2009 Summer Calculus 120S

The book for the course is "Calculus, Math 120, Yale University", by James Stewart, published by Cengage Learning (2009). This is a part (Chapters 12-16, and the Appendix) of "Multivariable Calculus Early Transcendentals" by the same author.

Here is the plan of the course:
  1. July 6        Sections 12.1, 12.2 - Coordinates and vectors.
  2. July 7        12.3, 12.4 - Dot product, projections, cross product.
  3. July 8        12.5 - Equations of lines and planes.
  4. July 9        13.1, 13.2 - Vector functions and space curves, Derivatives and integrals of vector functions.
  5. July 10      13.3 (arclength only), 13.4 (excluding tangent/normal decomposition and Kepler's laws) - Arclength, velocity and acceleration.
  6. July 13      14.1 - Functions of several variables, graphs, level curves.
  7. July 14      14.2, 14.3 - Limits and continuity, partial derivatives.
  8. July 15      14.4 - Tangent planes and linear approximations.
  9. July 16      14.5 - The chain rule and implicit differentiation.
  10. July 17      14.6 - Directional derivatives, the gradient vector, tangent planes to level surfaces.
  11. July 20      14.7 - Maxima and minima.
  12. July 21      15.1, 15.2 - Volumes and double integrals, average values, iterated integrals, Fubini's theorem.
  13. July 22      15.3 - Double integrals over general regions, types of regions, properties.
  14. July 23      15.4, 16.1 - Double integrals in polar coordinates, vector fields.
  15. July 24      16.2 - Line integrals of functions, line integrals of vector fields.
  16. July 27      16.3 - The fundamental theorem for line integrals, conservative vector fields, path independence.
  17. July 28      16.4 - Green's theorem.
  18. July 29      16.5 - Curl and divergence, properties, vector form of Green's theorem.
  19. July 30      16.6 - Parametric surfaces, tangent planes, surface area.
  20. July 31      16.7 - Surface integrals, orientation, surface integrals of vector fields.
  21. Aug 3        16.8 - Stokes' theorem.
  22. Aug 4        15.6, 15.7 - Triple integrals, Fubini's theorem, types of solid regions, triple integrals in cylindrical coordinates.
  23. Aug 5        15.8 - Triple integrals in spherical coordinates.
  24. Aug 6        16.9 - The divergence theorem.
  25. Aug 7        Final exam