- 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.

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