Math 53, Fall 2009
Instructor: Edward Frenkel
GSI: Dario Beraldo
Discussion times :
- Section 106: 3102 Etcheverry, MWF 10-11
- Section 107: 7 Evans, MWF 11-12
Office: 835 Evans
Office Hours: Thu 5:10-6:10pm, Fri 12:05-1:05pm, or by appointment
Useful pages
The page of the course on b-space
Old Math53 exams
Topics covered and quizzes
- 8/26. Introduction.
- 8/28. Parametric equations of cycloid and hypocycloid. Astroid, using complex exponentials.
- 8/31. Folium of Descartes. Cissoids: cissoid of Diocles, the folium as a cissoid.
- 9/02. Length of some hypocycloids. Quiz #1.
- 9/04. Areas in polar coordinates. Polar equations of the folium and area of the leaf.
- 9/07. Beach time.
- 9/09. Q&A. A trig identity using dot products. Quiz #2. Solution
- 9/11. Lines and planes in the space.
- 9/14. Q&A. Quiz #3. Solution
- 9/16. Quadric surfaces. Curves in the space; the helix.
- 9/18. Derivatives of vector functions. Functions of several variables and limits.
- 9/21. Q&A. Quiz #4. Solution
- 9/23. (Too) many partial derivatives.
- 9/25. Tangent planes and differentials.
- 9/28. Q&A. Worksheet. Solution
- 9/30. Review.
- 10/2. Discussion of the midterm.
- 10/5. Chain rule.
- 10/7. Directional derivatives and gradient.
- 10/9. Maxima and minima of functions of two variables.
- 10/12. Q&A. Quiz #5. Solution
- 10/14. Lagrange multipliers.
- 10/16. Some double integrals.
- 10/19. Q&A. Quiz #6. Solution
- 10/21. Double integrals in polar coordinates. Volume of the sphere.
- 10/23. Lagrange multipliers revisited. Triple integrals.
- 10/26. Q&A. Quiz #7. Solution
- 10/28. Spherical coordinates.
- 10/30. Change of variables in double (triple) integrals.
- 11/02. Q&A. Worksheet. Solution
- 11/04. Review.
- 11/06. Discussion of the midterm.
- 11/09. Vector fields. Curve integrals.
- 11/11. No class.
- 11/13. Conservative vector fields and fundamental theorem of curve integrals.
- 11/16. Q&A. Quiz #8. Solution
- 11/18. Green's formula and applications.
- 11/20. Surfaces in parametric form. Tangent plane to a parametric surface.
- 11/23. Q&A. Quiz #9. Solution
- 11/25. Surface integrals. Orientation and flux of a vector field across a surface.
- 11/27. Black Friday.
- 11/30. Q&A. Stokes' theorem.
- 12/02. Stokes' theorem again.. Quiz #10. Solution (it's finally here!)
- 12/04. Divergence theorem and applications.