Math 215 — Calculus III

This webpage contains my lecture notes and exam solutions for Math 215 at the University of Michigan.


Lecture notes

  1. §12.1. Coordinate systems
  2. §12.2. Vectors, §12.3. The dot product
  3. §12.4. The cross product
  4. §12.5. Equations of lines and planes I
  5. §12.5. Equations of lines and planes II, §12.6. Cylinders and quadric surfaces
  6. §13.1 + 13.2. Vector functions and curves
  7. §13.3. Arclength and curvature
  8. §13.4. Motion in space
  9. §14.1. Functions of several variables
  10. §14.3. Partial derivatives
  11. §14.4. Tangent planes and linear approximations
  12. §14.5. The chain rule
  13. §14.6. Directional derivatives and the gradient vector
  14. §14.7. Maximum and minimum values: local extrema
  15. §14.7. Maximum and minimum values: global extrema
  16. §14.8. Lagrange multipliers
  17. §15.1. Double integrals over rectangles
  18. §15.2. Double integrals over general regions: definitions
  19. §15.2. Double integrals over general regions: properties
  20. §15.3. Double integrals in polar coordinates
  21. §15.4 + 15.5. Applications of double integrals
  22. §15.6. Triple integrals: definitions and properties
  23. §15.6. Triple integrals: examples
  24. §15.17 + 15.8. Triple integrals in cylindrical/spherical coordinates
  25. §16.1. Vector fields
  26. §16.2. Line integrals
  27. §16.3. The fundamental theorem for line integrals
  28. §16.4. Green's theorem
  29. §16.5. Curl and divergence
  30. §16.6. Parametric surfaces
  31. §16.7. Surface integrals: scalar functions
  32. §16.7. Surface integrals: vector fields
  33. §16.8. Stokes' theorem
  34. §16.9. The divergence theorem


Past exam solutions

Exam 1

Exam 2

Final exam