Understanding Multivariable Calculus : Problems, Solutions, and Tips

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Thirty-six thirty minute lectures.
Disc 1: 1. A visual introduction to 3-D calculus -- 2. Functions of several variables -- 3. Limits, continuity, and partial derivatives -- 4. Partial derivatives: one variable at a time -- 5. Total differentials and chain rules -- 6. Extrema of functions of two variables -- disc 2: 7. Applications to optimization problems -- 8. Linear models and least squares regression -- 9. Vectors and the dot product in space -- 10. The cross product of two vectors in space -- 11. Lines and planes in space -- 12. Curved surfaces in space -- disc 3: 13. Vector-valued functions in space -- 14. Kepler's Laws: the calculus of orbits -- 15. Directional derivatives and gradients -- 16. Tangent planes and normal vectors to a surface -- 17. Lagrange multipliers: constrained optimization -- 18. Applications of lagrange multipliers -- disc 4: 19. Iterated integrals and area in the plane -- 20. Double integrals and volume -- 21. Double integrals in polar coordinates -- 22. Centers of mass for variable density -- 23. Surface area of a solid -- 24. Triple integrals and applications -- disc 5: 25. Triple integrals in cylindrical coordinates -- 26. Triple integrals in spherical coordinates -- 27. Vector fields: velocity, gravity, electricity -- 28. Curl, divergence, line integrals -- 29. More line integrals and work by a force field -- 30. Fundamental theorem of line integrals -- disc 6: 31. Green's Theorem: boundaries and regions -- 32. Applications of Green's Theorem -- 33. Parametric surfaces in space -- 34. Surface integrals and flux integrals -- 35. Divergence Theorem: boundaries and solids -- 36. Stokes's Theorem and Maxwell's Equations.
Lecturer: Dr. Bruce H. Edwards, Professor of Mathematics at the University of Florida.
DVD.

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