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Multivariable Calculus >> Content Detail



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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 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 #topicsreadings
I. Vectors and Matrices
1Vectors in 2- and 3-space

Dot Product
Text: Sections 17.3, 18.1, 18.2

2Determinants of Orders 2 and 3

Cross Product
Text: Section 18.3
Notes: Section D
3Matrices; Inverse Matrices
4Solving Systems of Linear Equations; Lines, Planes
5Parametric Curves; Velocity, AccelerationText: Sections 18.4, 17.1, 17.4
6Kepler's Second LawText: 17.7
Notes: Section K
Exam 1 (Covering Lectures 1-6)
II. Partial Derivatives
7Level Curves, Partial Derivatives, Tangent PlaneText: Sections 19.1-19.3
Notes: Section TA
8Max-Min Problems

Least Squares Approximation
Text: Section 19.7
Notes: Section LS
92nd Derivative Test; Boundaries and Infinity
10Differentials; Chain RuleText: Section 19.6
11Gradient, Directional DerivativeText: Section 19.5
12Lagrange MultipliersText: Section 19.8
13Non-independent Variables
14Partial Differential Equations

Review
Text: Section 19.8
Exam 2 (Covering Lectures 7-14)
III. Double and Triple Integrals
15Double and Iterated IntegralsText: Sections 20.1, 20.2
Notes: Section I.1
16Double Integrals in Polar Coordinates

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

Gravitational Attraction
Text: Section 20.7
IV. Vector Calculus in 2 and 3-space
20Line Integrals in the PlaneText: Section 21.1
Notes: Section V1
21Gradient Fields and Path IndependenceText: Section 21.2
Notes: Section V2.1
22Conservative Fields and Potential Functions
23Green's Theorem

2-dimensional Curl (Vorticity)
Text: Section 21.3
Notes: Section V4.3
24Simply-connected Regions

Review
Exam 3 (Covering Lectures 15-24, Except 18-19)
25Flux Form of Green's Theorem
26Vector Fields in 3-space; Surface Integrals and Flux
27Divergence (= Gauss's) TheoremText: Section 21.4
Notes: Section V10
28Divergence Theorem (cont.)
29Line Integrals in Space, Exactness, and Potentials
30Stokes' TheoremText: Section 21.5
Notes: Section V4.3, V13
31Understanding Curl

Review
Exam 4 (Covering Lectures 18-19, 25-31)
32Topological Issues
33Conservation Laws; Heat/Diffusion Equation
34Course Review
35Course Evaluation

Maxwell's Equations
Text: Section 21.6
Notes: Section V15

 








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