text:
User:Egm6321.f10.team5/hw3

= Problem 1 - Derive EOM (SC-N1-ODE) = From Meeting 13, p. 13-1 ~ p. 13-2

Given
A projectile of mass (m) is being shot through the air at an angle (α) to the horizontal with velocity (v). The projectile experiences a drag force due to air resistance, $$F_{air} = k v^n \,$$ Where $$k \,$$ is the coefficient of air resistance and is a constant in this problem. The force equations are therefore given as such, $$m(\frac {dv_x} {dt}) = -k v^{n} {\cos {\alpha}}$$ $$\displaystyle (Eq. 1.1) $$ $$m(\frac {dv_y} {dt}) = -k v^{n} {\sin {\alpha}} - mg$$ $$\displaystyle (Eq. 1.2) $$

Find
For the given situation: $$m(\frac {dv_y} {dt}) = -k v^{n} {\sin {\alpha}} - mg$$
 * 1) Derive the equations of motion for the projectile
 * 2) For the particular case $$k = 0 \,$$ verify that $$y(x)\,$$ is a parabola
 * 3) Consider $$k \ne 0 \,$$ and $$v_{xo}=0 \,$$, therefore

becomes

$$m(\frac {dv_y} {dt}) = -k v_y^{n} {\sin {\alpha}} - mg$$

 * 3.1 Find $$v_y (t)\,$$ and $$y(t) \,$$ for $$m = constant \,$$
 * 3.2 Find $$v_y (t)\,$$ and $$y(t) \,$$ for $$m = m(t) \,$$

Part 1
The projectile is given an initial velocity $$ v $$ in a direction that is at an angle $$ \alpha $$ to the horizontal. The Equations of motion (Eq. 1.1 and Eq. 1.2) given in the problem statement are acquired through summing the forces on the projectile and decomposing those forces into their vector quantities acting on the projectile. We sum the forces by looking at which ones are having an effect on the motion of the object.

1) inertia of the projectile after being fired from its initial position:

$$F_{inertia} = m(\frac {dv} {dt}) $$

which must be decomposed into its x and y components:

$$F_{x-inertia} = m(\frac {dv_x} {dt}) $$

$$F_{y-inertia} = m(\frac {dv_y} {dt}) $$

2) The effects of gravity on the y-component of the projectile's inertia:

$$F_{g} = -m g \,$$

$$g =  \,$$ acceleration  due  to  gravity

3) The force of air resistance on the projectile's motion decomposed into its x and y directional components:

$$F_{x-air} = -k v^{n} {\cos {\alpha}} \,$$

$$F_{y-air} = -k v^{n} {\sin {\alpha}} \,$$

Now if we sum the forces in the x and y directions and consider the force equilibrium in those directions we obtain the Equations of Motion given in the problem statement:

$$\sum {F_x} = m(\frac {dv_x} {dt}) = -k v^{n} {\cos {\alpha}}$$

$$\sum {F_y} = m(\frac {dv_y} {dt}) = -k v^{n} {\sin {\alpha}} - mg$$

Part 2
For the particular case where $$ k = 0 $$ equations 1.1 and 1.2 reduce to:

$$ m(\frac {dv_x} {dt}) = 0$$

which reduces to

$$ (\frac {dv_x} {dt}) = 0$$$$\displaystyle (Eq. 1.3) $$

and

$$m(\frac {dv_y} {dt}) = -mg $$

which reduces further to

$$(\frac {dv_y} {dt}) = -g $$$$\displaystyle (Eq. 1.4) $$

Now we can integrate Eqs. 1.3 and 1.4 with respect to time in order to get expressions for velocity and position in the x and y directions. We will start with the x-direction equations:

x-component:

$$ \frac {dv_x} {dt} = 0$$

Integrating with respect to time we obtain,

$$ v_x(t) = c_1 \,$$$$\displaystyle (Eq. 1.5) $$

Using the initial condition $$ v_x(t=0) = v_{xo} \,$$ the constant of integration $$ c_1 \,$$ can be found,

$$ c_1 = v_{xo} \,$$

So Eq. 1.5 becomes,

$$ v_x(t) = v_{xo} \,$$ $$\displaystyle (Eq. 1.6) $$

Now we repeat the same procedure for Eq. 1.4 to obtain the y component of the velocity vector. Once we integrate Eq. 1.4 with respect to time we get,

$$ v_y(t) = -gt + c_2 \,$$$$\displaystyle (Eq. 1.7) $$

Then using the initial condition $$ v_y(t=0) = v_{yo} \,$$ we can determine that $$ c_2 = v_{yo} \,$$ so then Eq. 1.7 becomes,

$$ v_y(t) = -gt + v_{yo} \,$$$$\displaystyle (Eq. 1.8) $$

Now we integrate Eq. 1.7 and 1.8 with respect to time once more to obtain the equations for position as a function of time in the x and y directions. After integrating with respect to time Eq. 1.7 and 1.8 become,

$$ x(t) = v_{xo}t + c_3 \,$$$$\displaystyle (Eq. 1.9) $$

and

$$ y(t) = - \frac 1 2 gt^2 + v_{yo}t + c_4 \,$$$$\displaystyle (Eq. 1.10) $$

Using initial conditions for position $$ x(t=0) = x_{o}\,$$ and $$ y(t=0) = y_{o}\,$$ then $$c_3\,$$ and $$c_4\,$$ can be solved for,

$$ c_3 = x_{o}\,$$

and

$$ c_4 = y_{o}\,$$

Plugging these values back into Eq. 1.9 and 1.10 yields the position equations for the x and y directions,

$$ x(t) = v_{xo}t + x_o \,$$$$\displaystyle (Eq. 1.11) $$

$$ y(t) = - \frac 1 2 gt^2 + v_{yo}t + y_o \,$$$$\displaystyle (Eq. 1.12) $$

To express y as a function of x we will manipulate eq. 1.11 to get t in terms of x. This yeilds the expression,

$$ t = \frac {x-x_o} {v_{xo}} \,$$$$\displaystyle (Eq. 1.13) $$

We then plug this value in for t in Eq. 1.12 to get,

$$ y(x) = - \frac 1 2 g(\frac {x-x_o} {v_{xo}})^2 + v_{yo}(\frac {x-x_o} {v_{xo}}) + y_o \,$$$$\displaystyle (Eq. 1.14) $$

to confirm that Eq. 1.14 is a parabola we can simply compare the general form of a parabolic function to Eq. 1.14,

$$ y(x) = ax^2 + bx + c \,$$

$$ y(x) = - \frac 1 2 g(\frac {x-x_o} {v_{xo}})^2 + v_{yo}(\frac {x-x_o} {v_{xo}}) + y_o \,$$

where $$a$$, $$b$$ and $$c$$ are all constants. It is apparent that Eq. 1.14 fits the form of a parabolic function so it can be concluded that our expression for $$y(x)$$ is a parabola.

Part 3
For the case where $$v_{xo}=0 \,$$, and $$k \ne 0$$ we can see from Eq. 1.1 that as long as $$v^n \ne 0 \,$$ then $$\alpha = 90^\circ \,$$ so that there are no net forces acting on the projectile in the x direction which leaves Eq. 1.2 as the net force acting on the projectile. However, since $$\alpha = 90^\circ \,$$ Eq. 1.2 can be re-written as,

$$m(\frac {dv_y} {dt}) = -k v_y^{n}- mg \,$$ $$\displaystyle (Eq. 1.15) $$

Part 3.1
Solving Eq. 1.15 for $$v_y(t)$$ and $$y(t)$$ when $$m =$$ constant. Start with the equation of motion (Eq. 1.15),

$$m(\frac {dv_y} {dt}) = -k (v_y)^{n}- mg \,$$

In order to solve this we must first show exactness. So we first put Eq 1.15 into a form that shows the first condition of exactness is met

$$m(\frac {dv_y} {dt})+ k v_y^{n}+ mg = 0\,$$ $$\displaystyle (Eq. 1.16) $$

So that we can see that the two parts, $$M(v_y,t)$$ and $$N(v_y,t)$$ are,

$$M(v_y,t)=k v_y^{n}+ mg $$

$$N(v_y,t)=m \,$$

Now that the first condition of exactness has been shown we must see if the second condition of exactness is met,

$$ M(v_y,t)_{v_y} = N(v_y,t)_t$$
$$\displaystyle (Eq. 1.17) $$

Which is clearly not met if $$m$$ is a constant

$$M(v_y,t)_{v_y} = knv_y^{n-1} \ne N(v_y,t)_{t} = \frac{dm(t)}{dt}$$
$$\displaystyle (Eq. 1.18) $$

Therefore, the equation is non-exact.

However, the equation can be made exact through the integrating factor method

Then expressing as a total derivative,

Keeping in mind that Eq. 1.20 is a sum of the forces so we can introduce the $$\phi$$ notation that will simplify the equation a bit.

$$ \sum F = \frac {\partial \phi} {\partial t} dt + \frac {\partial \phi} {\partial v_y} dv_y =0 $$

Therefore the $$\phi$$ derivatives are as follows,

$$\phi_t = h(v_y,t)(kv_y^n+mg)$$

$$\phi_{v_y} = h(v_y,t)m)$$

$$\phi_{t,v_y} = \phi_{v_y,t}$$

Now, we test for exactness. In order for Eq. 1.20 to be exact it must meet the condition,

$$h_{v_y}N+hN_{v_y}=h_tM+hM_t \,$$
$$\displaystyle (Eq. 1.21) $$

So we substitute the problem parameters into Eq. 1.21 and get,

$$\frac{\partial h(v_y,t)}{\partial v_y}(kv_y^n+mg)+h(v_y,t)\frac{\partial(kv_y^n+mg)}{\partial v_y} = \frac{\partial h(v_y,t)}{\partial t}m+h(v_y,t)\frac{\partial m}{\partial t}$$
$$\displaystyle (Eq. 1.22) $$

Letting $$\partial h / \partial v_y = 0$$ and since $$m$$ is a constant $$\partial m / \partial t = 0$$. So Eq. 1.22 reduces to,

$$h(v_y,t)\frac{\partial(kv_y^n+mg)}{\partial v_y} = \frac{\partial h(v_y,t)}{\partial t}m$$
$$\displaystyle (Eq. 1.23) $$

Now, we manipulate Eq 1.23 in order to obtain an expression for $$h(v_y,t)$$,

$$h(v_y,t)\frac{\partial(kv_y^n+mg)}{\partial v_y} = \frac{\partial h(v_y,t)}{\partial t}m$$
$$\displaystyle (Eq. 1.24) $$

$$h(v_y,t)\frac{nkv_y^n}{m} = \frac{\partial h(v_y,t)}{\partial t}$$
$$\displaystyle (Eq. 1.25) $$

$$h(v_y,t) = \exp(\frac{kv_y^n}{m}t)$$
$$\displaystyle (Eq. 1.26) $$

Therefore the $$\phi$$ derivative equations can be solved to get $$\phi$$,

$$ \phi_t = \exp(\frac{kv_y^n}{m}t)(kv_y^n+mg) $$
$$\displaystyle (Eq. 1.27) $$

$$ \phi = \int{\phi_t dt} = \int{ \exp(\frac{kv_y^n}{m}t)(kv_y^n+mg)dt} $$
$$\displaystyle (Eq. 1.28) $$

$$ \phi =(kv_y^n+mg)\frac{m}{kv_y^n}\exp(\frac{kv_y^n}{m}t)+f(v_y) = c_5 $$
$$\displaystyle (Eq. 1.29) $$

$$ \phi_v = m\exp(\frac{kv_y^n}{m}t) $$
$$\displaystyle (Eq. 1.30) $$

$$ \phi = \int{\phi_{v_y} dv_y} = \int{ m\exp(\frac{kv_y^n}{m}t)dv_y} = c_5 $$
$$\displaystyle (Eq. 1.31) $$

$$ \phi = m\int{\exp(\frac{kv_y^n}{m}t)dv_y} + f(t) = c_5 $$
$$\displaystyle (Eq. 1.32) $$

We can now combine these $$\phi$$ equations to come up with an expression of the sum of the forces that is exact,

$$ \sum F =\frac {\partial \phi} {\partial t} dt + \frac {\partial \phi} {\partial v_y} dv_y =\phi = m\int{\exp(\frac{kv_y^n}{m}t)dv_y} + (kv_y^n+mg)\frac{m}{kv_y^n}\exp(\frac{kv_y^n}{m}t) = c_5 $$
$$\displaystyle (Eq. 1.33) $$

This resulting equation is not integrable and therefore no explicit general form of $$v_y$$ was found. However, through the integrating factor method an exact non-linear expression was found. Numerical solutions can be found given a value of n, and initial conditions.

Part 3.2
For the condition where $$m=m(t) \ne 0$$, the integrating factor becomes even more complicated because in Eq 1.22 the initial simplification that occurs when $$ \frac {\partial m} {\partial t} = 0$$ does not happen. This will result in another implicit solution for $$v_y$$ when the integrating factor method is applied.

Author and Proof-reader
[Author] Rob Carroll

[Proof-reader] Scott Elliott

= Problem 2 - Derive EOM (SC-L1-ODE) = From Meeting 13, p. 13-3

Given
A system of pendulum.

Part 1
Derive the following equations.

Part 2
Write the above equations in the form of $$\dot x(t) = A(t) x(t) + B(t) u(t)$$. Find A, B, and u.

Part 1
We use Newtons's second law for Rotation which is $$\Sigma \tau = I \alpha$$ for the derivation. We note that there are three torques applied on the particle 1; gravitational torque, controlling torque, and spring torque. Gravitational torque is Controlling torque is Spring torque is Moment of inertia for the point mass is Angular acceleration for the point mass is We set up the equation of motion for the first particle. Apply the small-angle approximation which states that $$\sin x \approx x$$ and $$\cos x \approx 1$$ to simplify equation as We use the same techniques to derive the equation of motion for second particle. Gravitational torque is Controlling torque is Spring torque is Moment of inertia for the point mass is Angular acceleration for the point mass is We set up the equation of motion for the second particle. Apply the small-angle approximation which states that $$\sin x \approx x$$ and $$\cos x \approx 1$$ to simplify equation as

Part 2
We write $$\dot x(t) = A(t) x(t) + B(t) u(t)$$ in matrix form. We divide the both side of $$m_1 l^2 \ddot \theta_1\ = - k a^2 (\theta_1 - \theta_2) - l \theta_1 m_1 g + l u_1$$ by $$m_1 l^2$$ to get Similarly, we divide the both side of $$m_2 l^2 \ddot \theta_2\ = - k a^2 (\theta_2 - \theta_1) - l \theta_2 m_2 g + l u_2$$ by $$m_2 l^2$$ to get We can easily determine that the all the components on row 1 and row 3 of matrix A and matrix B are null except for $$A_{12}$$ and $$A_{34}$$, so we write that Now we plug in the expressions of $$\ddot \theta_1$$ and $$\ddot \theta_2$$ into the matrix.

Author and Proof-reader
[Author] Egm6321.f10.team5.abc

[Proof-reader] Mike Faraone / Oh, Sang min

= Problem 3 - Derive (L1-ODE-CC) = From Meeting 14, p. 14-1

Given
An L1-ODE-CC equation.

Find
Solve $$\dot x(t) = a(t) x(t) + b(t) u(t)$$ for the case where $$a(t)$$ and $$b(t)$$ are constant coefficients while u(t) is prescribed.

Solve
We state that $$\displaystyle a(t) = a$$ and $$\displaystyle b(t) = b$$ for this case. So we have the equation in the form of $$\displaystyle hx' + h'x = hk$$.

Note that we cannot use the equation of $$\displaystyle y(x) = \frac 1 {h(x)} \int^x h(s) d(s) ds$$

since the lower limit is bounded as $$\displaystyle t_0$$.

Deriving an equation for the lower bound

Apply the modified equation given above to our problem. It is possible to simplify the equation further as

Author and Proof-reader
[Author] Egm6321.f10.team5.abc

[Proof-reader] Mike Faraone / Oh, Sang min

= Problem 4 - Expand Taylor series(exponential and exponential matrix) = From Meeting 14, p. 14-2

Given

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

$$\displaystyle {e}^{x} = 1 + \frac{x}{1!} + \frac{x^2}{2!} + ... $$ $$\displaystyle \ = \sum_{k=0}^{\infty} \frac{x^k}{k!} $$
$$\displaystyle (4-1) $$
 * }
 * }

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

$$\displaystyle \underbrace{{e}^{\underline{A}}}_{\underline{A} \ : \ n \times n \ Matrix} = \underbrace{\underline{\mathit I }}_{n \times n \ Unit \ mat.} + \frac{\underline{A}}{1!} + \frac{\underline{A}^2}{2!} + ... $$ $$\displaystyle \ = \sum_{k=0}^{\infty} \frac{\underline{A}^k}{k!} $$
$$\displaystyle (4-2) $$
 * }
 * }

Find
1) Derive (4-1)

2) Derive (4-2)

Solve
Solution of 1)

Using Taylor series ,

$$f(a)+\frac {f'(a)}{1!} (x-a)+ \frac{f''(a)}{2!} (x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+ \cdots. $$

which can be written in the more compact sigma notation as

 * $$ \sum_{n=0} ^ {\infin } \frac {f^{(n)}(a)}{n!} \, (x-a)^{n} $$

In the particular case where a = 0, the series is also called a Maclaurin series
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

$$f(x) = f(0)+f'(0)x + \frac{f''(0)}{2!}x^2+\frac{f^{(3)}(0)}{3!}x^3+ \cdots .$$ $$ \ = \sum_{n=0} ^ {\infin } \frac {f^{(n)}(0)}{n!} \, (x)^{n}$$
$$\displaystyle (4-3) $$
 * }
 * }

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

$$\displaystyle f(x) := {e}^{x} $$
$$\displaystyle (4-4) $$
 * }
 * }

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

$$\displaystyle f(0) = 1, \ f'(x) = {e}^{x}, \ f'(0) = 1, \ ... $$
$$\displaystyle (4-5) $$
 * }
 * }

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

$$\displaystyle f(x) = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} \ ... $$
$$\displaystyle (4-6) $$
 * }
 * }

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

$$\therefore {e}^{x} = \sum_{k=0}^{\infty} \frac{x^k}{k!} $$
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 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * }
 * }
 * }

Solution of 2)

Using Taylor series and Maclaurin series

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$$\displaystyle f(\underline{x}) :=  \underbrace{{e}^{\underline{A}}}_{\underline{A} \ : \ n \times n \ Matrix} $$
$$\displaystyle (4-7) $$
 * }
 * }

<Background Knowledge> - Exponential Matrix, Identity Matrix

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

$$\displaystyle f(\underline{0}) = \underbrace{\underline{\mathit  I }}_{n \times n \ Unit \ mat.}, \ f'(\underline{x}) = {e}^{\underline{A}}, \ f'(\underline{0}) = \underline{\mathit  I }, \ ... $$
$$\displaystyle (4-8) $$
 * }
 * }

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

$$\displaystyle f(\underline{x}) = 1 + \underline{A} + \frac{\underline{A}^2}{2!} + \frac{\underline{A}^3}{3!} \ ... $$
$$\displaystyle (4-9) $$
 * }
 * }

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

$$\therefore {e}^{\underline{A}} = \sum_{k=0}^{\infty} \frac{\underline{A}^k}{k!} $$
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * }
 * }
 * }

Author and Proof-reader
[Author] Oh, Sang Min

[Proof-reader] Mike Faraone

= Problem 5 - Generalized to SC-L1-ODE-VC = From Meeting 14, p. 14-2

Given
Dimension of matrix

$$\displaystyle \underline{x} \ : \ n \times \ 1 $$

$$\displaystyle \underline{A} \ : \ n \times \ n $$

$$\displaystyle \underline{B} \ : \ n \times \ m $$

$$\displaystyle \underline{U} \ : \ m \times \ 1 $$

Find
Generalized (5-3) to SC-L1-ODE-VC

Solve
 SC-L1-ODE-CC can be generalized to SC-L1-ODE-CC as same as L1-ODE-CC is generalized to L1-ODE-VC

Using (5-1) ~ (5-3)

 SC-L1-ODE-VC

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

$$ \underline{x}(t)= {e}^{\int_{{t}_{0}}^{t}{e}^{\underline{A} (\tau)}d\tau}\cdot \underline{x}({t}_{0}) + \int_{{t}_{0}}^{t}{e}^{\int_{\tau}^{t}{e}^{\underline{A} (s)}ds} \cdot \underline{B}\cdot \underline{U}(\tau)d\tau $$
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * }
 * }
 * }

Dimension of matrix

$$\displaystyle \underline{x} \ : \ n \times \ 1 $$

$$\displaystyle \underline{A} \ : \ n \times \ n $$

$$\displaystyle \underline{B} \ : \ n \times \ m $$

$$\displaystyle \underline{U} \ : \ m \times \ 1 $$

Author and Proof-reader
[Author] Oh, Sang Min

[Proof-reader]

= Problem 6 - Obtaining SC-L1-ODE-CC with int. factor method = From Meeting 15, p. 15-1

Given
We are given a system of coupled linear first order ODEs with constant coefficients,
 * {| style="width:100%" border="0"

A part of the solution to this system is the state transition matrix, $$\underline{\Phi}$$, which has the properties
 * style="width:95%" | $$\displaystyle \underline{\dot{x}}(t)=\underline{A}\underline{x}(t)+\underline{B}\underline{u}(t)$$
 *
(6.A)
 * }
 * }
 * {| style="width:100%" border="0"

and
 * style="width:95%" | $$\displaystyle \frac{d}{dt}\underline{\phi}(t,t_0)=\underline{A}\underline{\phi}(t,t_0)$$
 *
(6.B)
 * }
 * }
 * {| style="width:100%" border="0"

where $$I$$ is the identity matrix.
 * style="width:95%" | $$\displaystyle \underline{\phi}(t_0,t_0)=I,$$
 *
(6.C)
 * }
 * }

Find
Use equations (6.A), (6.B), and (6.C), to obtain the following equation:
 * {| style="width:100%" border="0"

$$\displaystyle \underline{x}(t)=\underbrace{\left[{\rm exp}\underline{A}(t-t_0)\right]}_{\underline{\phi}(t,t_0)}\underline{x}(t_0)+\int\limits_{t_0}^{t}{\underbrace{\left[{\rm exp}\underline{A}(t-\tau)\right]}_{\underline{\phi}(t,\tau)}\underline{B}\underline{u}(\tau)\,d\tau} $$
 * style="width:95%" |
 * style="width:95%" |
 *
(6.D)
 * }

Solution
We can derive from $$\frac d {dt} \underline \phi (t,t_0) = \underline A \underline \phi (t,t_0)$$ that $$\underline A = \frac {\frac d {dt} \underline \phi (t,t_0)} {\underline \phi (t,t_0)}$$. Because $$\phi (t_0,t_0) = \underline 1$$ which is an identity matrix.

Author and Proof-reader
[Author] Egm6321.f10.team5.abc

Egm6321.f2010.team5.riveros 17:18, 6 October 2010 (UTC)

[Proof-reader] Michael Steinberg

= Problem 7 - Application SC-L1-ODE-CC about rolling control of rocket = From Meeting 15, p. 15-1

Given

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

 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

$$\displaystyle \delta $$  =   aileron angle(deflection)

$$\displaystyle \phi $$ =   roll angle

$$\displaystyle \omega $$ =  roll angular velocity

$$\displaystyle Q $$ =   aileron efflectiveness

$$\displaystyle \tau $$ = roll time constant

 * }
 * }
 * }

Find
Put (7-1) ~ (7-3) in form of (7-4)

Solve

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

$$
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

\begin{pmatrix} \dot\phi\\ \dot\omega\\ \dot\delta \end{pmatrix} = \begin{pmatrix} 0 & 1 & 0 \\ 0 & \frac{-1}{\tau} & \frac{Q}{\tau}\\ 0 & 0 & 0 \end{pmatrix}

\begin{pmatrix} \phi\\ \omega\\ \delta \end{pmatrix} + \begin{pmatrix} 0\\ 0\\ 1 \end{pmatrix} u $$

$$ \underline{A}= \begin{pmatrix} 0 & 1 & 0 \\ 0 & \frac{-1}{\tau} & \frac{Q}{\tau}\\ 0 & 0 & 0 \end{pmatrix}

, \ \underline{B}= \begin{pmatrix} 0\\ 0\\ 1 \end{pmatrix}

$$
 * }
 * }
 * }

Author and Proof-reader
[Author] Oh, Sang Min

[Proof-reader] Mike Faraone

= Problem 8 - Searching for solution without assuming = From Meeting 17, p. 17-1

Given
A second order nonlinear ordinary differential equation (N2-ODE) may be represented as follows (First Cond. of Exactness):

$$ F(x,y,y',y) = g(x,y,p) + f(x,y,p)y = 0 \! $$

where $$ p = y' \! $$

If both the first and second conditions of exactness (see Meeting 15, pp. 15-2, 15-3) are satisfied,

Find
Define the method for determining $$ h(x,y) \! $$ for the case when $$ h(x,y) \not= const \! $$

Solve
Using Eq. (8.3), the following partial derivatives can be obtained

Recalling the definition of $$ g \! $$ given in Eq. (8.1) and substituting (8.4) and (8.5) into (8.1) yields

Because we already know $$ g \! $$ from the N2-ODE given, we can set like terms equal in order to solve for $$ h(x,y) \! $$.

For example, should (8.6) simplify into the following form,

$$ ay' + b = h_x + h_y y' \! $$

then we may set $$ h_x = b \! $$ and $$ h_y = a \! $$ and solve for $$ h(x,y) \! $$.

Author and Proof-reader
[Author] Michael Steinberg

[Proof-reader]

=Problem 9 - Show the given equation satisfies the second condition for exactness= From Meeting 17, p. 17-2

Given
We are given a nonlinear second order ODE,
 * $$ \displaystyle

\underbrace{\phi_p}_{f}y + \underbrace{\phi_yy' + \phi_x}_{g} =\underbrace{(15p^4cos (x^2))}_{\phi_p}y + \underbrace{(6xy^2)}_{\phi_y}y' + \underbrace{(-6xp^5sin(x^2) + 2y^3)}_{\phi_x} = 0 $$ Thus,
 * $$ \displaystyle

f = \phi_p = 15p^4cos (x^2) $$ and,
 * $$ \displaystyle

g = \phi_yy' + \phi_x = (6xy^2)y' + (-6xp^5sin(x^2) + 2y^3) $$

Find
The second condition of exactness for nonlinear second order ODEs states that the ODE must satisfy the following two relations:
 * 1) $$ \displaystyle f_{xx}+2pf_{xy}+p^2f_{yy} = g_{xp}+pg_{yp}-g_{y}$$
 * 2) $$ \displaystyle f_{xp}+pf_{yp}+2f_{y}=g_{pp}$$

Show that the given equation satisfies the second condition of exactness.

First relation
The terms on the left hand side are found,
 * $$\displaystyle

f_{xx} = -60\,{p}^{4} \ {x}^{2} \ cos({x}^{2})-30\,{p}^{4} \ sin({x}^{2}) $$

 * $$\displaystyle

f_{xy} = 0 $$

 * $$\displaystyle

f_{yy} = 0 $$ Thus, the left hand side is,
 * $$\displaystyle

f_{xx}+2pf_{xy}+p^2f_{yy} = -60\,{p}^{4} \ {x}^{2} \ cos({x}^{2})-30\,{p}^{4}\sin({x}^{2}) $$ The individual terms on the right hand side are found,
 * $$\displaystyle

g_{xp} = 6\,{y}^{2}-30\,{p}^{4}\sin({x}^{2})-60\,{p}^{4}\ {x}^{2} \cos({x}^{2}) $$

 * $$\displaystyle

g_{yp} = 12\,xy $$

 * $$\displaystyle

g_{y} = 12\,xyp+6\,{y}^{2} $$ Thus, the right hand side is,
 * $$\displaystyle

g_{xp}+pg_{yp}-g_{y} = -60\,{p}^{4} \ {x}^{2} \ cos({x}^{2})-30\,{p}^{4}\sin({x}^{2}) $$ We then check for equality,
 * $$\displaystyle f_{xx}+2pf_{xy}+p^2f_{yy} =g_{xp}+pg_{yp}-g_{y} \implies -60\,{p}^{4} \ {x}^{2} \ cos({x}^{2})-30\,{p}^{4}\sin({x}^{2})=-60\,{p}^{4} \ {x}^{2} \ cos({x}^{2})-30\,{p}^{4}\sin({x}^{2})$$

Which is true.

Second relation
The individual terms on the left hand side are found,
 * $$\displaystyle

f_{xp} = -120\,{p}^{3} \ x \ sin({x}^{2}) $$

 * $$\displaystyle

f_{yp} = 0 $$

 * $$\displaystyle

f_{y} = 0 $$ Thus, the left hand side is,
 * $$\displaystyle

f_{xp}+pf_{yp}+2f_{y}=-120\,{p}^{3} \ x \ sin({x}^{2}) $$ The right hand side is then found,
 * $$\displaystyle

g_{pp}=-120\,{p}^{3} \ x \ sin({x}^{2}) $$

We check for equality,
 * $$\displaystyle f_{xp}+pf_{yp}+2f_{y}=g_{pp} \implies -120\,{p}^{3} \ x \ sin({x}^{2})=-120\,{p}^{3} \ x \ sin({x}^{2})$$

Which is also true; therefore, the given equation satisfies the second condition of exactness.

Author and Proof-reader
[Author] Egm6321.f2010.team5.riveros 06:20, 5 October 2010 (UTC)

[Proof-reader] Michael Steinberg / Oh, Sang min

= Problem 10 - Finish story = From Meeting 18, p. 18-3

Given
A nonlinear second order ODE.

Find
Assume $$\displaystyle h_y y' = 2 y^3$$ and solve $$\displaystyle (6 x y^2) y' + 2 y^3 = h_y y' + h_x$$.

Solve
We derive the following procedures according to the given assumption. Note from the equation of $$\displaystyle \ (6 x y^2) y' + 2 y^3 = h_y y' + h_x$$ that $$\displaystyle  \ h_x = (6 x y^2) y'$$. Take a derivative of $$\displaystyle \ h(x,y)$$ with respect to $$\displaystyle \ y$$ to find that Multiply by $$\displaystyle \ y'$$ to determine that $$\displaystyle \ k_1(y)$$ is a constant. Since $$\displaystyle \ {k_1}'(y) = 0$$, then $$\displaystyle \ k_1 (y) = k_1$$.

Author and Proof-reader
[Author] Egm6321.f10.team5.abc [Proof-reader] Oh, Sang min

= References =

= Contributing Members =

Egm6321.f10.team5.oh Solved and typed problems 4, 5 and 7 / proof-read problems 2, 3, 9 and 10

Michael Faraone Solved problem 2. Helped with part1 problem 1. proof-read and checked problems 2,3,4,7

Egm6321.f10.team5.abc Authored problem 2, problem 3, problem 6, problem 10.

Michael Steinberg Authored problem 8, assisted with problem 6, and proof-read problem 6, problem 9.

title: User:Egm6321.f10.team5/hw3


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User talk:Janelb

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Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:17, 25 September 2010 (UTC)

Best of the Best
Motherboard: ASUS Rampage III Extreme Processor: Intel Core i7-980X Extreme Edition Memory: 12GB Corsair Dominator GT DDR3-1866 C9 Case: Lian Li PC-A77F Power Supply: Corsair HX1000W Hard drive: Western Digital WD6000 600GB CD/DVD: Buffalo BR-H1216FBS-BK Keyboard and Mouse: Microsoft Wireless Laser Desktop 7000 Monitor: NEC Multisync 24WMGX3 Sound card: Asus Sonar DS Video card: Zotac Geforce GTX 480AMP! Modem: Linksys Wireless 54Mbps PCI

title: User talk:May Haas


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User talk:TuktA

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User talk:5280342rut

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User talk:EGM6321.F10.TEAM1.HW3

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title: User talk:EGM6321.F10.TEAM1.HW3


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User talk:Waris p

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Welcome to MUIC video homework
http://www.youtube.com/watch?v=-K0cXo98zLM

Specs on mobile equipment Homework
Iphone 4 •	CPU: 1 GHz Apple A4 processor •	Cortex-A8 CPU core paired with a PowerVR SGX 535 graphics processor (GPU) •	L2 cache •	The A4 processor package does not contain RAM •	There are two chips of 256 MB for a total of 512 MB •	RAM is connected to the processor using ARM's 64-bit-wide AMBA 3 AXI bus •	Storage 16 GB or 32 GB flash memory •	Memory 512 MB eDRAM •	Operating system iOS 4.1 •	Slate Smartphone

Backberry: Bold 9700 •	CPU: XScale 624 MHz processors •	Marvell PXA930: Browse devices based on this microprocessor •	Flash/RAM memory: 256 MB •	Operating system: BlackBerry OS; 5.0 •	External memory: up to 16GB

Acer Aspire One Netbook •	CPU: Intel Atom™ Processor N270 •	Genuine Windows XP Home Edition •      1GB (512MB onboard/512MB SODIMM slot) DDR2 533 SDRAM •	Integrated Intel Graphics Media Accelerator X3100 •	L2 cache •	160GB hard drive •	Less than 1 kilogram

As all we can see from iphone, backberry and netbook specifications, the most technologically advance goes to netbook because it has 1GB of RAM and hard drive upto 160GB. Also, the price is about 10,000 baht compared to backberry and iphone are more higher price. The operating system of netbook is using Genuine Windows XP Home Edition, which is more advance than those two competition. It is worth to buy netbok rather than smartphone because you can carry around with only one kilogram maximum. The netbook is like small laptop that you can play internet, games, listen to music and do assignments. Therefore, netbook is worth to buy and useful.

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text:
User:Josevivekk

Hello, I am Jose Vivek K from India. I am a young Mechanical Engineer presently working as a Planning and Estimation Engineer in Mumbai, India.

title: User:Josevivekk


text:
User talk:Josevivekk

What is the Difference Between Science, Technology and Engineering?

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text: Motivation and emotion/Book/2010/Overeating motivation


text: Template:Motivation and emotion/Textbook chapter link


text:
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text:
UTPA STEM/CBI Courses/Introduction to Mechanical Engineering/Process Improvement

Course Title: Introduction to Mechanical Engineering

Lecture Topic: Process Improvement Challenge

Instructor: Timmer

Institution:UTPA

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Utilize statistical techniques to compare data
 * Utilize design of experiments to improve process performance
 * Introduce mathematical modeling
 * Incorporate statistical analysis software in engineering

 * Sub Objectives- The objectives will require that students be able to:
 * Use Minitab statistical analysis software
 * Communicate results in oral and written formats

 * Difficulties- Students may have difficulty:
 * Accessing Minitab (available at UTPA)

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Improving the performance of any process using experimental design
 * Use statistical techniques to demonstrate process improvement

Model of Knowledge

 * Concept Map
 * Understand and document yield at starting point using statistical techniques
 * Find a better operating point
 * Understand and document yield at new and better operating point using statistical techniques
 * Compare starting and new operating point using statistical techniques

 * Content Priorities
 * Enduring Understanding
 * Using statistical techniques to understand performance measure
 * Using design of experiments to find improved operating point
 * Using statistical techniques to compare data
 * Important to Do and Know
 * Perform graphical analysis of data using appropriate statistical techniques
 * Perform numerical analysis of data using appropriate statistical techniques
 * Perform a response surface methodology design of experiments
 * Worth Being Familiar with
 * Linear regression and mathematical modeling
 * Central composite design
 * Statistical test of hypothesis

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * Identify location and type of stationary point from 3-D graphs
 * Use regression equation to predict response variable values
 * Homework (individual)
 * Pre-lecture quiz after student completes reading assignment
 * Summative Assessment
 * In-class quiz over lesson

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * Predict response variable values using regression output
 * Locate stationary plots by interpreting contour plots and 3-D plots
 * Determine type of stationary plots using contour plots and 3-D plots
 * Utilize second-order polynomial to predict response values
 * Understand stationary points

THE CHALLENGE

Your first job assignment as a new process engineer in a chemical plant is to improve the process yield. A higher yield generates higher profits. The chemical process is very simple and has two controllable factors: reactant flow (flow) and reactor temperature (temp). Improving the process yield is accomplishing by finding a new setting for reactant flow and reactor temperature that provides a higher yield.

Your success in the company, as well as the company’s future success, is dependent upon your ability to improve the process yield and document the improvements that you have made. The use of statistics and statistical analysis will be important in completing this challenge.

GENERATE IDEAS

What method would you propose to find new values for flow and temperature that improve yield? How would your method work if your process had 6 input variables or 8 input variables or 10 input variables?

How can you be sure that you found the best possible new setting?

How can you prove to management that you improved the process?

You can request instructor handouts via [mailto:timmer@utpa.edu%20Instructor%20handout%20request mailto:timmer@utpa.edu Instructor handout request].

MULTIPLE PERSPECTIVES

The goal of improving a process that contains a single output and multiple inputs is challenging. The functional relationship between the inputs and the output must be discovered. This typically involves designing, conducting and analyzing an experiment. An engineer must decide on how experiments to conduct and the settings for each experiment. Once the data is collected it must be analyzed to determine functional relationship between the inputs and outputs and improved settings must be found.

RESEARCH & REVISE

OVERVIEW. A series of short lectures will be presented to provide the details necessary to accomplish the conceptual map given above. Students should be reminded that design of experiments is an advanced analytical technique. In the Manufacturing Engineering curriculum students receive this material in MANE 2332 – Engineering Statistics and MANE 4311 – Quality Control. This problem has been reduced and simplified for a freshman level introduction to engineering course. Students desiring to perform a design of experiments project should seek professional help. Students will be provided a handout containing the lecture slides.

Lecture 1. Descriptive statistics. A recorded lecture will review descriptive statistics. Two key ideas is the use of numerical summaries (e.g. mean, median, mode, etc.) and graphical analysis (histograms, boxplots and dotplots). Include a discussion of sample sizes. Students will use the software package Minitab to calculate numerical summaries and create graphs.

Lecture 2. Data analysis using Minitab. This lecture will introduce students to the web-based application to generate data for their process improvement project. Students will be shown how to use Minitab to perform the analysis and create reports.

Lecture 3. Introduction to Design of Experiments. This lecture will introduce students to design of experiments. The emphasis is on the creation of a response surface methodology model (CCD). This lecture includes a demonstration of using Mintab to create a central composite design.

Lecture 4. Analyzing a CCD. This lecture will introduce students to regression analysis and graphical analysis of a CCD. Since this is a two-factor design the graphical approach is superior. Unfortunately due to time limitations, we will discuss model building and refining regression models that is usually required in problem with more factors. The use of Minitab to analyze a CCD will be included in this lecture.

Lecture 5. Comparing set points. This lecture will present suggestions for comparing the old and new setpoints. The analysis will be limited to descriptive statistics and graphical approaches. The use of Minitab to compare set points will be included in this lecture.

A student website is available at http://quality.engr.utpa.edu/cbi/ProcessImprovementChallenge/

TEST YOUR METTLE

The web-based simulation of the chemical plant can be found at http://quality.engr.utpa.edu/cbiProcessImprovement. Use the simulated chemical plant and your knowledge gained from the Research and Revise section to complete the attached worksheet.

GO PUBLIC

Your instructor will provide instructions for preparing a written report based upon your Test Your Mettle worksheet. Suggested formats are technical reports or Power Point Presentations. Time permitting oral presentations can be given.

Pre-Lesson Quiz

 * 1) What type of stationary point is displayed in the graph below?
 * 1) What type of stationary point is displayed in the graph below?
 * 1) What type of stationary point is displayed in the graph below?
 * 1) What is the predicted value for y when x=5 using the equation shown below?

Test Your Mettle Quiz

 * 1) From the contour plot and surface plot shown above, what type of stationary point is present?
 * 2) From the contour plot and surface plot shown above, what are the values of A and B at the stationary point?
 * 3) What is the predicted value of y from the equation below when A=1 and B=-1?


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UTPA STEM/CBI Courses/Dynamics/The Big Slip

Course Title: Dynamics

Lecture Topic: The Big Slip

Instructor: R.A. Freeman

Institution: UTPA

Backwards Design
Course Objectives
 * To master the fundamental concepts planar particle and rigid-body kinematic and dynamics analysis.
 * To understand that the mathematical models used for analysis are also used for design.
 * To be introduced to math and engineering software for dynamic analysis, simulation, and design of free and constrained planar particle and rigid-body systems.

 * Primary Objectives- By the end of the course students will be able to:
 * Solve for the one-dimensional kinematics of a particle using the basic relationships between position, velocity, acceleration, and time.
 * Solve problems involving the kinematics of one-dimensional constrained motion of particles, with specific application to pulley systems.
 * Describe two-dimensional motion of a particle using cartesian, polar, and path coordinate systems.
 * Convert from one coordinate system to another and solve problems involving a mixture of coordinate systems.
 * Apply the concepts of angular velocity and acceleration, along with the notions of relative velocity and acceleration and the vector cross product, to determine the velocity and acceleration of points fixed in rigid-bodies.
 * Apply the concept of an instant center to determine the velocities of points in single rigid-bodies and of the bodies themselves in constrained rigid-body systems/gear trains/linkages.
 * Determine the position, velocity, and acceleration of points fixed in rigid-bodies that are rolling without slip.
 * Describe the positions, velocities, and accelerations of all members of constrained planar-rigid-body linkages and gear-trains.
 * Determine the relative and absolute velocities and accelerations of independent particles, particles moving within rotating discs, and linkages containing prismatic joints in terms of the application of rotating-reference-frames and the notion of coincident points.
 * Apply Newton’s 2nd Law to obtain the differential equations of motion of free and constrained particles and rigid-bodies in one- and two-dimensions and to solve for forces, moments, and/or accelerations, including situations involving friction.
 * Apply the Work-Energy relationship to obtain the integral velocity-displacement equations of free and constrained particles and rigid-bodies in one- and two-dimensions and to solve for forces, moments, displacements, and/or velocities, including situations involving friction.
 * Apply the Linear and Angular Impulse and Momentum relationships, including Linear Impact, to obtain the integral velocity-time equations of free and constrained particles and rigid-bodies in one- and two-dimensions and to solve for forces, moments, velocities, and/or time, including situations involving friction.
 * Determine if a problem is solvable in terms of the relationship between the number of independent kinematics and kinetics equations available and the number of unknowns.

 * Sub Objectives- The objectives will require that students be able to:
 * Generate position equations using basic geometric and trigonometric relationships
 * Take derivatives of polynomials and trigonometric functions, including applying the chain rule.
 * Integrate polynomials and trigonometric functions.
 * Describe physical quantities (pos., vel., force, torque/moment) in terms of vectors.
 * Determine the magnitude and direction of vectors.
 * Apply the vector dot and cross products.
 * Solve systems of simultaneous linear equations (at least 2 equations in 2 unknowns)
 * Draw Free-Body-Diagrams

 * Difficulties- Students may have difficulty:
 * Drawing correct FBD’s
 * Decomposition of vectors
 * Simple differentiation and integration
 * Simultaneous use of multiple coordinate systems
 * Kinematic description of particles in terms of rotating reference frames
 * Description and determination of work done by forces
 * Determination of velocity as a function of position via work-energy due to integration difficulties
 * Understanding of the definition of angular momentum as the moment of the linear momentum about some point

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Thrill Rides: Roller-Coasters, Bungee Cords, Skydiving
 * Automotive Applications:
 * Particles: Race cars, passenger cars, road design, friction
 * Rigid-Bodies: Drive train / Transmission (Gearing), Steering (Linkages), Suspension (Shock absorbers and natural frequency)
 * Measurement devices: Accelerometers
 * Control devices: Attitude gyroscope
 * Power Tools (Gearing: force-velocity duality or virtual work or power balance)
 * Robotics
 * Biomechanics
 * Pulleys

Model of Knowledge

 * Concept Map

 * Content Priorities
 * Enduring Understanding
 * Basic Kinematic relationships between pos., vel., accel., and time (s, v, a, t)
 * Free-Body-Diagram (FBD): Generation and Interpretation
 * Relative position, velocity, and acceleration (unconstrained and constrained)
 * Coordinate systems: Rectangular/Cartesian, Path/Normal-Tangential, & Polar (Cyl.)
 * Trigonometry (sines, cosines, and tangents)
 * Newton’s 2nd Law
 * Euler’s Equation(s) of Motion
 * Friction

 * Important to Do and Know
 * Work – Energy
 * Impulse – Momentum
 * Impact
 * Instant Centers
 * Power Balance: Force-Velocity Duality
 * Algebra: parametric descriptions
 * Linear Algebra: solution of simultaneous equations
 * Basic Differential and Integral Calculus

 * Worth Being Familiar with
 * Geometry
 * Numerical integration

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * Computer simulations using both math and engineering software
 * Challenge solution presentations
 * Homework (groups)
 * Standard text book homework assigned
 * Challenge solution reports
 * Summative Assessment
 * Exams formulated to assess both Knowledge/Efficiency & Innovation/Transfer
 * Include problems identical to those addressed in class (just change the numbers) as well as those requiring both "near" (similar problem switching knowns and unknowns) and "far" (a totally different question addressable using the same theory) transfer

Legacy Cycle
OBJECTIVE

By the end of the module (2 or 3 class periods), students will be able to:
 * Describe the trajectory of a particle in "free" flight. This will include being able to determine, based on initial conditions, if, when, and how a target can be reached, and the corresponding "terminal" velocity.
 * Use Newton’s 2nd Law to determine the forces acting on a particle sliding down a 2 dimensional path.
 * Identify which forces acting on the particle do work and which do not.
 * Determine the velocity of a particle after it has traveled along a constrained path, including simple paths involving friction, using work-energy.

The objectives will require that students be able to:
 * Describe two-dimensional motion of a particle using cartesian coordinates.
 * Apply Newton’s 2nd Law to obtain the differential equations of motion of free and constrained particles in two-dimensions and to solve for forces, and/or accelerations, including situations involving friction.
 * Apply the Work-Energy relationship to obtain the integral velocity-displacement equations of free and constrained particles in one- and two-dimensions and to solve for forces, displacements, and/or velocities, including situations involving friction.

THE CHALLENGE Do you believe the big slip video is real? Make an argument in support of your conclusion.

Big Slip

GENERATE IDEAS

The class is asked what they believe is important to know or do in able to answer the challenge. It is expected that they will list:
 * Slide geometry
 * Slide friction
 * Ramp angle
 * Height and distance from ramp to pool
 * Velocity when leaving the ramp
 * Persons weight

MULTIPLE PERSPECTIVES

One could get other expert opinions but I usually serve as the expert. I generally point out that the problem can be broken into two phases of motion; one on the slide analyzed primarily using Work-Energy (especially if friction is assumed negligible), and one in the air analyzed as a particle ballistics problem. Various computer simulations are used to illustrate the effect of the different parameters including;Slide geometry, slide friction, ramp angle, height and distance from ramp to pool,velocity when leaving the ramp, persons weight, etc.

MP Simulations

RESEARCH & REVISE

The students are provided with "lecture notes" covering Newton's 2nd law, Work-Energy, and 1-D Friction. They are also provided with numerous solved problems illustrating the covered concepts.

R&R Notes, Examples,& Simulations

TEST YOUR METTLE

They are given textbook problems in the area of work-energy of particles, ballistics of particles, and mixed work-energy/ballistics problems. A nice example of the mixed problem involves a carnival game where a spring operated plunger shots a nickel up an incline, into the air, and (hopefully) into a cup. A computer simulation of this problem is also provided. TYM Simulations

GO PUBLIC

Each group (typically 2 students) is required to write a report addressing the challenge that is turned in to the instrutor. They are also required to create a presentation of their investigation that they may have to give to the class. I generally only have time for a couple of groups per challenge to present. The following is a simple grade sheet that I use for the challenge investigation/solution.

Big Slip Grade Sheet
 * Need estimates of:
 * Slide Geometry (Δh)
 * Slide friction
 * Ramp angle
 * Ballistic Geometry (Δx and Δy)
 * Flight time Δt (I measured it to be 2 seconds)
 * Need to calculate:
 * Vo from Work-Energy
 * Δx and Δy
 * Need to compare assumptions and calculations and conclude.

Pre-Lesson Quiz
PrePost questions

Test Your Mettle Quiz
PrePost questions


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UTPA STEM/CBI Courses/Statics/Truss Bridge

Course Title: Introduction to Mechanical Engineering

Lecture Topic: Statics / Truss Bridge

Instructor: Drs. Arturo A. Fuentes and Horacio Vazquez

Institution: UTPA

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Explain some aspects of the engineering design process
 * Understand and explain the concept of tension/compression
 * Understand the design of a truss bridge
 * Design and construct prototypes
 * Function in diverse teams
 * Document results and conclusions

 * Sub Objectives- The objectives will require that students be able to:
 * Understand brainstorm process
 * Understand and use basic engineering instrumentation and software
 * Understand and use engineering data presentation tools (graphs and tables)
 * Understand and use dimensions and units
 * Perform unit conversions

 * Difficulties- Students may have difficulty:
 * Understanding the concepts of tension and compression. They usually benefit from reviewing and practicing concepts related to the engineering design process and teamwork skills in a real engineering context.

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Introducing mechanics fundamentals to students early on in their careers allows them to connect their current knowledge to engineering applications. The mechanics knowledge gained provides a foundation and motivation to many courses in the mechanical, civil, and industrial engineering curriculum.

Model of Knowledge

 * Concept Map
 * Engineering Design Process
 * Role of Prototype/model testing and validation
 * Truss Bridge
 * Tension
 * Compression
 * Prototype Construction and Instrumentation
 * Teamwork Skills
 * Brainstorm skills
 * Engineering Documentation

 * Content Priorities
 * Enduring Understanding
 * Tension and Compression concepts, units, dimensions, unit conversion
 * Important to Do and Know
 * Teamwork Skills
 * Worth Being Familiar with
 * Software and instrumentation

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * Worksheet
 * Homework (individual)
 * Report
 * Quiz
 * Summative Assessment
 * Exam

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * Calculate tension or compression in different truss members
 * Design and construct a prototype truss bridge
 * Brainstorm multiple truss bridge designs
 * Evaluate the bridge designs in order to determine the best design

THE CHALLENGE

Your company’s bridge has failed and it is your job as the new design engineer to determine what could have caused the failure of the bridge and, as much as possible, defend the company.

GENERATE IDEAS

Your supervisor tells you that he will meet with you shortly to hear your initial thoughts, to share some information that might be useful, and to answer any questions that you might have. The information that you will provide will be used as testimony by the company in a court of law. Students will begin to brainstorm alone for a period of 5 minutes. They will then continue brainstorming with each other and share ideas for the next 10 minutes. [Ideally, groups will be of size 4 and different group members will be in charge of certain aspects of keeping the group in order]

MULTIPLE PERSPECTIVES

Different cases scenarios including overload, accidents, natural disasters, design errors, manufacturing errors, material quality issues, etc. Instructors will inform the students that during that day a truck skipped the weight station checkpoint. Also they will receive information about the maximum load permissible on the bridge members. Experts will also begin to present ideas behind models and their importance in real life applications.

RESEARCH & REVISE

The instructor will show a truss bridge presentation. The instructor will then show a presentation covering tension vs. compression in structural elements. A lecture over tension/compression will be presented which will include the effects of weight (force) on the member’s behavior. Having this information at hand the students will be supplied with Pasco equipment. Related to this topic, they will be free to use the equipment as they see fit. An illustration showing their bridge before failure will be provided to them.

TEST YOUR METTLE

Determine how much load (and type of load: tension or compression) is transferred to each member of the truss bridge structure when loads are placed at key points in the structure. A handout which asks the students to identify if a member is in compression or tension will be provided. Students will be asked to work on the handout individually and turn in at the end of 10 minutes or the professor's allotted time.

GO PUBLIC

Online Report:

Students will share their findings and possible challenge solution with the other group. Having shared what they thought could have caused the bridge to fail, they will return to their formal groups to finalize their solution, and turn it in to the instructor.


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UTPA STEM/CBI Courses/Computer Architecture/CPU Design

Course Title: Computer Architecture

Lecture Topic: CPU Design

Instructor: Yang Liu

Institution: University of Texas-Pan American

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Design a simple CPU to execute instructions

 * Sub Objectives- The objectives will require that students be able to:
 * Operate various components such as register files, memory, ALU, control, etc.
 * Implmenet data path and control path

 * Difficulties- Students may have difficulty:
 * Interaction between data path and control path
 * Timing among different components

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * CPU design engieer on Linkedin: http://www.linkedin.com/title/cpu+design+engineer/
 * Apple to expand CPU design group beyond iPad A4: http://www.appleinsider.com/articles/10/12/31/apple_to_expand_cpu_design_group_beyond_ipad_a4.html
 * News on NVIDIA' project of high performance CPU: http://www.anandtech.com/show/4099/nvidias-project-denver-nv-designed-high-performance-arm-core
 * Design and construction of simple CPU: http://cpuville.com/design.htm

Model of Knowledge

 * Concept Map
 * Data path
 * Register file
 * ALU
 * memory
 * Control path
 * Control
 * ALU control
 * Execution of instruction

 * Content Priorities
 * Enduring Understanding
 * CPU needs both data path and control path to execute instructions***
 * Important to Do and Know
 * issues for actual circuit implementation such as clocking methodology
 * Worth Being Familiar with
 * Much more complications in real word product CPU
 * Relationship between CPU design and instruction set

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * Exercise on how each component works
 * Exercise on how an instruction is executed on the data path and control path
 * Homework (individual)
 * calcuate the critical path for given delays of components
 * Summative Assessment
 * Write a simulator of a simple CPU

Legacy Cycle
OBJECTIVE By the next class period, students will be able to: The objectives will require that students be able to:
 * Design a simple CPU to execute instructions
 * Operate various components such as register files, memory, ALU, control, etc.
 * Implmenet data path and control path

THE CHALLENGE IPAD is a sucessful product of Apple. Apple decides to hire new engineers to design a new CPU for next generation of IPAD. You are hired after your graduation. Show the link to the news on Apple: http://www.appleinsider.com/articles/10/12/31/apple_to_expand_cpu_design_group_beyond_ipad_a4.html

How do you design a CPU for that purpose?

GENERATE IDEAS
 * Students discuss in pair what are needed inside a CPU
 * Students talk about the tools needed to design CPU if they know any

MULTIPLE PERSPECTIVES
 * Show the link to design and construction of simple CPU: http://cpuville.com/design.htm
 * Show the link to Application-Customized CPU: http://www.ibm.com/developerworks/power/library/pa-fpfxbox/?ca=dgr-lnxw07XBoxDesign

RESEARCH & REVISE
 * Students should know there are various components inside a CPU
 * Students discuss how to use various components in a CPU
 * Lectures on data path and control path is given
 * Students search more information from Internet on CPU

TEST YOUR METTLE
 * In-class exercises.

GO PUBLIC
 * Complete the simulator project

Pre-Lesson Quiz

 * 1) CPU only needs to read, process, and write data. Is this claim correct or not? Why or why not?

Test Your Mettle Quiz

 * 1) Assume register i holds integer value i. (a) if rr1=5, rr2=12, wr=6, wd=-1, and regWrite=0, what happens after accessing the register file(including output and any other changes)? (b) if rr1=5, rr2=12, wr=6, wd=-1, and regWrite=1, what happens after accessing the register file(including output and any other changes)? (c) if rr1=5, rr2=12, wr=5, wd=-1, and regWrite=0, what happens after accessing the register file(including output and any other changes)?
 * 2) (a) What does regDst=1 and regWrite=1 mean for R-format instructions? (b) Why are ALUsrc=1, memToReg=1, regWrite=1 and memRead=1 for lw instruciton? (c) Why do the values of regDst and memToReg not matter for beq instruction?
 * 3) Show the execution and critical path of instruction "add $s0, $s1, $s2" with given component delays.


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Talk:UTPA STEM/CBI Courses/Aquatic Entomology/Understanding Populations

Article Review
comment--Jmaustin 16:38, 25 September 2010 (UTC)

This is a well thought out CBI challenge that hits upon all elements of the learning cycle. It includes both pre and post quizes as a means for formative feedback. The challenge is one students should have no problem relating to real world situations, and should seed discussion amongs students. Overall great design, it may be useful to ask what if questions presenting scenarios based on the challenge question to stimulate futher group discussion.


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Talk:UTPA STEM/CBI Courses/Materials/Material Properties

article review
Comment I like very much the developed class on Materials Properties. My suggestion is to attach pictures of nanostructures, more visual explanation would be beneficial to this class. --129.113.174.134 16:40, 25 September 2010 (UTC)


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Talk:UTPA STEM/CBI Courses/Molecular Structure

article review
Your CBI posting on Molecular Structure for CHEM 1301 is very good. I have some comments below that you might consider to make the posting more complete or more helpful.

Course Objectives: Understanding various geometries might read better, Recognizing various geometries.

Sub Objectives: Draw Lewis structures and use the structures to determine electron domain geometries about a central atom.

Difficulties: maybe add recognizing shapes

Important to Do and Know: A knowledge of the Periodic Table and of the number of valence electrons that must be used for each element would be helpful. Also, students knowing the Rule of 8/Rule of 2 (for hydrogen) would be fundamental.

Summative Assessment: 1)  Writing correct Lewis dot diagrams for molecules or ions.  2)  Predict structures from Lewis dot diagram provided. 3) Draw Lewis dot diagram for a given molecule or ion and from the diagram, predict the structure of the molecule/ion using the VSEPR table.


text:
Talk:UTPA STEM/CBI Courses/Computer Science/Algorithm Design

Article review
This looks good. In the past, I have seen students have difficulty understanding the concept of recursion, so I think that presenting a few additional simple examples (such as computing an element of the Fibonacci sequence or a factorial) might be useful.


text:
Talk:UTPA STEM/CBI Courses/Circuits/Laplace Transform

Article Review
Real-World Context Examples: Audio System


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Talk:UTPA STEM/CBI Courses/Calculus/Inverse Trigonometric Functions

Article Review

 * During the 'research and revise' and then later during the 'test your mettle' and 'go public' portions you might ask the additional question(s): (a) how would your answer change if the screen was taller?  (b) how would the method change if the floor of the theatre was sloping upwards? (c) how would our answer change if the screen was angled downwards?  These questions could be given as a homework or a further discussion portion.

 * A further application which is directly related to the challenge question is the idea of perspective and how 3D objects are rendered in 2D.

 * A challenge question that could precede this one in the course would be to explain at what position a keystone corrector should be set for a video projection system. One could then revisit this question here by asking if the keystone corrector has changed the optimal viewing location we should use.

 * Time permitting students could experiment with their group: viewing a figure on the wall from different positions. The group could use pieces of string to demonstrate the rays -- I think this kind of hands on activity would more effectively engage students in finding methods to solve the problem analytically further in the cycle.

--Virgilpierce 16:46, 25 September 2010 (UTC)


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Talk:UTPA STEM/CBI Courses/Quantum Mechanics/Particles and Waves

article review
I think the design of this CBI course is very well planned. The main concept in quantum mechanics is to understand the difference between particle and wave. By listing in the objectives to understand the difference between wave and particles is really following backwards design. Anticipating the difficulties the students may encounter is a good idea to think how to address them since the beginning. The objectives are clearly identified; however, you didnt include a challenge question. Under challenge you just wrote better understanding of the fundamental of quantum mechanics. I thik according to the legacy cycle you need to include a challenge question in here. The you tube video is excellent for multiple persepectives, it will put everybody on the same page. The last think the course is lacking i think is the research and revise section from the legacy cycle. Overall I think it is a great application of the CBI.


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Talk:UTPA STEM/CBI Courses/Probability and Statistics/Binomial Distribution (Dr. Yanev)

Binomial Review
The author of this lecture has nicely and elaborately covered all aspects of Challenge Based Instruction.

In this review, I will go into each and every aspect and leave some comment.

In Backward Design part, Dr. Yanev has rightly pointed out that the students have to be acquainted with the binomial table for calculation of probabilities. But since the table has its own limitations, the students should also learn to use calculator to calculate them. It is also important for the students to realize that the binomial distribution arises from repeated trial experiment like coin tossing experiment and similar experiments. In sub objectives part, one has to mention that the students should have the idea of factorials and combinations to understand binomial probabilities. The difficulty part has been very nicely. Indeed, the students face difficulty in identifying a problem as a binomial problem. In real world context, one can add some examples like, passing and failing in test, hitting or missing a target, winning or losing a race/bet/draw etc.

In Model of Knowledge part, little bit of elaboration is needed as far as the concept map and concept priorities are concerned.

In the Legacy Cycle part, the General ideas part is to be addressed with care. How do students connect random variables to the challenge question is not clear. Students should already have a background on discrete random variables. Other parts in the legacy cycle have been addresses nicely.

Overall, it is a nice lesson plan by Dr. Yanev.--Schakraborty 16:54, 25 September 2010 (UTC)

Article Review
Overall very nice start. I would strength the potential applications of the binomial distribution because there are so many. I work in the quality area and many inspection problems can be modeled by the binomial distribution. From the wiki-page it is hard to determine the connection between the Bernoulli distribution and the binomial distribution. If if you are teaching in a BlackBoard environment, I have test banks of binomial probability questions that could be incorporated into assessments that I would share with you.


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Talk:UTPA STEM/CBI Courses/Introduction to VLSI

Article Review
Formative Assessment may include some feedbacks from the student discussion.


text:
Talk:UTPA STEM/CBI Courses/Mechatronics/Basic Electronics

Article Review
Under the Formative Assessment the group activites are great. Is the lab work done in groups also?

Really like the challenge question.--Eadame 16:55, 25 September 2010 (UTC)


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Talk:UTPA STEM/CBI Courses/Nutrition/Enzymes

Article Review
Hello Mrs. Teter, The challege you have posed is very unique and interesting. I have a couple of suggestions that may clear up a segment under the model of knowledge in content priorities. There is a section that states, Important to Do and Know you wrote, "Now protein can be denatured". Did you mean Know proteins can be denatured or Did you mean How proteins can be denatured? The other suggestion is to add quantaties and maybe a time factor. For example, the pineapples how much to use and for how long to bake the pineapples, since concentration and time tends to be a factor when looking at enzymes. I am actually interested in your answers to the previous questions since I would like to use it in my biology 1408 course.

Thanks and Great Application of CBI.


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Talk:UTPA STEM/CBI Courses/Calculus Based Physics

Article review
Comments: I would like to see you address the following remarks for motion in one dimension: 1. Include the difference between speed and velocity. 2. Limit the second part of the primary objectives to knowledge of differentiating and integrating with respect to time. 3. Include the difference between instantanous and average speed 4. For Real-World contexts, It will be nice to include a terminal speed for a sky diver.


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UTPA STEM/CBI Courses/Cancer Biology

Course Title: Cell Biology

Lecture Topic: Cell Signalling pathways in Cancer

Instructor: Jonathan Lieman

Institution: University of Texas Pan American

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Identify important genes that are commonly disrupted in tumorgenesis
 * Identify the relationship between genes and their role in regulation of the cell cycle
 * Identify key events in tumorgenesis

 * Sub Objectives- The objectives will require that students be able to:
 * Understand the importance of the Rb/E2F Pathway in tumorgenesis
 * Know the relationship and importance between cell proliferation and cell death in the cell

 * Difficulties- Students may have difficulty:
 * Understanding that genes that also control cell proliferation may also control cell death
 * Understanding the relationship between a diverse array of signaling pathways

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Understanding how drugs target tumors
 * Understand how mutations in key genes can lead to cancer

Model of Knowledge

 * Concept Map
 * Control of cell proliferation and cell death in tumorgenesis
 * The Rb/E2F Pathway
 * Tumor suppressor proteins
 * Rb
 * p53
 * p21
 * P16
 * Control over cell proliferation
 * Control over apoptosis
 * Intrinsic Apoptotic Pathways
 * Extrinsic Apoptotic Pathways
 * Integrins, Cytokines, growth factors
 * Receptors
 * Cell Signaling
 * Ras Map Kinase Pathway
 * Cyclin/Cdk activity

 * Content Priorities
 * Enduring Understanding
 * How is the cell cycle controlled
 * What is the relationship in the cell cycle between cell Proliferation and cell death
 * How does a single cell progress into a tumor
 * Important to Do and Know
 * What is a tumor suppressor gene? What are some important ones?
 * What is an oncogene? What are some important ones?
 * The cell cycle

 * Worth Being Familiar with
 * Knudson's two hit Hypothesis
 * The intrinsic and extrinsic apoptotic pathways

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * Group based problem discussion
 * Identify problems and present group findings to class
 * Homework (individual)
 * Reading of journal articles
 * Summative Assessment
 * In class exam

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * Identify the importance of the Rb/E2F pathway in cancer
 * Identify major signaling pathways and how they feed into the Rb/E2F pathway
 * Identify mechanisms the cell has to prevent tumors from developing

THE CHALLENGE

You are a cell. What challenges must you overcome to become a tumor? Be sure to mention key genes and signaling pathways, and obstacles you need to develop mutations within in order to achieve these lofty goals. Alternatively you are a drug developer. What specific characteristics or mutations found in tumors cells can you target to destroy them?

GENERATE IDEAS

Students will discuss in groups commonly mutated genes found in cancer cells as well as the consequences of these mutations.

MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

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Pre-Lesson Quiz
Various material can be tested here, depending on time constraints.

Test Your Mettle Quiz
Various material can be tested here, depending on time constraints.

title: UTPA STEM/CBI Courses/Cancer Biology


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Talk:UTPA STEM/CBI Courses/Measurements and Instrumentation/Temperature Measurement

This work was designed very well based on CBI format. It has all 6 steps of legacy cycles in a clear manner. I like the challenge question about when you have fever and put a thermoset in your mouth. Most of the students have experienced this situation in real life and maybe think about it before. The designed topic can be a very good examplar of how to design a course in CBI format.--129.113.174.113 17:01, 25 September 2010 (UTC)


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Talk:UTPA STEM/CBI Courses/Biology/Blood Circulation

Blood Circulation CBI Project Review
The challenge is appropriate and applicable at the freshman level. The students will definately be able to imangine themselves in this situation. My critique is primarily technical in nature.

Course Objectives

Comment 1: Switch primary and Sub objectives, the primary objectives should be more general and the sub objectives should be the supporting ideas. Comment 2: Maybe include some comparison with non mammalian organisms...May be too broad, just an idea. Comment 3: Under difficulties you may want to add what about basic circulatory system anatomy they will struggle with. I.e. vocab., flow of blood through the heart, which vessels carry oxigenated blood and which carry deoxigenated, function of valves, etc. My students always struggle with understanding the sequence of contractions (atria then ventricles) and how that relates to the the opening and closing of the valves and why. Coronary circulation may also be important here because they will need that to make their "diagnosis". Comment 4: Sorry out of time...taking CBI workshop.


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Talk:UTPA STEM/CBI Courses/Statics/Force Equilibrium

General comments
Comment: very good work along the CBI method. All items are well written and oranized. Intersting challenge question. It is very related with the force equilibrium. I am not quite understand about the knowledge checks - why 3 different of the checks are? --Jungseokho 17:03, 25 September 2010 (UTC)


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UTPA STEM/CBI Courses/Assembly Programming/Exception Handling

Course Title: Assembly Programming

Lecture Topic: Exception Handling

Instructor: Matt Patitz

Institution: UTPA

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Understand and modify an exception handler

 * Sub Objectives- The objectives will require that students be able to:
 * Debug by stepping into assembly code
 * Understand the basic mechanisms of exception handling
 * Know assembly language syntax and register usage conventions

 * Difficulties- Students may have difficulty:
 * Setting up the development environment
 * Ensuring that there are no unintended side-effects from the exception handler

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Understand the effects of errors in code

Model of Knowledge

 * Concept Map
 * System architecture
 * System components
 * Processor
 * ALU
 * Control
 * Register
 * Interconnects
 * Memory
 * System bus
 * I/O systems
 * Assembly programming
 * General syntax
 * Register conventions
 * Procedure calls and stack frames
 * Interface between OS and hardware
 * Exception handling

 * Content Priorities
 * Enduring Understanding
 * High level understanding of how exceptions are handled by the OS and hardware

 * Important to Do and Know
 * Debug mixed C and assembly language applications

 * Worth Being Familiar with
 * Specific registers containing exception information
 * Syntax of assembly language

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * Find and characterize errors code which will raise exceptions
 * Discuss modifications of exception handler and their impact on the system

 * Homework (individual)
 * Perform a programming project to modify the exception handler to handle a memory access error

 * Summative Assessment
 * Exam questions giving snippets of an exception handler in which students must correctly identify bugs and complete missing sections

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to:
 * Understand and modify an exception handler

The objectives will require that students be able to:
 * Debug by stepping into assembly code
 * Understand the basic mechanisms of exception handling
 * Know assembly language syntax and register usage conventions

THE CHALLENGE

You are the system administrator of a critical university system. Unfortunately, as a measure to save money, the university has hired several freshman programmers who haven't even completed Computer Science I to code new modules. How can you protect your system from the frequent crashes caused by the many errors introduced by these programmers?

GENERATE IDEAS

Have students come up with several examples of C++ code which would raise exceptions.

MULTIPLE PERSPECTIVES

As a class, discuss the examples that were generated. Pick two exception types and discuss how the OS could most gracefully handle them. Look at an incomplete exception handler and analyze its behavior.

RESEARCH & REVISE

In groups, students write a C++ code which raises the two types of exceptions selected. Then they practice executing it and debugging by stepping into the exception handler. Next, they implement the exception handling routines decided upon by the class.

TEST YOUR METTLE

Students are given feedback on their code, then a quiz which presents a new type of exception which they should be able to write a code to handle it in a specified way.

GO PUBLIC

Exam questions giving snippets of an exception handler in which students must correctly identify bugs and complete missing sections.

Pre-Lesson Quiz

 * 1) What are three possible causes of exceptions generated by C++ code?
 * 2) What mechanism is in place to handle these exceptions?

Test Your Mettle Quiz

 * 1) How many exceptions would be raised by a given piece of code?
 * 2) Which registers will contain information relevant to the exception when the exception handler begins execution?
 * 3) Fill in some missing code for proper handling of a particular type of exception.


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Talk:UTPA STEM/CBI Courses/Computer Science/Selection

Article Review
This is an excellent lesson plan. I especially like the generate ideas activity. Playing rock-paper-scissors is a fun, hands-on activity. By playing against each other the community aspect of learning is used. This activity allows the students to observe their own decision making and to think about why they are making their decisions.


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Talk:UTPA STEM/CBI Courses/Introduction to Mechanical Engineering/Engineering Estimation

Very good challenge of the Legacy. There are rooms to improve, but good start and organized.--Jungseokho 17:08, 25 September 2010 (UTC)


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UTPA STEM/CBI Courses/Anatomy and Physiology/Endocrine Imbalance

Course Title: Anatomy and Physiology

Lecture Topic: Endocrine System

Instructor: Bonnie Gunn

Institution:The University of Texas Pan American

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Describe negative and positive feedback mechanisms.
 * Explain the importance of homeostatic mechanisms.
 * Explain the significance of homeostatic imbalance.

 * Sub Objectives- The objectives will require that students be able to:
 * Define homeostasis.
 * Identify normal ranges in the body.
 * Identify causes of imbalance.
 * Describe hormone function.
 * Correlate homeostasis to endocrine function.

 * Difficulties- Students may have difficulty:
 * Describing the relationship between endocrine function and feedback systems.
 * Determining the interaction between endocrine function and the nervous system.
 * Identifying endocrine control by and on nonendocrine organs.
 * Tracing secondary signaling mechanisms.

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Treatment and complications of endocrine disorders such as diabetes.
 * Predicting side effects of misused synthetic hormones.
 * Understanding use of steroids in various illnesses.

Model of Knowledge

 * Concept Map
 * Homeostatis
 * Positive and negative feedback systems
 * Endocrine Control of homeostasis
 * Nervous system interatcion with the endocrine system
 * Hypothalamus
 * Nervous system function
 * Endocrine function
 * Pituitary Gland
 * Master gland
 * Infundibulum
 * Nervous system control of
 * Hormonal control of
 * Pituitary hormones and their effects on various organs
 * Hormonal imbalance
 * Causes
 * Diseases

 * Content Priorities
 * Enduring Understanding
 * The human body must remain in homeostasis.
 * Homeostatic imbalance causes disease.
 * Negative feedback mechanisms prevent homeostatic imbalance.
 * The endocrine system contributes to homeostasis.

 * Important to Do and Know
 * Endocrine organs secrete hormones
 * Many nonendocrine organs secrete hormones.
 * Diagram negative feedback.

 * Worth Being Familiar with
 * Chemical structure of hormones
 * Permeability of cellular membranes
 * Secondary messenger systems

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * "Clicker" questions in class
 * text
 * Homework (individual)
 * text
 * text
 * Summative Assessment
 * text
 * text

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * text
 * text
 * text
 * text
 * text
 * text

THE CHALLENGE Your mom's sister isn't feeling well. She is always tired and thirsty. When you went to San Antonio with her last weekend she stopped to use the bathroom 3 times. You also noticed her breath smells like pancake syrup. What endocrine homeostatic imbalance might cause these symptoms? What other symptoms would you look for to confirm your suspicions?

GENERATE IDEAS

text

MULTIPLE PERSPECTIVES

text

RESEARCH & REVISE

text

TEST YOUR METTLE

text

GO PUBLIC

text

Pre-Lesson Quiz
Various material can be tested here, depending on time constraints.

Test Your Mettle Quiz
Various material can be tested here, depending on time constraints.