| I. Vectors and Matrices |
| 1 |
Vectors in 2- and 3-space
Dot Product |
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| 2 |
Determinants of Orders 2 and 3
Cross Product |
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| 3 |
Matrices; Inverse Matrices |
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| 4 |
Solving Systems of Linear Equations; Lines, Planes |
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| 5 |
Parametric Curves; Velocity, Acceleration |
Problem set 1 due |
| 6 |
Kepler's Second Law |
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Exam 1 (Covering Lectures 1-6) |
Problem set 2 due |
| II. Partial Derivatives |
| 7 |
Level Curves, Partial Derivatives, Tangent Plane |
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| 8 |
Max-Min Problems
Least Squares Approximation |
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| 9 |
2nd Derivative Test; Boundaries and Infinity |
Problem set 3 due |
| 10 |
Differentials; Chain Rule |
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| 11 |
Gradient, Directional Derivative |
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| 12 |
Lagrange Multipliers |
Problem set 4 due |
| 13 |
Non-independent Variables |
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| 14 |
Partial Differential Equations
Review |
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Exam 2 (Covering Lectures 7-14) |
Problem set 5 due |
| III. Double and Triple Integrals |
| 15 |
Double and Iterated Integrals |
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| 16 |
Double Integrals in Polar Coordinates
Applications |
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| 17 |
Change of Variables |
Problem set 6 due |
| 18 |
Triple Integrals in Rectangular and Cylindrical Coordinates |
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| 19 |
Spherical Coordinates
Gravitational Attraction |
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| IV. Vector Calculus in 2 and 3-space |
| 20 |
Line Integrals in the Plane |
Problem set 7 due |
| 21 |
Gradient Fields and Path Independence |
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| 22 |
Conservative Fields and Potential Functions |
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| 23 |
Green's Theorem
2-dimensional Curl (Vorticity) |
Problem set 8 due |
| 24 |
Simply-connected Regions
Review |
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Exam 3 (Covering Lectures 15-24, Except 18-19) |
Problem set 9 due |
| 25 |
Flux Form of Green's Theorem |
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| 26 |
Vector Fields in 3-space; Surface Integrals and Flux |
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| 27 |
Divergence (= Gauss's) Theorem |
Problem set 10 due |
| 28 |
Divergence Theorem (cont.) |
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| 29 |
Line Integrals in Space, Exactness, and Potentials |
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| 30 |
Stokes' Theorem |
Problem set 11 due |
| 31 |
Understanding Curl
Review |
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Exam 4 (Covering Lectures 18-19, 25-31) |
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| 32 |
Topological Issues |
Problem set 12 due |
| 33 |
Conservation Laws; Heat/Diffusion Equation |
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| 34 |
Course Review |
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| 35 |
Course Evaluation
Maxwell's Equations |
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