| LEC # | TOPICS | READINGS |
|---|---|---|
| I. Vectors and matrices | ||
| 0 | Vectors | Text: Section 12.1 |
| 1 | Dot product | Text: Section 12.2 |
| 2 | Determinants; cross product | Text: Section 12.3 Notes: Section D |
| 3 | Matrices; inverse matrices | Notes: Sections M.1 and M.2 |
| 4 | Square systems; equations of planes | Text: Pages 798-800 Notes: Section M.4 |
| 5 | Parametric equations for lines and curves | Text: Sections 12.4 and 10.4 |
| 6 | Velocity, acceleration Kepler's second law | Text: Section 12.5, page 818 Notes: Section K |
| 7 | Review | |
| II. Partial derivatives | ||
| 8 | Level curves; partial derivatives; tangent plane approximation | Text: Sections 13.2 and 13.4 Notes: Section TA |
| 9 | Max-min problems; least squares | Text: Pages 878-881, 884-885 Notes: Section LS |
| 10 | Second derivative test; boundaries and infinity | Text: Section 13.10, through page 930 Notes: Section SD |
| 11 | Differentials; chain rule | Text: Sections 13.6-13.7 |
| 12 | Gradient; directional derivative; tangent plane | Text: Section 13.8 |
| 13 | Lagrange multipliers | Text: Section 13.9, through page 922 |
| 14 | Non-independent variables | Notes: Section N |
| 15 | Partial differential equations; review | Notes: Section P |
| III. Double integrals and line integrals in the plane | ||
| 16 | Double integrals | Text: Section 14.1-14.3 Notes: Section I.1 |
| 17 | Double integrals in polar coordinates; applications | Text: Sections 14.4-14.5 Notes: Section I.2 |
| 18 | Change of variables | Text: Section 14.9 Notes: Section CV |
| 19 | Vector fields and line integrals in the plane | Text: Section 15.2 Notes: Section V1 |
| 20 | Path independence and conservative fields | Text: Section 15.3 |
| 21 | Gradient fields and potential functions | Notes: Section V2 |
| 22 | Green's theorem | Text: Section 15.4 |
| 23 | Flux; normal form of Green's theorem | Notes: Sections V3 and V4 |
| 24 | Simply connected regions; review | Notes: Section V5 |
| IV. Triple integrals and surface integrals in 3-space | ||
| 25 | Triple integrals in rectangular and cylindrical coordinates | Text: Sections 12.8, 14.6, and 14.7 Notes: Section I.3 |
| 26 | Spherical coordinates; surface area | Text: Section 14.7 Notes: Sections I.4, CV.4, and G |
| 27 | Vector fields in 3D; surface integrals and flux | Notes: Sections V8 and V9 |
| 28 | Divergence theorem | Text: Section 15.6 Notes: Section V10 |
| 29 | Divergence theorem (cont.): applications and proof | Text: Section 15.6, Pages 1054-1055 Notes: Section V10 |
| 30 | Line integrals in space, curl, exactness and potentials | Text: Pages 1017-1018 Notes: Sections V11 and V12 |
| 31 | Stokes' theorem | Text: Section 15.7 Notes: Section V13 |
| 32 | Stokes' theorem (cont.); review | |
| 33 | Topological considerations Maxwell's equations | Notes: Sections V14 and V15 |
| 34 | Final review | |
| 35 | Final review (cont.) | |
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: Edwards, Henry C., and David E. Penney. Multivariable Calculus. 6th ed. Lebanon, IN: Prentice Hall, 2002. ISBN: 9780130339676.
"Notes" refers to the "18.02 Supplementary Notes and Problems" written by Prof. Arthur Mattuck.