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English | Mp4 MPEG4 320x240 220 Kbps | AAC 80.0 Kbps 44.1 Khz

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.

Course Features

I. Vectors and matrices

1 Dot product

2 Determinants; cross product

3 Matrices; inverse matrices

4 Square systems; equations of planes

5 Parametric equations for lines and curves

6 Velocity, acceleration - Kepler's second law

7 Review

II. Partial derivatives

8 Level curves; partial derivatives; tangent plane approximation

9 Max-min problems; least squares

10 Second derivative test; boundaries and infinity

11 Differentials; chain rule

12 Gradient; directional derivative; tangent plane

13 Lagrange multipliers

14 Non-independent variables

15 Partial differential equations; review

III. Double integrals and line integrals in the plane

16 Double integrals

17 Double integrals in polar coordinates; applications

18 Change of variables

19 Vector fields and line integrals in the plane

20 Path independence and conservative fields

21 Gradient fields and potential functions

22 Green's theorem

23 Flux; normal form of Green's theorem

24 Simply connected regions; review

IV. Triple integrals and surface integrals in 3-space

25 Triple integrals in rectangular and cylindrical coordinates

26 Spherical coordinates; surface area

27 Vector fields in 3D; surface integrals and flux

28 Divergence theorem

29 Divergence theorem (cont.): applications and proof

30 Line integrals in space, curl, exactness and potentials

31 Stokes' theorem

32 Stokes' theorem (cont.); review

33 Topological considerations - Maxwell's equations

34 Final review

35 Final review (cont.)

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