18.02 | Spring 2006 | Undergraduate

Multivariable Calculus

Readings

Listed in the table below are reading assignments for each lecture session.

“Text” refers to the course textbook: Simmons, George F. Calculus with Analytic Geometry. 2nd ed. New York, NY: McGraw-Hill, 1995. ISBN: 0070576424.

“Notes” refers to the “18.02 Supplementary Notes and Problems” written by Prof. Mattuck.

Lec # topics readings
I. Vectors and Matrices
1 Vectors in 2- and 3-space

Dot Product

Text: Sections 17.3, 18.1, 18.2

2 Determinants of Orders 2 and 3

Cross Product

Text: Section 18.3
Notes: Section D
3 Matrices; Inverse Matrices

4 Solving Systems of Linear Equations; Lines, Planes

5 Parametric Curves; Velocity, Acceleration Text: Sections 18.4, 17.1, 17.4
6 Kepler’s Second Law Text: 17.7
Notes: Section K

Exam 1 (Covering Lectures 1-6)

II. Partial Derivatives
7 Level Curves, Partial Derivatives, Tangent Plane Text: Sections 19.1-19.3
Notes: Section TA
8 Max-Min Problems

Least Squares Approximation

Text: Section 19.7
Notes: Section LS
9 2nd Derivative Test; Boundaries and Infinity

10 Differentials; Chain Rule Text: Section 19.6
11 Gradient, Directional Derivative Text: Section 19.5
12 Lagrange Multipliers Text: Section 19.8
13 Non-independent Variables

14 Partial Differential Equations

Review

Text: Section 19.8

Exam 2 (Covering Lectures 7-14)

III. Double and Triple Integrals
15 Double and Iterated Integrals Text: Sections 20.1, 20.2
Notes: Section I.1
16 Double Integrals in Polar Coordinates

Applications

Text: Sections 20.3, 20.4
Notes: Section I.2
17 Change of Variables Text: Section 20.3
18 Triple Integrals in Rectangular and Cylindrical Coordinates Text: Sections 20.5, 10.6
19 Spherical Coordinates

Gravitational Attraction

Text: Section 20.7
IV. Vector Calculus in 2 and 3-space
20 Line Integrals in the Plane Text: Section 21.1
Notes: Section V1
21 Gradient Fields and Path Independence Text: Section 21.2
Notes: Section V2.1
22 Conservative Fields and Potential Functions

23 Green’s Theorem

2-dimensional Curl (Vorticity)

Text: Section 21.3
Notes: Section V4.3
24 Simply-connected Regions

Review

Exam 3 (Covering Lectures 15-24, Except 18-19)

25 Flux Form of Green’s Theorem

26 Vector Fields in 3-space; Surface Integrals and Flux

27 Divergence (= Gauss’s) Theorem Text: Section 21.4
Notes: Section V10
28 Divergence Theorem (cont.)

29 Line Integrals in Space, Exactness, and Potentials

30 Stokes’ Theorem Text: Section 21.5
Notes: Section V4.3, V13
31 Understanding Curl

Review

Exam 4 (Covering Lectures 18-19, 25-31)

32 Topological Issues

33 Conservation Laws; Heat/Diffusion Equation

34 Course Review

35 Course Evaluation

Maxwell’s Equations

Text: Section 21.6
Notes: Section V15

Course Info

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As Taught In
Spring 2006
Learning Resource Types
Problem Sets
Exams