Extra practice vector problems [Goes with 10.2-4. Highly recommended.]
| Section 10.4 | Cross Product Parallelogram Theorem [Goes with 10.4, Optional Reading] |
| Section 10.5 Answers | Maxima Computer Examples |
| Section 10.6 (Minimal notes) | Maple Computer Examples |
| Section 10.7 | Frenet-Serret formulas and Torsion [Goes with Section 10.8, Optional Reading] |
| Section 10.8 Plot for last example. | Curvature Animation of osculating circle for an ellipse.
|
| Section 10.9 | Be A Roller Coaster Designer! |
| 11.1, in progress | |
| Section 11.2 Limits | |
| Section 11.3 Partial Derivatives | Extra Practice Partial Derivative Problems |
| Section 11.4 | Video on Tangent Planes. (18 min, 16 sec) Text for video. Graphic for video.
Video with captions added. |
| Section 11.5 | |
| Section 11.6 | Contour and Gradient Vector Plots Example |
| Section 11.7 | Quadratic Surface Animation
Second Derivative Test in n variables, by Brian D. Sittinger [Goes with Section 11.7, Optional Reading]
|
| Section 11.8 | Lagrange Multipliers Extra Example: Notes, Video (8 min, 42 sec), Static Images From Video.
Video with captions added. |
| Sections 12.1 & 2 (Rough) | Double Integral done by computer example |
| Section 12.3 Double Integrals in Polar Coords | Polar Animations - Just For Fun! |
| Section 12.4 Application: Moments | Law of the Lever [Goes with 12.4. Optional Reading.]
Visual Pattern Recognition by Moment Invariants, Ming-Kuei Hu, IRE Transactions on Information Theory, Volume: 8, Issue: 2, 1962. [Goes with 12.4. Optional reading] |
| Section 12.5 Triple Integrals (revised) | |
| Section 12.6 Cylindrical Coords | |
| Section 12.7 Spherical Coords | Spherical Volume Element Proof [Optional Reading] |
| Section 13.1 Vector Fields | Vector Field Examples
Escher Stairs |
| Section 13.2 Line Integrals | |
| Section 13.3 Path Independence | |
| Section 13.4 Green's Theorem | Area with Green's Theorem Example [Goes with 13.4. Optional Reading.] (Maple version)
Area with Green's Theorem Example [Goes with 13.4. Optional Reading.] (Maxima version) |
| Section 13.6 Surface Area | This is a long hard section. |
| Section 13.7 Flux | |
| Section 13.5 div & curl | Extra Practice Problems [Goes with Section 13.5, Recommended.]
Finding Vector Potentials [Goes with Section 13.5, Optional Reading.] |
| Section 13.8 Stokes' Theorem | Knots About Stokes' Theorem [Optional Reading] |
| Section 13.9 Divergence Theorem | |
| | Vector Calculus Differential Identities [Goes with Chapter 13.] |
| | Vector Calculus Summary with Examples [Goes with Chapter 13.] |
| | Mixed 3D Examples [Goes with Chapters 12 & 13.] |
| | |
| | |
| | Two Good Books |
