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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.
Course readings.
| 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.) |
|