18.02 | Spring 2006 | Undergraduate

Multivariable Calculus

Calendar

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

Dot Product

2 Determinants of Orders 2 and 3

Cross Product

3 Matrices; Inverse Matrices

4 Solving Systems of Linear Equations; Lines, Planes

5 Parametric Curves; Velocity, Acceleration Problem set 1 due
6 Kepler’s Second Law

Exam 1 (Covering Lectures 1-6) Problem set 2 due
II. Partial Derivatives
7 Level Curves, Partial Derivatives, Tangent Plane

8 Max-Min Problems

Least Squares Approximation

9 2nd Derivative Test; Boundaries and Infinity Problem set 3 due
10 Differentials; Chain Rule

11 Gradient, Directional Derivative

12 Lagrange Multipliers Problem set 4 due
13 Non-independent Variables

14 Partial Differential Equations

Review

Exam 2 (Covering Lectures 7-14) Problem set 5 due
III. Double and Triple Integrals
15 Double and Iterated Integrals

16 Double Integrals in Polar Coordinates

Applications

17 Change of Variables Problem set 6 due
18 Triple Integrals in Rectangular and Cylindrical Coordinates

19 Spherical Coordinates

Gravitational Attraction

IV. Vector Calculus in 2 and 3-space
20 Line Integrals in the Plane Problem set 7 due
21 Gradient Fields and Path Independence

22 Conservative Fields and Potential Functions

23 Green’s Theorem

2-dimensional Curl (Vorticity)

Problem set 8 due
24 Simply-connected Regions

Review

Exam 3 (Covering Lectures 15-24, Except 18-19) Problem set 9 due
25 Flux Form of Green’s Theorem

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

27 Divergence (= Gauss’s) Theorem Problem set 10 due
28 Divergence Theorem (cont.)

29 Line Integrals in Space, Exactness, and Potentials

30 Stokes’ Theorem Problem set 11 due
31 Understanding Curl

Review

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

32 Topological Issues Problem set 12 due
33 Conservation Laws; Heat/Diffusion Equation

34 Course Review

35 Course Evaluation

Maxwell’s Equations

Course Info

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As Taught In
Spring 2006
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Problem Sets
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