Math 13 - Spring 2010
Dartmouth College
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Lecture | Topics | Some Standard Examples/Concepts |
---|---|---|
Day 1 | Review of algebra and geometry in Euclidean space (1.1-1.5) | Vector notation, dot and cross products, lines, planes |
Day 2 | Matrices; polar and cylindrical coordinates (1.6 -1.7) | Basic matrix operations, determinant and area, cartesian and polar coordiantes |
Day 3 | Functions in several variables (2.1 - 2.3) | Graphing surfaces, review of limits, continuity and partial derivatives |
Day 4 | Derivatives (2.3-2.5) | properties of partial derivatives, the chain rule |
Day 5 | Directional derivatives and the gradient (2.6) | |
Day 6 | Parametrized curves (3.1) | |
Day 7 | Arclength (no curvature) (3.2) | |
Day 8 | Vector fields (3.2) | |
Day 9 | Gradient, divergence, curl, and the Del operator (3.4) | |
Day 10 | Double integrals (5.1) | |
Day 11 | Double integrals (5.2) | |
Day 12 | Changing the order of integration (5.3) | |
Day 13 | Triple integrals (5.4) | |
Day 14 | Change of variables (5.5) | linear transformations, the Jacobian |
Day 15 | Applications of Integration (5.6) | average value, center of mass |
Day 16 | Scalar and vector line integrals (6.1) | |
Day 17 | Scalar and vector line integrals (6.1) | |
Day 18 | Green's Theorem (6.2) | |
Day 19 | Conservative vector fields (6.3) | path independence, potential functions, "partial integration" |
Day 20 | Parametrized surfaces (7.1) | |
Day 21 | Areas of surfaces (7.1) | |
Day 22 | Surface integrals (7.2) | |
Day 23 | Surface integrasl (7.2) | |
Day 24 | Stokes's theorem (7.3) | |
Day 25 | Stokes's theorem (7.3) | |
Day 26 | Gauss's Theorem (7.3) | |
Day 27 | Gauss' theorem (7.3) | |
Day 28 | Path Independence and the Fundamental Theorem of Calculus |