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Multivariable Calculus >> Content Detail



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Calendar

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

Dot Product
2Determinants of Orders 2 and 3

Cross Product
3Matrices; Inverse Matrices
4Solving Systems of Linear Equations; Lines, Planes
5Parametric Curves; Velocity, AccelerationProblem set 1 due
6Kepler's Second Law
Exam 1 (Covering Lectures 1-6)Problem set 2 due
II. Partial Derivatives
7Level Curves, Partial Derivatives, Tangent Plane
8Max-Min Problems

Least Squares Approximation
92nd Derivative Test; Boundaries and InfinityProblem set 3 due
10Differentials; Chain Rule
11Gradient, Directional Derivative
12Lagrange MultipliersProblem set 4 due
13Non-independent Variables
14Partial Differential Equations

Review
Exam 2 (Covering Lectures 7-14)Problem set 5 due
III. Double and Triple Integrals
15Double and Iterated Integrals
16Double Integrals in Polar Coordinates

Applications
17Change of VariablesProblem set 6 due
18Triple Integrals in Rectangular and Cylindrical Coordinates
19Spherical Coordinates

Gravitational Attraction
IV. Vector Calculus in 2 and 3-space
20Line Integrals in the PlaneProblem set 7 due
21Gradient Fields and Path Independence
22Conservative Fields and Potential Functions
23Green's Theorem

2-dimensional Curl (Vorticity)
Problem set 8 due
24Simply-connected Regions

Review
Exam 3 (Covering Lectures 15-24, Except 18-19)Problem set 9 due
25Flux Form of Green's Theorem
26Vector Fields in 3-space; Surface Integrals and Flux
27Divergence (= Gauss's) TheoremProblem set 10 due
28Divergence Theorem (cont.)
29Line Integrals in Space, Exactness, and Potentials
30Stokes' TheoremProblem set 11 due
31Understanding Curl

Review
Exam 4 (Covering Lectures 18-19, 25-31)
32Topological IssuesProblem set 12 due
33Conservation Laws; Heat/Diffusion Equation
34Course Review
35Course Evaluation

Maxwell's Equations

 








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