Homework Assignments for Math 226

Prof. Jill Dietz
Fall '99

Date 

In Class 

Assignment

Due Date

What's Next? 
What we did today.  Homework based on today's lecture. Due at 12:55pm. Read this in the book and think about the questions. 
Fri. 9/10 Intro and graphing in 3d 1.1/1,3,4,5,7,17,24,25,26 Wed. 9/15 Sections 1.1 and 1.2 
  1. Let P=(1,2,3) and Q=(2,4,6). Find the distance b/w P and Q and find the midpoint of the line segment joining them. 
  2. In ex. 1 of section 2, where is the curve at time t=-1? 
  3. Find a parametrization of the line y=-2x+6 in the first quadrant. 
  4. Find a parametrization of the circle with center (1,2) and radius 3.
Mon. 9/13 Parametrizations 1.2/1,3,4,6,7,8,10,11,13,14 Fri. 9/17 Section 1.3 
  1. In ex. 1, is the ant going faster at x=1 or x=3? 
  2. Compare your velocity vectors if you run along a curve vs. walk along it. 
  3. The vector pointing from (-1,2) to (2,3) is equivalent to which of the three vectors shown on page 30? 
  4. Write the vector pointing from (1,2,3) to (2,4,6) as a linear combination of the three standard basis vectors i, j, and k. 
Wed. 9/15 Polar coor's and vectors
  • Appendix A/ 1,6,13,16 (for these four, find one pair only), 
  • App. A/ 29,44,55,63-66 (do these seven for fun only) 
  • App. A/58,59 
  • section 1.3/ 1,5,7,9,10
 Mon 9/20 Section 1.4 
  1. Use the ideas on page 40 to find a parametrization of the line through (1,2,3) in the direction of (2,0,-1) 
  2. In example 2, what is the fly's position at time t=pi? what direction is it flying in? and what is its speed?
  3.  Let g(t)=(e^t,t^5), find g'(t) and an anti-derivative of g.
Fri 9/17 section 1.4
  1. Let p(t)=(t^3+2t-1,7t,sin(5t)) give your position at time t. Where are you at time t=3? What direction are you pointing at that time? How fast are you going at that time?
  2. Find a parametrization of the line through (1,2,3) pointing in the direction of the basis vector j.
  3.  Find a parametrization of the line segment starting at (1,2,3), pointing in the direction of (-3,1,2) and having length 10.
  4. A missile is fired at an angle of 45 degrees at a speed of 1000 feet per second. What is the missile's horizontal displacement after 20 seconds? What about its vertical displacement? How fast is it going at t=20 and in what direction?
 Wed 9/22 Section 1.5 
  1. In example 6, where is the particle at time t=100 if the initial velocity vector is (2,-1) and the initial position vector is (3,3)?
  2. In example 9, suppose the initial angle is 45 degrees. When does the projectile land and where?
Mon 9/20 section 1.5 1.5/ 3,5,7,9,10,11,12,13,14,19 Fri 9/24 Section 1.6 
  1. Find the dot product of u=(-2,3) and v=(4,1).
  2.  Use Thm. 4 to find the angle between u and v above.
Wed 9/22 section 1.6 1.6/ 5,8,18,19,20,22,24,31,39 Mon 9/27 Section 1.7 
  1. In example 1, what equation will parametrize the line 5 times as fast as the first equation and in the same direction?
  2. In ex. 2, where does the line intersect the plane x-y+z-1=0 (if at all)?
  3. In ex. 4, do you remember how to use linear algebra to find solutions to the set of 3 equations in 2 unknowns?
  4.  In ex. 5, find another point on the first plane.
  5. How many parameters does it take to parametrize a plane living in 10-dimensional space?
Fri 9/24section 1.7, lines and planes 1.7/ 1abd (don't plot), 5abc (just find the scalar eqns in x, y and z), 12,13,19,28,32Wed 9/29 Section 1.8, no questions
Mon 9/271.8 and 2.1
  1. 1.8/ 1ab,2,9,31
  2. 2.1/ 2abc,3abc,5abc,7,12,15
  3. Go to the AMCL and do the following
    1. Login as usual.
    2. Type gdesk at the unix prompt.
    3. You'll probably be told that you have a non-standard .xinitrc file. If so, let the computer make you a new one and reboot. Regardless of what you're told, you'll probably have to reboot.
    4. Login in again and you should see a Maple icon in your window. Click on it and see if it opens.
    5. When you're done, send me a message saying either 1) everything is fine or 2) linux sucks. Do not send both messages.
Homework is due Fri 10/1, AMCL is due before class on Wed 9/29. No more questions until I'm convinced you actually want them.
Wed 9/29maple stuff Maple worksheet (just the homework part, not the in-class part) Mon 10/4 2.2
Fri 10/12.2, partial deriv's 2.2/ 1abde,5ade,7ad,12,13 (You may use Maple)Wed 10/6 --
Mon 10/4review Review for Exam 1Wed 10/6 Exam 1
Wed 10/6Exam 1 None-- More partials
Fri 10/8partials 2.2/ 4a,6,8,11,14,16,20Wed 10/13 2.3
Mon 10/11t.planes 2.3/ 2a,4ad(just give an eqn in x,y,z),6b,7ac,10,Fri 10/13 gradient
Wed 10/13gradients 2.4/ 1b,2b,4a,7,8ab,11,16Wed 10/20 -
Fri 10/15gradients Worksheet 1
  • Due Wed 10/20 for those who were in class.
  • Due Thurs 10/21 for those who skipped class.
 -
Wed 10/20, HW#152nd deriv test 2.6/ 3ad,4ad and 2.7/ 1,3ab,4cd,7,8,9,20,22Mon 10/25 optimization
Fri 10/22, HW#16boundary extrema
  • 2.7/ 2,3c also
  • Classify the extrema for f(x,y)=x^2-2xy+2y on the rectangle [0,3]x[0,2].
  • Classify the extrema for g(x,y)=y*sqrt(x)-y^2-x+6y on the rectangle [0,9]x[0,5].
Wed 10/27 optimization
Mon 10/25, HW#17optimization The optimization problems on the reviewFri 10/29 review
Wed 10/27review Prepare for exam 2Fri 10/29 Exam 2
Fri 10/29Exam 2 none-- Integration
Mon 11/1, HW#18integration 3.1/ 1,2,4aFri 11/5 more integrals
Wed 11/3, HW#19double integrals 3.2/ 1abc,2ab,8,9Mon 11/8 --
Fri 11/5, HW#20polar regions On the worksheet, Polar Regions #2,3,4,5,11Wed 11/10 --
Mon 11/8, HW#21cyl & sph. coor's
  1. 3.4/1a,c,e
  2. Use cylindrical coordinates to find the volume of the solid bounded by the paraboloids z=x^2+y^2 and z=36-3x^2-3y^2.
  3. Use spherical coordinates to find the volume of the solid bounded below by the cone phi=pi/6 and above by the sphere x^2+y^2+z^2=4 (the solid looks like an ice cream cone).
Fri 11/12 more integration
Wed 11/10, HW#22more integrals 3.4/1bdf,8,9,11,15Mon 11/15 change of variables
Fri 11/12, HW#23change of variables
  1. Use the change of variables x=2u+v, y=u-v to compute the double integral over R of (x+y)dA, where R is the parallelogram formed by (0,0), (3,-3), (5,-2), (2,1).
  2. Use an appropriate change of variables to compute the double integral over R of (x^2+y^2)dA, where R is the region bounded by the equation 4x^2+9y^2=36.
  3. Use the change of variables u=xy, v=xy^2 to compute the double integral over R of (xy^2)dA, where R is the region bounded by xy=1, xy=4, xy^2=1 and xy^2=4.
  4. Evaluate the double integral over R of cos[(x-y)/(x+y)]dA, where R is the triangle bounded by x+y=1, x=0 and y=0.
Wed 11/17 --
Mon 11/15, HW#24vector fields
  1. Sketch (by hand) the vector field f(x,y)=(2x,0) on the rectangle [-2,2]x[-2,2].
  2. Find the equation of the flow line of f(x,y)=(x,y) through the point (2,3). Use Maple to get a picture of the vector field, then hand sketch the flow line you found through (2,3).
  3. Is the vector field f(x,y)=(3x^2y+y,x^3+2xy) a gradient field? If so what is the function g so that f=gradient of g?
  4. Is the vector field f(x,y)=(3x^2y+y^2,x^3+2xy) a gradient field? If so what is the function g so that f=gradient of g?
  5. 5.1/1abcd
Fri 11/19 line integrals
Wed 11/17, HW#25line integrals 5.2/ 1 (don't calculate, just guess),2(don't calculate, just guess),5adf,6adf,7ac,8 Mon 11/22 review for exam 3
Fri 11/19review for exam 3 review for exam 3Mon 11/22 exam 3
Mon 11/22exam 3 have a good breakright away stuff
Mon 11/29, HW#26Green's Thm 5.3/ 1ace,3,8,12Fri 12/3 surfaces
Wed 12/1, HW#27surfaces and integrals
  1. Choose different integer values for a and b and plot the following surface given parametrically: r(s,t)=( (a+b*sin(s))*cos(t), (a+b*sin(s))*sin(t), b*cos(s) ). Make sure you choose values for a and b so that a is less than b, a=b and a is greater than b. What surface do you get and what happens if a is less than b vs. a is greater than b? Submit your answers to the questions with ONE plot of the surface.
  2. 5.5/ 3
Mon 12/6 flux
Fri 12/3, HW#28flux 5.6/ 1 (discuss the sign only after Monday's class), and 4Wed 12/8 divergence and curl
Mon 12/6, HW#29divergence and curl
  1. Let f be a scalar field (such as f(x,y,z)=x+y+z) and let F be a vector field (such as F(x,y,z)=(x,y,z)). For each of the following, determine if the statement is meaningful. If it is meaningful, is the result a scalar or a vector field?

    curl f, grad f, div F, curl(grad f), grad F, grad(div F), div(grad f), grad(div f), curl(curl F), div(div F), (grad f) x (div F), div(curl(grad f))

  2. 5.6/ 6, 7abc, 8 (just the div part)
  3. Remember, to plot the 2d vector field f(x,y)=(x,y), type: fieldplot([x,y],x=-3..3,y=-3..3);
Fri 12/10 curl
Wed 12/8, HW#30Stokes' and Div. Thms 5.7/ 1,3,7,10Mon 12/13 wrap up
Remember, homework must be given to me by the beginning of class on the due date.
Late homework will not be accepted.
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