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Multivariable Calculus >> Content Detail



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: Amazon logo 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 #TOPICSREADINGS
I. Vectors and matrices
0VectorsText: Section 12.1
1Dot productText: Section 12.2
2Determinants; cross product

Text: Section 12.3

Notes: Section D

3Matrices; inverse matricesNotes: Sections M.1 and M.2
4Square systems; equations of planes

Text: Pages 798-800

Notes: Section M.4

5Parametric equations for lines and curvesText: Sections 12.4 and 10.4
6

Velocity, acceleration

Kepler's second law

Text: Section 12.5, page 818

Notes: Section K

7Review
II. Partial derivatives
8Level curves; partial derivatives; tangent plane approximation

Text: Sections 13.2 and 13.4

Notes: Section TA

9Max-min problems; least squares

Text: Pages 878-881, 884-885

Notes: Section LS

10Second derivative test; boundaries and infinity

Text: Section 13.10, through page 930

Notes: Section SD

11Differentials; chain ruleText: Sections 13.6-13.7
12Gradient; directional derivative; tangent planeText: Section 13.8
13Lagrange multipliersText: Section 13.9, through page 922
14Non-independent variablesNotes: Section N
15Partial differential equations; reviewNotes: Section P
III. Double integrals and line integrals in the plane
16Double integrals

Text: Section 14.1-14.3

Notes: Section I.1

17Double integrals in polar coordinates; applications

Text: Sections 14.4-14.5

Notes: Section I.2

18Change of variables

Text: Section 14.9

Notes: Section CV

19Vector fields and line integrals in the plane

Text: Section 15.2

Notes: Section V1

20Path independence and conservative fieldsText: Section 15.3
21Gradient fields and potential functionsNotes: Section V2
22Green's theoremText: Section 15.4
23Flux; normal form of Green's theoremNotes: Sections V3 and V4
24Simply connected regions; reviewNotes: Section V5
IV. Triple integrals and surface integrals in 3-space
25Triple integrals in rectangular and cylindrical coordinates

Text: Sections 12.8, 14.6, and 14.7

Notes: Section I.3

26Spherical coordinates; surface area

Text: Section 14.7

Notes: Sections I.4, CV.4, and G

27Vector fields in 3D; surface integrals and fluxNotes: Sections V8 and V9
28Divergence theorem

Text: Section 15.6

Notes: Section V10

29Divergence theorem (cont.): applications and proof

Text: Section 15.6, Pages 1054-1055

Notes: Section V10

30Line integrals in space, curl, exactness and potentials

Text: Pages 1017-1018

Notes: Sections V11 and V12

31Stokes' theorem

Text: Section 15.7

Notes: Section V13

32Stokes' theorem (cont.); review
33

Topological considerations

Maxwell's equations

Notes: Sections V14 and V15
34Final review
35Final review (cont.)

 








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