The Undergraduate Program Committee
Date: June 23, 2000
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Lecture | Topics | Some Standard Examples/Concepts |
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Day 1 | Review of algebra and geometry in Euclidean space (1.1 - 1.5) | Vector notation, dot and cross products, lines, planes |
Day 2 | Curves in Euclidean space (1.6) | Curves, tangent vector, tangent line |
Day 3 | Graphs, level surfaces, partial derivatives, and continuity (2.1 - 2.2) | |
Day 4 | Differentiability, the derivative matrix, tangent planes (2.3) | |
Day 5 | The Chain Rule, Gradients and Directional Derivatives (2.4 - 2.5) | |
Day 6 | Directional Derivatives and Implicit differentiation (2.5 - 2.6) | |
Day 7 | Curves and acceleration (4.1) | |
Day 8 | Arclength (4.2) | |
Day 9 | Vector Fields (4.3) | |
Day 10 | Divergence and Curl (4.4) | |
Day 11 | Divergence and Curl (4.4 / 5.1) | |
Day 12 | Volume and Cavalieri's Principle (5.1) | |
Day 13 | Double integral over a rectangle (5.2 / 5.3) | |
Day 14 | Double Integral over other regions (5.3) | |
Day 15 | Triple Integrals (5.4) | |
Day 16 | Change of Variables, cylindrical and spherical coordinates (5.5) | |
Day 17 | Change of Variables, cylindrical and spherical coordinates (5.5) | |
Day 18 | Applications (5.6) | Center of Mass, moments of inertia |
Day 19 | Line Integrals (6.1) | |
Day 20 | Line Integrals (6.1) | |
Day 21 | Parametrized surfaces (6.2) | |
Day 22 | Area of a surface (6.3) | |
Day 23 | Surface Integrals (6.4) | |
Day 24 | Green's theorem (7.1) | |
Day 25 | Stokes' Theorem (7.2) | |
Day 26 | Stokes' Theorem (7.2) | |
Day 27 | Gauss' theorem (7.3) | |
Day 28 | Path Independence and the Fundamental Theorem of Calculus (7.4) | |