Math 20550 Calculus III (Spring 2016)
Multivariable Calculus
| Lecture Number | Date | Section | Topic | |
|---|---|---|---|---|
| Lecture 1 | Jan | 13 | 12.1 | 3D coordinates |
| Tutorial | (in tutorial) | 14 | 12.2 | Vectors |
| Lecture 2 | 15 | 12.3-4 | Dot Product, Cross Product | |
| Lecture 3 | 18 | 12.4 | Cross Product (finish) | |
| Lecture 4 | 20 | 12.5 | Lines, Planes | |
| Lecture 5 | 22 | 12.5 | Planes | |
| Lecture 6 | 25 | 13.1 | Vector Functions, Space Curves | |
| Lecture 7 | 27 | 13.2 | Derivatives, Integrals | |
| Lecture 8 | 29 | 13.3 | Arc Length | |
| Lecture 9 | Feb | 1 | 13.3 | Normal and Binormal Vectors |
| Lecture 10 | 3 | 13.4 | Motion in Space | |
| Lecture 11 | 5 | 14.1 | Functions of Several Variables | |
| Lecture 12 | 8 | 14.2 | Limits, Continuity | |
| Lecture 13 | 10 | 14.3 | Partial Derivatives | |
| Lecture 14 | 12 | 14.5 | Chain Rule | |
| Lecture 15 | 15 | Instructor's Choice | ||
| Exam 1 | 16 | Exam 1 | ||
| Lecture 16 | 17 | 14.6 | Directional Derivatives, Gradients | |
| Tutorial | (in tutorial) | 18 | 14.6 | Tangent Planes, Normal Lines |
| Lecture 17 | 19 | 14.7 | Local Maxima, Local Minima, Saddle Points | |
| Lecture 18 | 22 | 14.7 | Maxima and Minima on Bounded Regions | |
| Lecture 19 | 24 | 14.8 | Lagrange Multipliers (one constraint) | |
| Lecture 20 | 26 | 14.8 | Lagrange Multipliers (two constraints) | |
| Lecture 21 | 29 | 15.1 | Double Integrals over Rectangles | |
| Lecture 22 | Mar | 2 | 15.2-3 | Iterated Integrals, General Regions |
| Lecture 23 | 4 | 15.3 | Double Integrals over General Regions | |
| Spring Break | 5-13 | Spring Break | ||
| Lecture 24 | 14 | Instructor's Choice | ||
| Exam 2 | 15 | Exam 2 | ||
| Lecture 25 | 16 | 15.4 | Polar Coordinates | |
| Tutorial | (in tutorial) | 17 | 15.5 | Mass, Centers of Mass, and Moments |
| Lecture 26 | 18 | 15.7 | Triple Integrals | |
| Lecture 27 | 21 | 15.8 | Triple Integrals in Cylindrical Coordinates | |
| Lecture 28 | 23 | 15.9 | Triple Integrals in Spherical Coordinates | |
| Good Friday | 25 | Easter Holiday | ||
| Easter Monday | 28 | Easter Holiday | ||
| Lecture 29 | 30 | 15.10 | Change of Variables in Multiple Integrals | |
| Lecture 30 | Apr | 1 | 16.2 | Line Integrals of Functions |
| Lecture 31 | 4 | 16.1-2 | Vector Fields, Line Integrals | |
| Lecture 32 | 6 | 16.3 | Fundamental Theorem of Line Integrals | |
| Lecture 33 | 8 | 16.4 | Green's Theorem | |
| Lecture 34 | 11 | 16.5 | Curl, Divergence | |
| Lecture 35 | 13 | 16.6 | Parametric Surfaces, Tangent Planes, Area | |
| Lecture 36 | 15 | 16.7 | Surface Integrals, Flux Integrals | |
| Lecture 37 | 18 | Instructor's Choice | ||
| Exam 3 | 19 | Exam 3 | ||
| Lecture 38 | 20 | 16.8 | Flux Integrals, Stokes' Theorem | |
| Lecture 39 | 22 | 16.8 | Stokes' Theorem | |
| Lecture 40 | 25 | 16.9 | Divergence Theorem | |
| Lecture 41 | 27 | Review | ||
| Final Exam | May | 6 | Final Exam | |
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