Preparation Problems#
Complete all preparation problems before class time on the scheduled date.
Week 15#
Day 15A: Monday, December 4th
No prep problem for today.
Day 15B: Wednesday, December 6th
No prep problem for today.
Day 15C: Friday, December 8th
Posted aftert Wednesday’s class.
Week 14#
Day 14A: Monday, November 27th
Evaluate the line integral where \(\int_{C}\vec{F}\cdot d\vec{r}\) where:
\(\vec{F}(x,y)=\langle -y, x \rangle \)
\(C\) is the curve with parametrization \(\vec{r}(t)=\langle 3\cos t, 3 \sin t \rangle \) and \(0 \leq t \leq\pi\)
Day 14B: Wednesday, November 29th
Evaluate the line integral where \(\int_{C}\vec{F}\cdot d\vec{r}\) where:
\(\vec{F}(x,y)=\langle 2xy^2, 2x^2y \rangle \)
\(C\) is the curve with parametrization \(\vec{r}(t)=\langle 3\cos t, 3 \sin t \rangle \) and \(0 \leq t \leq\pi /2\)
Day 14C: Friday, December 1st
No prep problem for today.
Week 13#
Day 13A: Monday, November 20th
Evaluate the following line integral where \(C\) is the line segment from \((2,1)\) to \((4,-3)\)
Day 13B: Wednesday, November 22nd
Thanksgiving Recess. No preparation for today.
Day 13C: Friday, November 24th
Thanksgiving Recess. No preparation for today.
Week 12#
Day 12A: Monday, November 13th
Plot the vectors for the vector plane \(\langle x+2, y \rangle \) at the points listed below:
\((0,0)\)
\((2,0)\)
\((0,2)\)
\((2,2)\)
Plot these on a single \(xy\)-plane. Use a straight edge to help with your sketch (neatness counts).
Day 12B: Wednesday, November 15th
Calculate the curl and the divergence of the vector field \(\vec{F}=\langle x^2, y^2, z^2 \rangle \)
Day 12C: Friday, November 17th
Find a potential function for the vector field:
Week 11#
Day 11A: Monday, November 6th
No prep problem for today.
Day 11B: Wednesday, November 8th
Calculate the following triple integral by converting to cylindrical coordinates:
Day 11C: Friday, November 10th
Convert the following points:
Spherical to Cartesian: \(\left( 5, \dfrac{-\pi}{2}, \dfrac{\pi}{2} \right)\)
Cartesian to Spherical: \(\left( -4, 0, 4 \right)\)
Week 10#
Day 10A: Monday, October 30th
No prep problem assigned for today.
Day 10B: Wednesday, November 1st
Find the volume of the solid bounded by the planes \(y=0\), \(z=0\), and the paraboloid \(z=4-x^2-y^2\).
Day 10C: Friday, November 3rd
Calculate the following triple integral where \(B=[1,2]\times[0,4]\times[0,1]\)
Week 9#
Day 9A: Monday, October 23rd
Calculate the following double integral where \(D = \{ (x,y) | -2\leq x \leq 2, \quad -x^2\leq y \leq x^2+1 \}\)
Day 9B: Wednesday, October 25th
Describe the following regions of the \(xy\)-plane as a Type 1 region using two inequalities. Sketch the region.
Region bounded between \(x=0\), \(x=5\), \(y=4x\) and \(y=1-x^2\)
Region bounded between \(y=x^2+1\) and \(y=5-x^2\)
Region bounded by \(x^2+y^2=4\)
Day 9C: Friday, October 27th
No prep problem for today.
Week 8#
Day 8A: Monday, October 16th
Find and classify the critical point(s) of the following function:
Day 8B: Wednesday, October 18th
Find the extreme values of the function \(f(x,y)=4x^2+y^2\) on the circle \(x^2+y^2=1\).
Day 8C: Friday, October 20th
Calculate the iterated integral:
Week 7#
Day 7A: Monday, October 9th
No preparation problem assigned for today.
Day 7B: Wednesday, October 11th
Calculate the directional derivative of \(f(x,y)=5x^4-3xy^2\) where the unit vector is given by the following angles:
\(\theta = \pi\)
\(\theta = \pi/4\)
\(\theta = \pi/3\)
Day 7C: Friday, October 13th
Find the critical point(s) for the following function:
Week 6#
Day 6A: Monday, October 2nd
No preparation problem assigned for today.
Day 6B: Wednesday, October 4th
Find the equation of the plane tangent to the surface \(z=3x^2+4y^2\) at the point \(P(1,-1,7)\).
Day 6C: Friday, October 6th
Find \(\dfrac{dz}{dt}\) when \(t=0\) for:
where \(x=4\cos (2t)\) and \(y=4 \sin (2t)\).
Week 5#
Day 5A: Monday, September 25th
Find and sketch the domain of the following functions:
\(f(x,y)=\sqrt{y-3x}\)
\(g(x,y)=\dfrac{5}{y-x^2}\)
Day 5B: Wednesday, September 27th
Organize and bring all of your completed notes, problems, and papers with you to class.
Day 5C: Friday, September 29th
Study for Midterm Exam 1
Week 4#
Day 4A: Monday, September 18th
No problem assigned for today.
Day 4B: Wednesday, September 20th
Calculate the TNB-frame for the following curve:
Day 4C: Friday, September 22nd
A moving particle starts at an initial position \(\vec{r}(0)=\lange 3,2,1\rangle\) and initial velocity \(\vec{v}(0)=\langle 0,1,-2\rangle\). Find the position function \(\vec{r}(t)\) given the acceleration:
Week 3#
Day 3A: Monday, September 11th
V6: Find a linear equation for the plane that passes through the points \(P(2,0,1)\), \(Q(0,1,3)\), \(R(1,2,0)\).
Day 3B: Wednesday, September 13th
Find the domain of the vector function \(\vec{r}(t)= \langle \sqrt{1-t^2}, t^2, \ln(t) \rangle\).
Find the parametric equations for the line of intersection between the planes \(2x-y+3z=5\) and \(x+y-2z = 8\). (We did an example of this during class on Monday.)
Day 3C: Friday, September 15th
Find the arc length of the section of the circular helix given by
from the point \((0,0,2)\) to the point \((2,2\pi,0)\).
Week 2#
Day 2A: Monday, September 4th
No preparation problems assigned for today.
Day 2B: Wednesday, September 6th
V4: Calculate the cross product \(\vec{a} \times \vec{b}\) of the following vectors: \( \vec{a}=\langle 2, 0, 1 \rangle \qquad \vec{b} = \langle 0, 2, 2 \rangle \)
V4: Find a unit vector orthogonal to both of the following vectors: \( \vec{a}=\langle 1, 0, 3 \rangle \qquad \vec{b} = \langle -1, 2, 1 \rangle \)
Day 2C: Friday, September 8th
V5: Find parametric and symmetric equations for the line that passes through the points \(A(0,4,5)\) and \(B(-2,1,-1)\)
Week 1#
Day 1A: Monday, August 28th
No preparation problems assigned for today.
Day 1B: Wednesday, August 30th
Sketch the graph of the surface in \(\mathbf{R}^3\) given by the equation \(x=3\). On this graph, plot the points \((3,2,3)\) and \((3,2,-2)\)
Day 1C: Friday, September 1st
V3: Calculate the dot product \(\vec{a} \cdot \vec{b}\) of the following vectors: \( \vec{a}=\langle 2, -3 \rangle \qquad \vec{b} = \langle 0, 4 \rangle \)
V3: Calculate the dot product \(\vec{a} \cdot \vec{b}\) of the following vectors: \( \vec{a}=\langle 1, 9, 3 \rangle \qquad \vec{b} = \langle -4, 2, 3 \rangle \)
Show all work for these problems, do not just write the answer.