# Homework

In case you miss a homework assignment in class, you can find it below. Unless otherwise specified, all problems are from the 2nd Edition of University Calculus: Early Transcendentals published by Addison Wesley (Pearson). When I return graded homework, I may post some solutions here too; see the downloading help if you have trouble reading them. See the grading policies for general instructions on doing homework and how it will be graded.

These assignments are subject to change, but any changes will be announced in class and marked here with strong emphasis at least one day before the due date. Due dates will only change in case of emergency or if the discussion spills over into the next day. (Every due date except the first and last is a Wednesday.)

Here is the assigned homework:

1. Vectors, curves:
• Date due: January 13 Tuesday.
• Problems from the Chapter 11 Practice Exercises (pages 644&645):
• Show what numerical calculations (if any) you make: 17, 19, 25, 29, 31, 35, 37, 43, 50;
• No additional work needed: 67, 69.
• Extra credit (essay): Explain your background in mathematics and what you are going to use this course for.
• Problems from §12.1 (pages 655–657):
• Show at least one intermediate step for each calculation: 1, 4, 6, 7;
• Show also the velocity vector at the given value of t: 11, 14;
• Show also the velocity and acceleration vectors at t = 0: 15, 17;
• Show at least one intermediate step for each: 19, 20;
• No additional work needed: 23.
• Problems from §12.2 (pages 661–663):
• Show at least one intermediate step for each: 1, 4, 6, 12, 15, 17;
• Show what calculations you make or what equations you solve: 21, 22.
2. Multivariable functions:
• Date due: January 21 Wednesday.
• Problems from §13.1 (pages 692–694):
• Show what numerical calculations you make: 3, 4;
• Show what equations or inequalities you solve: 7, 9, 10;
• Label each contour with its value of c: 15;
• No additional work needed: 18, 24, 30, 31–36, 40, 42;
• State the value of c used: 52, 54, 59, 62.
• Problems from §13.2 (pages 700–703):
• Show what numerical calculations you make: 2, 6, 11;
• Show the rewritten expressions: 18, 23;
• Show what numerical calculations you make: 28;
• Show what equations or inequalities (if any) you solve: 31, 32, 36, 39;
• State which paths you use: 43, 46;
• Give a reason: 55.
3. Integration on curves:
• Date due: January 28 Wednesday.
• Problems from §15.2 (pages 844–847):
• Show what one-variable integrals you evaluate: 14, 16, 17, 23, 24.
• Problems from §15.1 (pages 832–834):
• No additional work needed: 1–8;
• Show what one-variable integrals you evaluate: 10, 13, 16, 22, 30, 35.
• Problems from §12.3 (pages 667&668): Show what one-variable integrals you evaluate: 1, 5, 8, 9, 11, 15, 18.
• Some answers: DjVu format, PDF format.
4. Vector fields and differential forms:
• Date due: February 9 Monday.
• Problems from §15.2 (pages 844–847):
• No additional work needed: 5, 6;
• Show what one-variable integrals you evaluate: 10, 11, 19, 22, 29;
• No additional work needed: 39–44.
1. Given F = 2xi − 3xj + 4xyk = ⟨2x, −3x, 4xy⟩, express F ⋅ dr = F ⋅ T ds as a differential form (using r = ⟨x, y, z⟩).
2. Given F = x2i + 3j = ⟨x2, 3⟩, express F ⋅ dr = F ⋅ T ds and F × dr = F ⋅ n ds as differential forms (using r = ⟨x, y⟩).
5. Partial differentiation, directional derivatives and gradients:
• Date due: February 16 Monday.
• Problems from §13.3 (pages 711–714):
• Show at least one intermediate step for each: 3, 4, 10, 12, 24, 26, 30, 39;
• Show the first-order partial derivatives along the way: 43, 46;
• No additional work needed: 55;
• Show what limits you evaluate: 57;
• Show what algebraic equations you verify: 75, 82.
• Problems from §13.4 (pages 721&722):
• Use any method (including differentials), but show at least one intermediate step for each derivative: 2, 4, 7, 10;
• No additional work needed: 19, 20;
• Show at least one intermediate step: 27, 28, 33, 41.
• Problems from §13.5 (pages 729&730):
• Show at least one intermediate step: 2, 3, 7, 8;
• Show the gradient, the differential, or the partial derivatives; and show either the direction of u or a result before adjusting for the magnitude of u: 14, 15, 16;
• Show the gradient as an intermediate step: 20, 23;
• Problems from §13.6 (pages 737–739):
• Show the gradient, the differential, or the partial derivatives: 3, 6, 10, 13, 14.
• Problems from §15.2 (pages 844–847): Show at least one intermediate step: 1, 4.
6. Applications of partial differentiation:
• Date due: February 23 Monday.
• Problems from §13.6 (pages 737–739):
• Show what numerical calculations you make: 19;
• Show the gradient, the differential, or the partial derivatives: 29;
• Show what calculations you make or what inequalities you solve: 33;
• Show the gradient, the differential, or the partial derivatives: 39, 50.
• Problems from §13.7 (pages 745–748): Show what equations you solve and what numerical calculations you make: 2, 7, 9, 15, 27, 32, 34, 37, 43, 52, 57.
• Problems from §13.8 (pages 755–757): Show what equations you solve and what numerical calculations you make: 1, 5, 10, 11, 16, 23, 29.
7. Multiple integration:
• Date due: March 2 Monday.
• Problems from §14.1 (pages 767&768):
• Show at least the intermediate one-variable integral: 3, 7, 10;
• Show at least an iterated integral and an intermediate one-variable integral: 15, 20;
• Show a two-variable iterated integral: 25.
• Problems from §14.2 (pages 774–777):
• No additional work needed: 1, 2, 7, 9, 12, 14, 17;
• Show also the intermediate one-variable integral: 19, 23;
• No additional work needed: 35, 41;
• Show also the intermediate one-variable integral: 47, 51;
• Show a two-variable iterated integral: 57, 61.
• Problems from §14.5 (pages 792–795):
• Show also the two intermediate integrals: 3;
• No additional work needed: 6;
• Show at least the two intermediate integrals: 9, 15;
• No additional work needed: 21;
• Show a three-variable iterated integral: 25, 29, 34.
• Problems from §14.3 (page 779):
• Show what integrals you evaluate: 1, 4, 7, 12;
• No additional work necessary: 13, 14, 17;
• Show what integrals you evaluate: 20, 21.
• Problems from §14.6 (pages 800–802): Show what integrals you evaluate: 3, 14, 19, 25, 29.
8. Change of variables:
• Date due: March 9 Monday.
• Problems from §14.4 (pages 784–786):
• No additional work needed: 1, 3, 5, 7;
• Show the iterated integrals in polar form: 9, 17, 20;
• No additional work needed: 23, 24;
• Show what iterated integrals you evaluate: 28, 29, 34;
• Show the iterated integral in polar form: 37.
• Problems from §14.7 (pages 810–813):
• Show also the two intermediate integrals for each: 1, 2, 8;
• Show the iterated integrals: 12;
• Show the iterated integral in cylindrical coordinates: 14;
• Show also the two intermediate integrals for each: 23;
• Show the iterated integral in spherical coordinates: 37;
• Show what iterated integrals you evaluate: 43, 46, 57, 77.
• Extra credit problem from §14.8 (pages 821–823): Show a calculation of dA in u and v, and show the double integral in u and v (and you may want to make a further shift to polar coordinates to make it easier to evaluate this integral): 12.
9. Integrals on surfaces, conservative vector fields and exact differential forms:
• Date due: March 16 Monday.
• Problems from §15.5 (pages 878–880):
• No additional work needed: 2, 3, 6, 9, 13;
• Show what integrals you evaluate: 20, 23.
• Problems from §15.6 (pages 877–889):
• Show what parmetrisations you use and what iterated integrals you evaluate: 1, 5, 8, 11, 16, 17, 19, 23, 25, 34, 35, 37, 41;
• Show what integrals you evaluate: 45.
• Problems from §15.3 (pages 856–858):
• Show what calculations you make to check: 1, 3, 6;
• Show what integrals you take: 7, 8, 11;
• Show what numerical calculations you make: 14, 17, 21;
• Explain: 25.
10. Stokes Theorems:
• Date due: Never.
• Problems from §15.4 (pages 867–869): Show what integrals you evaluate: 1, 4, 7, 9, 12, 15, 21, 24, 26, 33.
• Problems from §15.7 (pages 898–900):
• Show what integrals you evaluate: 1, 3, 5, 6, 9, 14, 17;
• Show what calculations you make: 19, 26.
• Problems from §15.8 (pages 909–911):
• Show what calculations you make: 1, 2;
• Show what integrals you evaluate: 6, 7, 8, 13;
• Explain: 17.
That's it!
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