- I-Learn, Class Pictures, Learning Targets, Text Book Practice
- Prep Tasks: Unit 1 - Motion, Unit 2 - Derivatives, Unit 3 - Integration, Unit 4 - Vector Calculus
Motion
These problems were given on the unit itself. I'll move them here at some point.
Differentiation
- Partial Derivatives: section 4.3 exercises 118-134
- Higher Order Partial Derivatives: section 4.3 exercises 135-144, 149-151, 156-158
- Tangent Planes: section 4.4 exercises 170-181 (Ignore the hint, and just compute a differential and then substitute. The text uses a different method.) Then 212-214.
- Linear Approximation: section 4.4 exercises 207-211
- Chain Rule: section 4.5 exercises 215-229, 239-247
- Directional Derivatives: section 4.6 exercises 263-273
- Gradients: section 4.6 exercises 290-293
- Second Derivative Test: section 4.7 exercises 310-313, 318-340
- Lagrange Multipliers: section 4.8 exercises 358-379, 380-392
Integration
- Evaluating iterated integrals:
- (over 2D rectangular regions) section 5.1 exercises 13-34,
- (over 2D general regions) section 5.2 exercises 74-85, 90 - 93,
- (triple integrals) section 5.4 exercises 181-188, 191-212
- Average value:
- (over rectangular regions) section 5.1 exercises 35-38,
- (over general regions) section 5.2 exercises 94-95,
- (over polar regions) section 5.3 exercises 158-159
- (using triple integrals) section 5.4 exercises 221-221, 235-236
- Swapping the order of integration: section 5.2 exercises 96-101
- Polar Coordinates: section 5.3 122-157
- Volume: With all these, I strongly suggest setting up the corresponding triple integral first, and then evaluating the triple integral
- section 5.2 exercises 102-115,
- section 5.3 exercises 160-169
- section 5.4 exercises 219-220, 225-228, 231-232, 237-239
- Cylindrical and Spherical Coordinates: section 5.5 The exercises span the entire unit, which involves evaluating, setting up, computing volume and/or average value, etc. Any are great. Use software to automate the integration after you set up the integral.
- Center of Mass: section 5.6 There are double integral problems, triple integral problems, as well as polar/cylindrical/spherical problems. Pick a section that you want practice with, set up the integral, and use software to see how you did.
- Change-of-variables: section 5.7 exercises 356-361, 378-387, 390-397
Vector Calculus
Coming soon. I have not heard from anyone who is looking for problems to practice with, so I have not priortitized this. If you want some suggestions, please shoot me an email and I'll make sure to prioritize selecting problems to help with what you're looking for.
- Potentials and the Fundamental Theorem of Line integrals section 6.3
- Divergence and Curl section 6.5
- Green's Theorem 6.4
- Surface integrals 6.6
- Stokes' Theorem 6.7
- Divergence Theorem 6.8
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