Readings

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

"Text" refers to the course textbook: Amazon logo 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