- Introduction and review:
- Date assigned: April 1 Monday;
- Date due: April 2 Tuesday;
- Problems from the Chapter 11 Practice Exercises (pages 644&645):
- Show what numerical calculations 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;
- Some
**answers**: DjVu format, PDF format.

- Curves:
- Date assigned: April 2 Tuesday;
- Date due: April 3 Wednesday;
- Problems from §12.1 (pages 655–657):
- Show at least one intermediate step for each calculation: 1, 4, 6, 7;
- Show the velocity vector at the given value of
*t*: 11, 14; - Show 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;
- Some
**answers**: DjVu format, PDF format.

- Multivariable functions:
- Date assigned: April 4 Thursday;
- Date due: April 8 Monday;
- 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; - Some
**answers**: DjVu format, PDF format.

- Limits and continuity with multivariable functions:
- Date assigned: April 9 Tuesday;
- Date due: April 10 Wednesday;
- 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;
- State which paths you use: 43, 46;
- Give a reason: 55;

- Extra credit:
Either explain why
the limit as (
*x*,*y*) approaches (0, 0) of*x*+*y*divided by √*x*+ √*y*is zero, or find a curve along which the limit is not zero.

- Partial differentiation:
- Date assigned: April 11 Thursday;
- Date due: April 15 Monday;
- Problems from §13.3 (pages 711–714):
- Show at least one intermediate step for each: 3, 4, 10, 12, 24, 26, 30;
- 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;
- Some
**answers**: DjVu format, PDF format.

- Problems from §13.4 (pages 721&722): Show at least one intermediate step: 27, 28, 33, 41.

- Directional derivatives:
- Date assigned: April 16 Tuesday;
- Date due: April 17 Wednesday;
- 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;
- Show the gradient, the differential, or the partial derivatives; but you need not sketch the gradient in your final answer: 28;

- Problems from §13.6 (pages 737–739):
- Show the gradient, the differential, or the partial derivatives: 3, 6, 10, 13, 14.

- Linear approximation:
- Date assigned: April 18 Thursday;
- Date due: April 22 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.

- Optimisation:
- Date assigned: April 23 Tuesday;
- Date due: April 25 Thursday;
- 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, 55;
- 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, 31, 33.

- Integration along (pseudo)-oriented curves:
- Date assigned: April 29 Monday;
- Date due: April 30 Tuesday;
- Problems from §15.1 (pages 832–834): No additional work needed: 1–8;
- Problems from §15.2 (pages 844–847):
- No additional work needed: 1, 4, 5;
- Show what one-variable integrals you evaluate: 10, 11, 14, 16, 17, 23, 24, 29.

- More integration on curves:
- Date assigned: May 1 Wednesday;
- Date due: May 2 Thursday;
- Problems from §15.1 (pages 832–834): Show what one-variable integrals you evaluate: 10, 13, 16, 22, 30, 35;
- Problems from §15.2 (pages 844–847): Show what one-variable integrals you evaluate: 19, 22;
- Problems from §12.3 (pages 667&668): Show what one-variable integrals you evaluate: 1, 5, 8, 11, 15, 18.

- Multiple integration:
- Dates assigned: May 6 Monday;
- Date due: May 7 Tuesday;
- 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.

- Applications of multiple integration:
- Dates assigned: May 8 Wednesday;
- Date due: May 13 Monday;
- 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, 23;

- Problems from §14.6 (pages 800–802): Show what integrals you evaluate: 3, 14, 19, 25, 29.

- Change of variables in multiple integration:
- Dates assigned: May 14 Tuesday;
- Date due: May 15 Wednesday;
- Problems from §14.8 (pages 821–823):
- No additional work needed: 1;
- Show what iterated integrals you evaluate: 6, 12;
- No additional work needed: 20.

- Multiple integration in polar coordinates:
- Dates assigned: May 16 Thursday;
- Date due: May 20 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.

- Integrals on surfaces:
- Date assigned: May 22 Wednesday;
- Date due: May 28 Tuesday;
- 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.

- Conservative vector fields and exact differential forms:
- Date assigned: May 29 Wednesday;
- Date due: May 30 Thursday;
- 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 calculation you make: 14, 17, 21;
- Explain: 25.

- Green's Theorem:
- Date assigned: June 3 Monday;
- Date due: June 4 Tuesday;
- Problems from §15.4 (pages 867–869): Show what integrals you evaluate: 1, 4, 7, 9, 12, 15, 21, 24, 26, 33.

- Gauss's Theorem and Stokes's Theorem:
- Date assigned: June 5 Wednesday;
- Date due: June 11 Tuesday;
- 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;

- 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.

Go back to the the course homepage.

This web page and the files linked from it were written between 2003 and 2013 by Toby Bartels, last edited on 2013 June 12. Toby reserves no legal rights to them.

The permanent URI of this web page
is
`http://tobybartels.name/MATH-2080/2013s/homework/`

.