| Lec # | topics | readings |
|---|---|---|
| I. Vectors and Matrices | ||
| 1 | Vectors in 2- and 3-space Dot Product | Text: Sections 17.3, 18.1, 18.2 |
| 2 | Determinants of Orders 2 and 3 Cross Product | Text: Section 18.3 Notes: Section D |
| 3 | Matrices; Inverse Matrices | |
| 4 | Solving Systems of Linear Equations; Lines, Planes | |
| 5 | Parametric Curves; Velocity, Acceleration | Text: Sections 18.4, 17.1, 17.4 |
| 6 | Kepler's Second Law | Text: 17.7 Notes: Section K |
| Exam 1 (Covering Lectures 1-6) | ||
| II. Partial Derivatives | ||
| 7 | Level Curves, Partial Derivatives, Tangent Plane | Text: Sections 19.1-19.3 Notes: Section TA |
| 8 | Max-Min Problems Least Squares Approximation | Text: Section 19.7 Notes: Section LS |
| 9 | 2nd Derivative Test; Boundaries and Infinity | |
| 10 | Differentials; Chain Rule | Text: Section 19.6 |
| 11 | Gradient, Directional Derivative | Text: Section 19.5 |
| 12 | Lagrange Multipliers | Text: Section 19.8 |
| 13 | Non-independent Variables | |
| 14 | Partial Differential Equations Review | Text: Section 19.8 |
| Exam 2 (Covering Lectures 7-14) | ||
| III. Double and Triple Integrals | ||
| 15 | Double and Iterated Integrals | Text: Sections 20.1, 20.2 Notes: Section I.1 |
| 16 | Double Integrals in Polar Coordinates Applications | Text: Sections 20.3, 20.4 Notes: Section I.2 |
| 17 | Change of Variables | Text: Section 20.3 |
| 18 | Triple Integrals in Rectangular and Cylindrical Coordinates | Text: Sections 20.5, 10.6 |
| 19 | Spherical Coordinates Gravitational Attraction | Text: Section 20.7 |
| IV. Vector Calculus in 2 and 3-space | ||
| 20 | Line Integrals in the Plane | Text: Section 21.1 Notes: Section V1 |
| 21 | Gradient Fields and Path Independence | Text: Section 21.2 Notes: Section V2.1 |
| 22 | Conservative Fields and Potential Functions | |
| 23 | Green's Theorem 2-dimensional Curl (Vorticity) | Text: Section 21.3 Notes: Section V4.3 |
| 24 | Simply-connected Regions Review | |
| Exam 3 (Covering Lectures 15-24, Except 18-19) | ||
| 25 | Flux Form of Green's Theorem | |
| 26 | Vector Fields in 3-space; Surface Integrals and Flux | |
| 27 | Divergence (= Gauss's) Theorem | Text: Section 21.4 Notes: Section V10 |
| 28 | Divergence Theorem (cont.) | |
| 29 | Line Integrals in Space, Exactness, and Potentials | |
| 30 | Stokes' Theorem | Text: Section 21.5 Notes: Section V4.3, V13 |
| 31 | Understanding Curl Review | |
| Exam 4 (Covering Lectures 18-19, 25-31) | ||
| 32 | Topological Issues | |
| 33 | Conservation Laws; Heat/Diffusion Equation | |
| 34 | Course Review | |
| 35 | Course Evaluation Maxwell's Equations | Text: Section 21.6 Notes: Section V15 |
Table of Contents
Study Materials
Readings
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Listed in the table below are reading assignments for each lecture session.
"Text" refers to the course textbook: Simmons, George F. Calculus with Analytic Geometry. 2nd ed. New York, NY: McGraw-Hill, 1995. ISBN: 0070576424.
"Notes" refers to the "18.02 Supplementary Notes and Problems" written by Prof. Mattuck.