source characteristics: accessibility, credibility

 * d. Activating mechanisms that are proximate to information seeking behavior
 * i. Risk/reward theory: each decision to act will be influenced by the risks associated with acting/not acting, and the rewards for acting/not acting
 * ii. Self-efficacy: each decision to act will be influence by the potential actor's beliefs about whether s/he can successfully achieve the desired outcome
 * One aspect of social learning theory

 * e. Information seeking behavior
 * i. Passive attention to information in the environment, e.g., recognizing landmarks when navigating
 * ii. Passive search for information, e.g., daily reading of the newspaper for information pertinent to personal daily life
 * iii. Active search for information, e.g., doing an online search
 * iv. Ongoing search for information, e.g., regular scanning of tables of contents

 * f. Information processing and use
 * i. Retrieval is not the end of the process; the information retrieved is used in some way
 * ii. The result is the context of information need for the next cycle

 * g. Lessons learned from Wilson's model
 * i. An information need involves more than just a lack of needed information
 * Context, affective responses to the situation, intervening variables, activating mechanisms
 * ii. When an information need is experienced, it is likely that information seeking will be undertaken

 * If desired, use learning activity 12.a, Discussion activity: Personal experiences of an information need (25 minutes)

Anomalous state of knowledge (ASK) - Belkin (1980)

 * Graphic: Belkin, 1980, Figure 2

 * a. Assumptions
 * i. The IR situation is a communication system
 * The mediating role of the participants is a primary determinant of success/failure
 * ii. Representing users' needs is as important as representing texts for the success of the system

 * b. Conceptual state of knowledge: each person has knowledge; that body of knowledge moves from state to state as information is acquired and used
 * i. One possible state is the anomalous state of knowledge
 * Anomalies can be gaps/lacks, uncertainties, incoherence
 * ii. The user realizes his/her information need and so finds him/herself in an anomalous state of knowledge, which is then transformed into a request

 * c. Lessons to be learned from Belkin's work
 * i. An anomalous state of knowledge is the primary motivator of information seeking behaviors
 * ii. Difficulties can arise during the information retrieval process because it is difficult or impossible for someone to specify a query when their knowledge state is anomalous

Information needs (Taylor, 1968)

 * a. Levels of information need and how they relate to Belkin's model
 * i. Visceral need
 * Actual, but unexpressed
 * Conscious, or possibly unconscious need
 * Inexpressible in linguistic terms
 * ii. Conscious need
 * Ill-defined area of indecision; Ambiguous, rambling
 * Conversation about the need may reduce ambiguity
 * iii. Formalized need
 * Formal statement of the need
 * Explicitly expressed
 * iv. Compromised need
 * As presented to the information system
 * The librarian may be part of the information system, in the user's view
 * Restated, to accommodate the characteristics of the information system: indexing structure, format/medium of information objects

 * b. Assumptions underlying this framework
 * i. Libraries should be communication centers, rather than passive warehouses
 * ii. A particular inquiry "is merely a micro-event in a shifting non-linear adaptive mechanism"

 * c. Lessons learned from Taylor's work
 * i. The inquirer has already gone through several stages before approaching the librarian or DL
 * ii. It is likely that the inquirer will have difficulty expressing a query (i.e., expressing a compromised need) in a form that will result in successful retrieval (in agreement with Belkin's view)

Relevance judgments and their relation to information needs

 * a. The information needs experienced at the beginning of the process, along with the characteristics of the user, are reflected in the relevance judgments made near the end of the process
 * i. Making relevance judgments about retrieved documents is based on whether they satisfy the information need

 * b. Various types of relevance (Sarcevic, 2006; Borlund, 2003)
 * i. System/algorithmic relevance
 * ii. Topical/subject relevance
 * The one most often though of
 * iii. Cognitive relevance or pertinence
 * iv. Situational relevance or utility

 * The subjective nature of relevance judgments make them difficult to incorporate realistically into IR experiments, but most definitions of relevance judgments do consider them to be subjective and/or specific to the user's situation

 * c. While topicality is a primary consideration as people make relevance judgments, they also take into account other aspects of the document and its relation to the situation (Yuan et al., 2002)
 * i. Novelty: uniqueness of the source; the user's familiarity with the source (negative)
 * ii. Currency: whether the source is up to date
 * iii. Quality of the information the source provides
 * iv. The presentation and comprehensiveness of the information
 * v. Other aspects of the source, e.g., that the source is well known in the field
 * vi. Information aspects of the source, e.g., that it describes treatments or techniques or provides examples
 * vii. Appeal: whether the source is interesting or enjoyable

DL design can support the articulation of information needs
There are a variety of ways that DL design can support the articulation of information needs

 * a. Browsing support: when the query cannot be readily specified
 * Examples:
 * i. Previews and overviews of a large collection: Library of Congress America Memory Project (Collection Finder). http://memory.loc.gov/ammem/collections/finder.html
 * ii. Dynamic Queries Demos, available via the Open Video Repository. http://www.open-video.org/details.php?videoid=709
 * iii. Hyperbolic browser: Inxight VizServer (formerly Star Tree). Online Demos available in right column. http://www.inxight.com/products/vizserver/

 * b. Relevance feedback: using the information in a relevance judgment to implicitly specify the query
 * Examples:
 * i. Google, "Similar pages" link with each retrieved document

 * c. Personalization: modifying the system features to match the user's mode of information seeking
 * Examples:
 * i. MyLibrary, Los Alamos National Laboratory, http://library.lanl.gov/lww/mylibweb.htm

 * If desired, used learning activity 12.b, Brainstorming/discussion activity: Observable indicators of an information need (20 minutes), or 12.c, Design exercise: Designing a system to support the expression of information needs (40 minutes)
 * If desired, assign learning activity 12.d, Out-of-class exercise: Criteria used to make relevance judgments, for completion after this class session (60 minutes, plus 15 minutes at the beginning of the next class period)

Readings to be assigned

 * i. Case, D. O. (2002). Information needs and information seeking. In Looking for Information: A Survey of Research on Information Seeking, Needs, and Behavior. Amsterdam: Academic Press, 64-78.
 * ii. Belkin, N. J. (1980). Anomalous states of knowledge as a basis for information retrieval. Canadian Journal of Information Science, 5, 133-143.
 * iii. Saracevic, T. (2006). Relevance: A review of the literature and a framework for thinking on the notion in information science. Part II. In Advances in Librarianship, 30, 3-71. [Assign Section VI. Models of relevance: How relevance was reviewed and reviewed, and how a few models came out of reviews, 21-30.]
 * iv. Taylor, R. S. (1968). Question-negotiation and information seeking in libraries. College & Research Libraries, 29(3), 178-194.
 * v. Wilson, T. D. (1997). Information behaviour: An interdisciplinary perspective. Information Processing & Management, 33(4), 551-572.

Additional supporting references on information needs

 * i. Dervin, B. (1983). Information as a user construct: The relevance of perceived information needs to synthesis and interpretation. In Ward, S. A., & Reed, L. J. (eds.), Knowledge Structure and Use:  Implications for Synthesis and Interpretation, Philadelphia: Temple University Press, 153-183.
 * ii. Folkman, S., & Lazarus, R.S. (1985). If it changes it must be a process: Study of emotion and coping during three stages of a college examination. Journal of Personality and Social Psychology, 48(1), 150-170.
 * iii. Frants, V. I., & Brusch, C. B. (1988). The need for information and some aspects of information retrieval systems construction. Journal of the American Society for Information Science, 39(2), 86-91.
 * iv. Hert, C. A. (1996). User goals on an online public catalog. Journal of the American Society for Information Science, 47(7), 504-518.
 * v. Markey, K. (1981). Levels of question formulation in negotiation of information need during the online presearch interview: A proposed model. Information Processing & Management, 17(5), 215-225.
 * vi. Weigts, W.; Widdershoven, G.; Kok, G.; Tomlow, P. (1993). Patients' information seeking actions and physicians' responses in gynaecological consultations. Qualitative Health Research, 3, 398-429.

Additional supporting references on relevance

 * i. Barry, C.L. (1994). User-defined relevance criteria: An exploratory study. Journal of the American Society for Information Science, 45(3), 149-159.
 * ii. Borlund, P. (2003). The concept of relevance in IR. Journal of the American Society for Information Science & Technology, 54(10), 913-925.
 * iii. Cooper, W.S. (1973). On selecting a measure of retrieval effectiveness, part I: The "subjective" philosophy of evaluation. Journal of the American Society for Information Science, 24, 87-100.
 * iv. Cosijn, E., & Ingwersen, P. (2000). Dimensions of relevance. Information Processing & Management, 36(4), 533-550.
 * v. Greisdorf, H. (2003). Relevance thresholds: A multi-stage predictive model of how users evaluate information. Information Processing & Management, 39(3), 403-423.
 * vi. Harter, S.P. (1992). Psychological relevance and information science. Journal of the American Society for Information Science, 43(9), 602-615.
 * vii. Mizzaro, S. (1997). Relevance: The whole history. Journal of the American Society for Information Science, 48(9), 810-832.
 * viii. Park, T.K. (1993). The nature of relevance in information retrieval: An empirical study. Library Quarterly, 63(3), 318-351.
 * ix. Schamber, L., Eisenberg, M.B., & Nilan, M.S. (1990). A re-examination of relevance: Toward a dynamic, situational definition. Information Processing & Management, 26(6), 755-776.
 * x. Swanson, D.R. (1986). Subjective versus objective relevance in bibliographic retrieval systems. Library Quarterly, 56(4), 389-398.
 * xi. Wang, P., & Soergel, D. (1998). A cognitive model of document use during a research project. Study I. Document selection. Journal of the American Society for Information Science, 49(2), 115-133.
 * xii. Wilson, P. (1973). Situational relevance. Information Storage & Retrieval, 9(8), 457-471.
 * xiii. Yuan, X.-J., Belkin, N. J., & Kim, J.-Y. (2002). The relationship between ASK and relevance criteria. Proceedings of SIGIR 2002, 359-360.

Concept map

 * None

Exercises / Learning activities

 * a. Discussion activity: Personal experiences of an information need (25 minutes)
 * To follow the review of Wilson's generalized model of information behavior
 * Students in the class should be formed into pairs. In each pair, one student will interview the other.  (This process should later be repeated, reversing roles.)  The person being interviewed should be asked to recall a recent experience of having an information need.  The need may have been something significant (e.g., finding sources to use for a research project) or something inconsequential (e.g., finding the start time for Saturday's football game). The interviewer should ask about the content of the information need, the context in which it arose, and the process through which it was pursued (successfully or unsuccessfully).  The pair should then evaluate what was learned about this example of an information need and see if Wilson's model fully describes the process.  Were there aspects of the information-seeking episode that are not covered in Wilson's model?  Are there aspects of Wilson's model that did not occur during this information-seeking episode?

 * b. Brainstorming/discussion activity: Observable indicators of an information need (20 minutes)
 * To follow discussion of Taylor's levels of needs, or at the end of the class period
 * An information need is experienced in an individual's consciousness. But at some point, if the person decides to pursue it, there are observable indicators that a need has been experienced.
 * Form the students into small groups of 2-3 people. Each group should get 10 minutes to brainstorm as many indicators of information needs as possible. They may include those they've observed, those they've enacted, or others they can imagine.
 * At the end of the 10 minute brainstorming period, ask each group to share several of those they listed, including one indicator that they believe is frequently observable, one that is rare, and one that has possible implications for digital library design.

 * c. Design exercise: Designing a system to support the expression of information needs (40 minutes)
 * To follow discussion of Taylor's levels of needs, or at the end of the class period
 * Divide the class into design teams of 3-4 students each. Each team will develop a rough (i.e., paper-and-pencil) prototype of a DL interface that will specifically focus on assisting the user in successfully "compromising" the information need. Because the system designs may be targeted to particular DLs and their users, each of the following situations can be distributed to a different team:
 * The DL will provide access to a collection of Eastern European history journals for historians across Europe, working on projects with funding from the European Union. The projects are most often focused on understanding the cultural and social history of the region during the 14th-18th centuries.
 * The DL will provide access to social science statistical data gathered through federally-funded research. Social scientists whose work is supported by grants from a number of federal agencies, including NSF, now require that they deposit their raw data set and a coding manual for it in this DL. It is expected that other researchers will be able to retrieve data from this DL for secondary analysis or for comparative studies.
 * The DL is a joint effort by a number of natural history museums and will eventually provide access to images, videos, and text related to all the animals and plants of the world. It is intended that school children, their teachers, and the general public will be the primary users of this DL. It will serve as a general-purpose reference work for these audiences.
 * The DL will provide access to manuscripts and letters written by slaves in the U.S. before the Civil War. It is expected that the primary source materials in the DL will be used by history scholars to support their research work.
 * The DL will provide access to manuscripts and letters written by slaves in the U.S. before the Civil War. It will be used by high school and community college teachers to develop materials they can use in their classrooms to teach about slavery during this period.
 * The DL will provide access to books, essays, stories, and videos, all in English, from a variety of countries. It will be used by children in grades 1-5 to support their schoolwork and their leisure time activities.
 * Note that the design task is NOT to develop a full-scale DL interface. Instead, the students should focus their attention on developing a way in which the DL can provide assistance to the intended users in formulating queries, based on their information needs.
 * Allow approximately 20-30 minutes for teams to develop their ideas. Be sure to check in with them every 5-7 minutes, to respond to questions and to ensure that they are still working on the assigned goal rather than getting side-tracked.
 * Each team should draw one screen image on the whiteboard, and briefly describe their prototype. In particular, they should be encouraged to describe the design decisions they made and the assumptions underlying those decisions.

 * Out-of-class exercise: Criteria used to make relevance judgments (60 minutes, plus 15 minutes at the beginning of the next class session)
 * The students should work in pairs for this exercise, so teams should be formed before the end of the class period.

 * Each member of the class will be both an interviewer and an interviewee, playing each role in turn. The interviewee will select an assignment that he or she recently completed that involved the use of a DL to search for relevant materials. With the interviewer present, the interviewee will complete the search again. For at least five of the items retrieved, the interviewee will be asked by the interviewer to examine all the available document information elements and comment on how he or she came to a decision about whether that document was relevant to the assignment or not. Once the five items have been reviewed, the two students will reverse roles and complete the process again. The second interviewee will select an assignment that he or she recently completed that involved the use of a DL, and will repeat their recent search while being interviewed.
 * Based on the notes taken during the interviews, each student should summarize the relevance criteria applied by their partner, and the user characteristics and document information elements that were pertinent to those decisions. A table like the following could be used for reporting these data:

 * These results should be reported to the class members and the course instructor before the next class period, preferably through direct entry into a class wiki or other collaborative tool.

 * During the next class period, the results could be reviewed and compared to the results found by similar studies (e.g., Barry, 1994; Park, 1993), using an adaptation of the table above for integrating the data, as shown here.

Evaluation of learning outcomes

 * 1. Design assignment (modified from in-class exercise described in 10.b.): Designing a system to support the expression of information needs (6-8 hours)

 * a. Divide the class into design teams of 2-3 students each. Each team will develop a rough (i.e., paper-and-pencil) prototype of a DL interface that will specifically focus on assisting the user in successfully "compromising" the information need. Because the system designs may be targeted to particular DLs and their users, each of the following situations can be distributed to a different team:
 * i. The DL will provide access to a collection of Eastern European history journals for historians across Europe, working on projects with funding from the European Union. The projects are most often focused on understanding the cultural and social history of the region during the 14th-18th centuries.
 * ii. The DL will provide access to social science statistical data gathered through federally-funded research. Social scientists whose work is supported by grants from a number of federal agencies, including NSF, now require that they deposit their raw data set and a coding manual for it in this DL. It is expected that other researchers will be able to retrieve data from this DL for secondary analysis or for comparative studies.
 * iii. The DL is a joint effort by a number of natural history museums and will eventually provide access to images, videos, and text related to all the animals and plants of the world. It is intended that school children, their teachers, and the general public will be the primary users of this DL. It will serve as a general-purpose reference work for these audiences.
 * iv. The DL will provide access to manuscripts and letters written by slaves in the U.S. before the Civil War. It is expected that the primary source materials in the DL will be used by history scholars to support their research work.
 * v. The DL will provide access to manuscripts and letters written by slaves in the U.S. before the Civil War. It will be used by high school and community college teachers to develop materials they can use in their classrooms to teach about slavery during this period.
 * vi. The DL will provide access to books, essays, stories, and videos, all in English, from a variety of countries. It will be used by children in grades 1-5 to support their schoolwork and their leisure time activities.
 * b. (The instructor may also wish to use an existing DL(s) as the basis for this assignment, in order to make the design task more concrete.)
 * c. Note that the design task is NOT to develop a full-scale DL interface. Instead, the students should focus their attention on developing a way in which the DL can provide assistance to the intended users in formulating effective queries, based on their information needs.
 * d. In addition, each team should document three of their most important design decisions, providing a rationale for each decision. The design decision rationale may use information about the target audience, information about the collection, existing design guidelines, existing DLs, or research study results as evidence to support the decision.
 * e. Assignment deliverables: (1) An annotated drawing of one screen image, representing the primary interface for the query formulation aspect of the DL; (2) documentation of three design decisions, including the rationale for each.
 * f. Evaluation rubrics: The assignment should be evaluated based on the quality of the proposed design (i.e., its ability to improve the ease and/or clarity with which the intended users can express their information needs), the quality of the three individual design decisions, and the comprehensiveness and quality of the evidence used to support each of the three design decisions.

Glossary

 * No glossary terms needed.

Additional useful links

 * None

Contributors

 * a. Developers:
 * i. Barbara Wildemuth
 * b. Evaluators:
 * Christine Borgman, UCLA
 * Boots Cassel, Villanova University
 * Alannah Fitzgerald, Concordia University
 * Gary Marchionini, UNC

title: Digital Libraries/Info needs, relevance


text:
User:Egm6321.f09.Team1/HW2

= Problem 1 - Integrating Factor Method =

Given
General form of a First Order Nonlinear Ordinary Differential Equations(N1-ODE) is given by,
 * {| style="width:100%" border="0" align="left"

F(x, y(x),\dot y(x)) = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }

By using $$\displaystyle F=\frac{d}{dx} \phi(x,y(x))$$ we get

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

F = \underbrace{\frac{\partial \phi}{\partial x}}_{M(x,y)} + \underbrace{\frac{\partial \phi}{\partial y}}_{N(x,y)} \frac{dy}{dx} = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * }
 * }

We can multiply this by an Integrating Factor, $$\displaystyle h(x,y)$$, to get

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

h F = h M + h N \frac{dy}{dx} = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }

Then it follows that an exactness condition for an N1ODE's is, with equation 2 as the special case where $$h=1$$

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

(hM)_y = (hN)_x
 * $$\displaystyle
 * $$\displaystyle

$$ $$
 * $$\displaystyle (Eq. 4)
 * }
 * }

Given that $$\displaystyle h_x N = 0$$, it is found that
 * {| style="width:100%" border="0" align="left"

\Rightarrow -h_y M + h(N_x - M_y) = 0 $$ $$ or
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 5)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\Rightarrow \frac{h_y}{h} = \frac{1}{M}(N_x - M_y) = -g(y) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 6)
 * }
 * }

Find
Complete the details to obtain Euler's Integrating factor $$\displaystyle h(y)$$.

Solution
Integrate equation 6
 * {| style="width:100%" border="0" align="left"

\int \frac{h_y}{h} dy = - \int g(y) dy $$ $$ This yields
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 7)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\ln h = - \int^y g(y) dy $$ $$ The final equation is
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 8)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

h = e^{- \int^y g(y) dy} $$ $$
 * $$\displaystyle (Eq. 9)
 * }
 * }

= Problem 2 - Finding Integrating Factor =

Given

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

y' + \frac{1}{x}y = x^2 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }

Find
1. Show that the solution for the integrating factor is $$h(x) = x$$ 2. Solve for $$y$$

Solution
1. With an integrating factor, $$h(x)$$, we should get the equation
 * {| style="width:100%" border="0" align="left"

(hy)' = h x^2 $$ $$ Using $$h(x) = x$$ yields
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

xy' + y = x^3 $$ $$ Dividing the above equation with $$x$$ yields the original equation
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

y' + \frac{1}{x} y = x^2 $$ $$ Hence, $$h(x) = x$$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

2. Substituting $$h(x) = x$$ into equation 2 yields
 * {| style="width:100%" border="0" align="left"

(xy)' = x^3 $$ $$ Next, we integrate the above equation
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 4)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

xy = \frac{x^4}{4} + C $$ $$ where $$C$$ is a constant. The final form of this equation is
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 5)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

y = \frac{x^3 }{4} + \frac{C}{x} $$ $$
 * $$\displaystyle (Eq. 6)
 * }
 * }

= Problem 3 - L1-ODE-VC Exactness =

Given

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

\frac{1}{2} x^2 y' + \left[ x^4 y + 10 \right] = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1)
 * }
 * }

Find
Show that equation 1 has an exact solution

Solution
The first exactness condition for an N1-ODE is satisfied of the equation can be written in the form
 * {| style="width:100%" border="0" align="left"

M(x,y) + N(x,y) y'= 0 $$ $$ This is fulfilled if
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 2)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

M(x,y) =  x^4 y + 10 $$ $$ and
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

N(x,y) = \frac{1}{2} x^2 $$ $$ The second exactness condition requires that
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

(hM)_y = (hN)_x $$ $$ where $$h = h(x,y)$$ is an integrating factor. Equation 5 expands to
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

h_y M + h M_y = h_x N + h N_x $$ $$ If $$h = h(y)$$, equation 6 can be written
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\frac{h_y}{h}  = \frac{1}{M} \left(N_x - M_y\right) $$ $$ Substituting in $$M$$ and $$N$$ yields
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\frac{h_y}{h}  = \frac{1}{x^4 y + 10} \left(x - x^4\right) $$ $$ Integrating both sides with respect to $$y$$ yields
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\ln h  = \ln \left( y + \frac{10}{x^4}\right) \frac{1}{x^4}\left(x - x^4\right) + C_1 $$ $$ or
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 9)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

h = \exp\left[\ln \left( y + \frac{10}{x^4}\right) \left(x^{-3} - 1\right) + C_1\right] $$ $$ or
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 10)
 * }
 * }

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

h = C_2 \left( y + \frac{10}{x^4}\right)^{(x^{-3} - 1)} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 10)
 * }
 * }

Hence, both exactness criteria are fulfilled and there is an exact solution to the given equation.

= Problem 4 - L1-ODE-VC Exactness =

Given

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

\frac{1}{3} x^3 y^4 y' + \left(5x^3 + 2 \right) \left(\frac{1}{5} y^5 \right) = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1)
 * }
 * }

Find
Show that equation 1 is an exact nonlinear, first order ODE.

Solution
With

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

M = \left(5x^3 + 2 \right) \left(\frac{1}{5} y^5 \right) $$ $$ and
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 2)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

N = \frac{1}{3} x^3 y^4 $$ $$ we get
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

M + N y'= 0 $$ $$ Hence, the first exactness condition is satisfied. The second exactness condition is
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

(hM)_y = (hN)_x $$ $$ Expanding equation 5 yields
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

h_y (5 x^3 + 2) \frac{y^5}{5} + h (5 x^3 + 2) y^4= h_x \frac{1}{3} x^3 y^4 + h x^2 y^4 $$ $$ If we choose $$h = x^{-3} y^{-5}$$, both sides of equation 6 equals zero, and hence the second exactness condition is fulfilled. Equation 5 becomes
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\left[(5 + 2 x^{-3}) \frac{1}{5}\right]_y = \left[\frac{1}{3} y^{-1} \right]_x $$ $$ Hence, equation 1 is an exact non-linear first order ODE.
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }

= Problem 5 - N2-ODE-VC Exactness =

Given
Consider the following equation
 * {| style="width:100%" border="0" align="left"

xy y'' + x(y')^2 + y y' = 0 $$ $$ Using
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

f(x,y,p) = xy $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 2)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

g(x,y,p) = x(y')^2 + y y' = 0 $$ $$ Equation 1 can be written
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

f(x,y,p) y'' + g(x,y,p) = 0 $$ $$ Hence, the first exactness condition is fulfilled.
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)
 * }
 * }

Find
Show that the second exactness condition is satisfied for equation 1.

Solution
Note: Equation 1 can be rewritten
 * {| style="width:100%" border="0" align="left"

(xyy')' = 0 $$ $$ First, we write $$f$$ and $$g$$ as
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

f(x,y,p) = xy $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 2)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

g(x,y,p) = x p^2 + y p = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)
 * }
 * }

The second condition of exactness is given by
 * {| style="width:100%" border="0" align="left"

f_{xx} + 2p f_{xy} + p^2 f_{yy} = g_{xp} + p g_{yp} - g_y $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

f_{xp} + p f_{yp} + 2 f_y = g_pp $$ $$ Substituting $$f$$ and $$g$$ into equation 6 and 7 yields
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

0 + 2p \cdot 1 + p^2 \cdot 0 = 2p + p \cdot 1 - p $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

0 + p \cdot 0 + 2 x = 2x $$ $$ or
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 9)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

2p = 2p $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

2 x = 2x $$ $$ Hence, the second exactness condition is fulfilled.
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 9)
 * }
 * }

= Problem 6: Derive the second exactness condition for N2-ODE=

Given
A general N2-ODE is given in the form:

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

F(x,y,y',y) = 0 = f(x,y,p)y + g(x,y,p) $$ $$ where
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

f(x,y,p):=\phi_p(x,y,p) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 2)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

g(x,y,p):=\phi_x + \phi_y(x,y,p)p $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)
 * }
 * }

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

p:=y'. $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)
 * }
 * }

Find
Derive the second condition of exactness (given in Eq. 5)

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

f_{xp}+pf_{yp} + 2f_y = g_{pp} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }

Solution
Differentiate Eq. 3 with respect to p
 * {| style="width:100%" border="0" align="left"

g_p = \phi_{xp} + \phi_y + p\phi_{yp} $$ $$ Note that $$\displaystyle f = \phi_p$$, so
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

g_p = f_{x} + \phi_y + p f_{y} $$ $$ Differentiate a second time
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

g_{pp} = f_{xp} + \phi_{py} + f_{y} + p f_{yp} $$ $$ Substitute $$\displaystyle f = \phi_p$$ again
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

g_{pp} = f_{xp} + p f_{yp} + 2f_{y} $$ $$
 *
$$\displaystyle (Eq. 9)
 * }
 * }

= Problem 7: Deriving First Condition for N2-ODE Exactness Criterion =

Given
A general N2-ODE is given in the form:

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

F(x,y,y',y) = 0 = f(x,y,p)y + g(x,y,p) $$ $$ where
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

f(x,y,p):=\phi_p(x,y,p) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 2)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

g(x,y,p):=\phi_x + \phi_y(x,y,p)p $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)
 * }
 * }

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

p:=y'. $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)
 * }
 * }

Find
Derive the first exactness condition given by Eq 5.

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

f_{xx} + 2p f_{xy} + p^2 f_{yy} = g_{xp} + p g_{yp} - g_{y} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)

 * }
 * }

Solution
We know that $$\displaystyle \phi_{xy}=\phi_{yx}$$

where,

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

\phi_{x} = g - p ( g_p - f_x) + p^2 f_y $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)

 * }
 * }

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

\phi_{y} = g_p - f_y p - f_x $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)

 * }
 * }

Taking the partial derivative of (6) with respect to $$\displaystyle y$$ and the partial derivative of (7) with respect to $$\displaystyle x$$ gives

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

\phi_{xy} = g_y - p_y ( g_p - f_x) - p (g_{py} - f_{xy}) + 2 p_y f_y + p^2 f_{yy} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)

 * }
 * }

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

\phi_{yx} = g_{px} - f_{yx} p - f_y p_x - f_{xx} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 9)

 * }
 * }

Since (8) and (9) are equal

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

g_y - \cancelto{0}{p_y} g_p + \cancelto{0}{p_y} f_x - p g_{py} + p f_{xy} + 2 \cancelto{0}{p_y} f_y + p^2 f_{yy} = g_{px} - f_{yx} p - f_y \cancelto{0}{p_x} - f_{xx} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 10)
 * }
 * }

Re-arranging terms yields

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

$$\displaystyle f_{xx} + 2 p f_{xy} + p^2 f_{yy}  = g_{xp} + p g_{yp} - g_y $$ $$
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 *
$$\displaystyle (Eq. 11)
 * }
 * }

= Problem 8: Applying N2-ODE Exactness Criterion=

Given
The following N2-ODE,

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

(8 x^5y')y''+2x^2y'+20x^4(y')2+4xy=0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1) )
 * }
 * }

Find
Is this ODE exact?

Solution
The 2 exactness conditions are given by,

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

1: f_{xx} + 2pf_{xy} + p^2f_{yy} = g_{xp} + pg_{yp} - g_{y} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 2)

 * }
 * }

and

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

2: f_{xp} + pf_{yp} + 2f_{y} = g_{pp} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)

 * }
 * }

By substituting $$\displaystyle p=y'$$, into Eq. 1, the result is:

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

(8 x^5p)y''+2x^2p+20x^4(p)2+4xy=0 $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)

 * }
 * }

From (4) and knowing the form of a N2-ODE (See Problem 7 Eq. 1),

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

f(x,y,p)=8 x^5p $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }

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

g(x,y,p)=2x^2p+20x^4(p)2+4xy $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * }
 * }

Taking the partial derivatives of (5) and (6) respectively yields

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

\begin{array}{*{20}l} {f_x = 40x^4 p} & {f_{xx}  = 160x^3 p} & {g_x  = 4xp + 80x^3 p^2  + 4y} & {g_{xp}  = 4x + 160x^3 p}  \\ {} & {f_{xy} = 0} & {g_y  = 4x} & {g_{yp}  = 0}  \\ {} & {f_{xp} = 40x^4 } & {g_p  = 2x^2 p^2  + 40x^4 p} & {g_{pp}  = 40x^4 }  \\ {f_y = 0} & {f_{yy}  = 0} & {} & {}  \\ {} & {f_{yp} = 0} & {} & {}  \\ \end{array} $$
 * $$\displaystyle
 * $$\displaystyle

 * }
 * }

Substituting the elements of Eq. 2 results in

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

(160x^3 p) + 2 p (0) + p^2 (0)  = (4x + 160x^3 p) + p (0) - (4x) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)
 * }
 * }

Applying algebra yields:

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

160x^3 p = \cancel{4x} + 160x^3 p - \cancel{4x} $$
 * $$\displaystyle
 * $$\displaystyle
 * style= |
 * }
 * }

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

 * style="width:30%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

1=1 $$ $$
 *
$$\displaystyle (Eq. 8)
 * }
 * }

Therefore, the first relation is satisfied

Substituting derived element into Eq. 3 results in

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

(0) + p(0) + 2(0) = (0) $$
 * $$\displaystyle
 * $$\displaystyle
 * style= |
 * }
 * }

Then,

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

 * style="width:30%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

0=0 $$ $$
 *
$$\displaystyle (Eq. 9)
 * }
 * }

Therefore, the second relation is satisfied

Because the 2 exactness conditions are met ( Eq. 8 and Eq. 9), the N2-ODE is exact.

= Problem 9: Exactness of N2-ODE=

Given
The following N2-ODE,

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

\sqrt{x}y''+2xy'+3y=0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1) )
 * }
 * }

Find
Is this ODE exact?

Solution
The 2 exactness conditions are given by,

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

1: f_{xx} + 2pf_{xy} + p^2f_{yy} = g_{xp} + pg_{yp} - g_{y} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 2)

 * }
 * }

and

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

2: f_{xp} + pf_{yp} + 2f_{y} = g_{pp} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)

 * }
 * }

By substituting $$\displaystyle p=y'$$, into Eq. 1, the result is:

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

(\sqrt{x})y''+(2xp+3y)=0 $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)

 * }
 * }

From Eq. 4 and knowing the form of a N2-ODE (See Problem 7 Eq. 1),

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

f(x,y,p)=\sqrt{x} $$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }

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

g(x,y,p)=2xp+3y $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * }
 * }

Taking the partial derivatives of (5) and (6) respectively yields

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

\begin{array}{*{20}l} {f_x = \frac{x^{-0.5}}{2}} & {f_{xx}  = -\frac{x^{-1.5}}{4}} & {g_x  = 2p} & {g_{xp}  = 2}  \\ {} & {f_{xy} = 0} & {g_y  = 3} & {g_{yp}  = 0}  \\ {} & {f_{xp} = 0 } & {g_p  = 2x} & {g_{pp}  = 0 }  \\ {f_y = 0} & {f_{yy}  = 0} & {} & {}  \\ {} & {f_{yp} = 0} & {} & {}  \\ \end{array} $$
 * $$\displaystyle
 * $$\displaystyle

 * }
 * }

Substituting the elements of Eq. 2 results in

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

(-\frac{x^{-1.5}}{4}) + 2 p (0) + p^2 (0)  = (2) + p (0) - (3) $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

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

 * style="width:30%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

(-\frac{x^{-1.5}}{4}) = -1 $$ $$
 *
$$\displaystyle (Eq. 7)
 * }
 * }

Obviously, these equations are not equal, therefore given N2-ODE is NOT EXACT.

=Contributing Team Members= Egm6321.f09.Team1.vasquez 13:52, 23 September 2009 (UTC)

Egm6321.f09.Team1.AH 18:19, 23 September 2009 (UTC)

Egm6321.f09.Team1.sallstrom 18:29, 23 September 2009 (UTC)

Egm6321.f09.Team1.andy 18:48, 23 September 2009 (UTC)

title: User:Egm6321.f09.Team1/HW2


text: File:PEW 21-9-2009.pdf

title: File:PEW 21-9-2009.pdf