18.02 | Fall 2007 | Undergraduate
Multivariable Calculus

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.)

Course Info
Instructor
Departments
As Taught In
Fall 2007
Learning Resource Types
theaters Lecture Videos
assignment Problem Sets
grading Exams with Solutions
notes Lecture Notes