Readings

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.

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.)