You can always do more homework problems!
You may need to practise the material
if you want to remember it
for the final exam,
a subsequent course, or the rest of your life.
If you bought MyMathLab access
with your course textbook (or separately),
then you can find supplementary problems there;
use Course ID `bartels18672`

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(However, MyMathLab is *not required* for this section.)

Here is the assigned homework:

- Introduction, vectors:
- Date due: April 9 Wednesday.
- Extra credit (essay): Explain your background in mathematics and what you are going to use this course for.
- Problems from §11.1 (pages 605&606):
- No additional work needed: 1, 3, 7, 8, 11, 19, 25, 29, 30, 35, 37, 39;
- Show what numerical calculation you make or what equation you solve: 41, 45;
- No additional work needed: 49, 51, 52;
- Show at least two intermediate steps: 57;
- No additional work needed: 59;
- Show at least two intermediate steps: 62.

- Problems from §11.2 (pages 614–616):
- Show at least one intermediate step for each part: 3, 7, 8, 11, 13, 15, 18, 19;
- Show also
**u**,**v**, and**w**as appropriate in each picture: 23; - Show at least one intermediate step for part c: 31;
- Show at least one intermediate step: 34, 35;
- Show what numerical calculations you make or what equations you solve: 42, 47.

- Problems from §11.3 (pages 622–624):
- Show at least one intermediate step for each result: 1, 5, 7, 8;
- Show what numerical calculations you make or what equations you solve; you may leave exact answers involving trigonometric operations: 10, 11, 23.
- Show what algebraic calculation you make to find each slope: 31, 32;
- Show at least one intermediate step of algebra: 35, 38.

- Problems from §11.4 (pages 628–630):
- Show at least one intermediate step for each part: 3, 6, 11, 12, 17, 20, 21;
- No additional work needed: 23, 27, 28, 29, 31;
- Show what numerical calculations (possibly combined into vectors) you make: 35, 38, 39, 43.

- Problems from §11.5 (pages 636–638):
- No additional work needed: 3, 7, 8, 11;
- Show at least one intermediate step: 13, 15, 18, 19, 23, 31, 34, 35, 42, 47.

- Curves, multivariable functions:
- Date due: April 16 Wednesday.
- 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.

- 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.

- Multivariable limits and continuity,
integration on unoriented curves:
- Date due: April 23 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;
- Show what equations or inequalities (if any) you solve: 31, 32, 36, 39;
- State which paths you use: 43, 46;
- Give a reason: 55.

- 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.

- Vector fields and differential forms,
integration on (pseudo)-oriented curves:
- Date due: April 30 Wednesday.
- Problems from §15.2 (pages 844–847):
- No additional work needed: 5, 6;
- Show what one-variable integrals you evaluate: 10, 11, 14, 16, 17, 19, 22, 23, 24, 29;
- No additional work needed: 39–44.

- Additional problems (no additional work needed):
- Given
**F**(*x*,*y*,*z*) = 2*x***i**− 3*x***j**+ 4*x**y***k**= ⟨2*x*, −3*x*, 4*x**y*⟩, express**F**⋅ d**r**=**F**⋅**T**d*s*as a differential form (using**r**= ⟨*x*,*y*,*z*⟩). - Given
**F**(*x*,*y*) =*x*^{2}**i**+ 3**j**= ⟨*x*^{2}, 3⟩, express**F**⋅ d**r**=**F**⋅**T**d*s*and**F**× d**r**=**F**⋅**n**d*s*as differential forms (using**r**= ⟨*x*,*y*⟩).

- Given

- Partial differentiation, directional derivatives and gradients:
- Date due: May 8 Thursday.
- 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;
- 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.

- Problems from §15.2 (pages 844–847): Show at least one intermediate step: 1, 4.

- Applications of partial differentiation:
- Date due: May 19 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.

- Multiple integration:
- Date due: May 28 Wednesday.
- 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.

- Change of variables:
- Date due: June 3 Tuesday.
- 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 d
*A*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.

- Integrals on surfaces,
conservative vector fields and exact differential forms:
- Date due: June 9 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.

- 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.

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