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Multivariable Calculus >> Content Detail



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Calendar

LEC #TOPICSKEY DATES
I. Vectors and matrices
0Vectors
1Dot product
2Determinants; cross product
3Matrices; inverse matrices
4Square systems; equations of planesProblem set 1 due
5Parametric equations for lines and curves
6

Velocity, acceleration

Kepler's second law

7ReviewProblem set 2 due
Exam 1 (covering lectures 1-7)
II. Partial derivatives
8Level curves; partial derivatives; tangent plane approximation
9Max-min problems; least squaresProblem set 3 due
10Second derivative test; boundaries and infinity
11Differentials; chain rule
12Gradient; directional derivative; tangent planeProblem set 4 due
13Lagrange multipliers
14Non-independent variables
15Partial differential equations; reviewProblem set 5 due
Exam 2 (covering lectures 8-15)
III. Double integrals and line integrals in the plane
16Double integralsProblem set 6 due
17Double integrals in polar coordinates; applications
18Change of variables
19Vector fields and line integrals in the planeProblem set 7 due
20Path independence and conservative fields
21Gradient fields and potential functions
22Green's theoremProblem set 8 due
23Flux; normal form of Green's theorem
24Simply connected regions; review
Exam 3 (covering lectures 16-24)Problem set 9 due
IV. Triple integrals and surface integrals in 3-space
25Triple integrals in rectangular and cylindrical coordinates
26Spherical coordinates; surface area
27Vector fields in 3D; surface integrals and fluxProblem set 10 due
28Divergence theorem
29Divergence theorem (cont.): applications and proof
30Line integrals in space, curl, exactness and potentials
31Stokes' theoremProblem set 11 due
32Stokes' theorem (cont.); review
Exam 4 (covering lectures 25-32)
33

Topological considerations

Maxwell's equations

Problem set 12 due
34Final review
35Final review (cont.)
36Final exam

 








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