Math 53: Schedule and homework assignments
Michael Hutchings, Spring 2014
- Please note that
topics listed for a given lecture may be covered in the previous or
subsequent lecture.
- Each lecture lists the sections of the book that will be covered; it is best to read these before the lecture if possible.
- Sections of the book that do not appear below (e.g. 10.6) will not be covered in the course, and reading these is optional.
- Quizzes will emphasize the sections listed but may review earlier material as needed.
- For extra practice, the review problems at the end of each chapter are highly recommended.
Part 1. Geometric preliminaries.
- Lecture Jan 21. Introduction; parametrized curves. 10.1, 10.2.
- Lecture Jan 23. Polar coordinates. 10.3, 10.4.
- Homework due Jan 24.
10.1: 9, 19, 21, 24, 28, 31, 33, 37, 45.
- Homework due Jan 27.
10.2: 3, 7, 11, 17, 31, 41, 51.
10.3: 11, 19, 23, 39, 54, 55.
- Lecture Jan 28. Three-dimensional space, vectors, dot product. 12.1, 12.2, 12.3.
- Quiz Jan 29: covers 10.1-10.3.
- Lecture Jan 30. Determinant, cross product. 12.4.
- Homework due Jan 31:
10.4: 5, 17, 27, 31, 41, 47.
12.1: 7, 20, 33, 41.
12.2: 7, 25, 29, 51.
- Homework due Feb 3:
12.3: 1, 11, 35, 27, 55, 63, 64.
12.4: 13, 19, 29, 43, 44, 48, 53.
- Lecture Feb 4. Lines and planes, quadric surfaces. 12.5, 12.6.
- Quiz Feb 5: covers 10.4, 12.1-12.4.
- Lecture Feb 6. Vector-valued functions, space curves. 13.1, 13.2.
- Homework due Feb 7: 12.5: 1, 5, 7, 19, 27, 39, 45, 53, 61, 71.
12.6: 21-28, 41, 45.
- Homework due Feb 10:
13.1: 21-26, 27, 41, 47.
13.2: 3, 23, 27, 41, 51, 53, 54.
Part 2. Differentiation.
- Lecture Feb 11. Functions of several variables. Limits and continuity. 14.1, 14.2.
- Quiz Feb 12: covers Part 1.
- Lecture Feb 13. Partial derivatives, tangent planes, linear approximation. 14.3, 14.4.
- Homework due Feb 14. 14.1: 13, 36, 59-64, 65, 69. 14.2: 5, 7, 9, 11, 13, 29, 31, 39.
- Lecture Feb 18. The chain rule. 14.5.
- Homework due Feb 19. 14.3: 10, 25, 45, 47, 51, 53, 61, 74, 77. 14.4: 1, 3, 19, 21, 25, 35.
- Quiz Feb 19: covers 14.1-14.4.
- Lecture Feb 20. Directional derivative, gradient, maxima and minima. 14.6, 14.7.
- Homework due Feb 21: 14.5: 5, 7, 13, 14, 15, 21, 27, 31, 35, 39, 45, 53.
- Homework due Feb 24. 14.6: 7, 11, 21, 41, 49, 51, 63. 14.7: 3, 5, 29, 31, 39, 41, 47.
- Lecture Feb 25. More maxima and minima. Lagrange multipliers. 14.8.
- Quiz Feb 26: covers 14.5, 14.6, 14.7.
- Lecture Feb 27: Review for the midterm.
- No homework due Feb 28.
- No homework due Mar 3.
- Mar 4: Midterm #1, in class. Covers up to 14.7.
Part 3. Integration.
- Lecture Mar 6: Double integrals. 15.1, 15.2, 15.3.
- Homework due Mar 7: 14.8: 1, 3, 11, 14, 19, 21, 22, 31, 37. 15.1: 11, 13.
- Homework due Mar 10: 15.2: 3, 15, 19, 24, 25, 31. 15.3: 14, 22, 23, 27, 43, 49, 51, 56.
- Lecture Mar 11: More double integrals. 15.4, 15.5, 15.6.
- Quiz Mar 12: covers 14.8, 15.1, 15.2, 15.3.
- Lecture Mar 13: Triple integrals. 15.7.
- Homework due Mar 14: 15.4: 5, 11, 17, 21, 27, 29, 35. 15.5: 3,9. 15.6: 3, 7.
- Homework due Mar 17: 15.7: 9, 13, 17, 19, 29, 36, 37, 42, 53.
- Lecture Mar 18: Triple integrals in cylindrical and spherical coordinates. 15.8, 15.9..
- Quiz Mar 19: covers 15.4, 15.5, 15.6, 15.7.
- Lecture Mar 20: Change of variables, Jacobian. 15.10.
- Homework due Mar 21: 15.8: 7, 8, 15, 17, 21, 25, 29. 15.9: 7, 15, 21, 23, 27.
- Homework due Mar 31: 15.9: 28, 30, 39. 15.10: 11, 13, 15, 17, 19, 23, 25, 27, 28.
- Lecture Apr 1: Review for the midterm.
- Apr 3: Midterm #2, in class. Covers up to 15.10, with emphasis on 14.8 and Chapter 15.
- No homework due Apr 4.
- No homework due Apr 7.
Part 4. Vector calculus.
- Lecture Apr 8: Vector fields and line integrals. 16.1, 16.2.
- Quiz Apr 9: Reviews material from parts 1 and 2 as needed.
- Lecture Apr 10: The fundamental theorem of line integrals. 16.3.
- Homework due Apr 11: 16.1: 11-18. 16.2: 1, 5, 14, 17, 18, 19, 33.
- Homework due Apr 14: 16.2: 41, 49, 50. 16.3: 3, 5, 7, 13, 19, 25, 26, 31, 33.
- Lecture Apr 15: Green's theorem. 16.4.
- Quiz Apr 16: covers 16.1, 16.2, 16.3.
- Lecture Apr 17: Curl and divergence. Parametrized surfaces. 16.5, 16.6.
- Homework due Apr 18: 16.4: 1, 4, 8, 11, 18, 19, 22, 23, 28, 30.
- Homework due Apr 21: 16.5: 13, 15, 17, 20, 27, 31. 16.6: 1, 13, 14, 23, 34.
- Lecture Apr 22: Surface integrals. 16.7.
- Quiz Apr 23: covers 16.5, 16.5, 16.5.
- Lecture Apr 24: Stokes' theorem. 16.8
- Homework due Apr 25: 16.6: 39, 45, 61. 16.7: 5, 15, 23, 26, 29, 43, 49.
- Homework due Apr 28: 16.8: 3, 7, 9, 11(a), 13, 16, 17, 18.
- Lecture Apr 29: Divergence theorem. 16.9.
- Quiz Apr 30: covers 16.7, 16.8.
- Lecture May 1: Summary and review. 16.10
- Homework due May 2: 16.9: 1, 7, 9, 12, 17, 18, 19, 24, 26.
- No homework due May 5. Optional discussion section for review.
- No lecture May 6.
- No quiz May 7. Optional discussion section for review.
- No lecture May 8.
- No discussion section or homework due May 9.
- Final exam: Thursday May 15, 7pm-10pm, location TBA. Covers the entire class, with more emphasis on Chapter 16.