Calculus of Several Variables: Math 10B
Winter 2005, MWF 8:10-9:00 a.m. in Sproul Hall 2340
Announcements
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We talked about some physics and engineering applications of the material in this course. If you want to see more mathematical applications, take a look at these notes.
Illustration for the Jordan curve example (look at the picture at the very end).
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The final exam will be held on Wednesday, March 16, 3-6 p.m., in the usual classroom. It will be comprehensive, and will cover sections 5.1-5.5, 6.1-6.3, 7.1-7.6, 8.1-8.4.
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The last quiz will be on March 10.
Homework
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Homework 7, due March 10.
- Read Chapter 8.
- Section 8.1, problems 3a, 6a, 7.
- Section 8.2, problems 5, 9, 10, 23.
- Section 8.3, problems 3, 4, 12, 13, 15a, 17.
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The second midterm was held on Friday, February 25, during class. It covered mostly Chapter 7. It has now been graded, and the results are available on iLearn.
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Homework 6, due February 24.
- Read Chapter 7.
- Section 7.4, problems 3, 4, 12.
- Section 7.5, problems 1, 7, 10, 11.
- Section 7.6, problems 1, 2, 4, 5.
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Homework 5, due February 17.
- Read sections 7.1-7.4.
- Section 7.1, problems 3a, 4a, 12. Do not do problem 12 part (b).
- Section 7.2, problems 1ab, 2ad, 4, 6, 10, 15.
- Section 7.3, problems 1, 5. Do not do problem 3.
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The first midterm was held on Wednesday, February 2, during class. It has now been graded, and the results are available on iLearn. Practice midterm I consisted of problems 3,7 from the Review Exercises for Chapter 5, and problems 6, 16 from the Review Exercises for Chapter 6.
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Homework 4, not to be turned in, for practice only.
- Read sections 6.3-6.4.
- Section 6.3, problems 1, 5, 12, 14, 15.
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Homework 3, due January 27.
- Read Chapter 6
- Section 6.2, problems 2, 3, 8, 9, 19, 23, 24, 27.
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Homework 2, due January 20.
- Read Chapter 5, sections 6.1-6.3.
- Section 5.4, problems 1a, 2ac, 14.
- Section 5.5, problems 1, 3, 7, 11, 13.
- Section 6.1, problems 1, 3, 7.
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Homework 1, due January 13.
- Read Chapter 5.
- Section 5.1, problems 1a, 2a, 4, 9.
- Section 5.2, problems 1bc, 2bc, 6, 12.
- Section 5.3, problems 1, 8.
Syllabus
Professor: Michael Anshelevich, 250 Surge.
Office hours: MW 9-10, F 10-11 a.m.
TA: Thao-Nhi Luu, discussion sections Thursdays 1-2, 7-8 p.m.
Text: Marsden and Thomba, Vector Calculus, 5th ed., Freeman, 2003. Supplementary material is available at this website.
Prerequisites: Single-variable integration (Math 9BC), vectors, vector-valued functions, multi-variable differentiation (Math 10A).
Course outline:
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Integration over regions and volume (Chapter 5).
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Change-of-variable formula for multiple integrals (Chapter 6).
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Integration over paths and surfaces (Chapter 7).
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Fundamental theorems of vector calculus (Chapter 8).
Exams: We will have in-class midterms on February 2nd and February 25th. The final exam is on Wednesday, March 16th, 3-6 p.m. No make-up exams will be given. If, under completely exceptional circumstances, you need to miss a midterm, the weights of the other exams will be adjusted accordingly. If you miss the final, you automatically fail the course. The exams are closed book, closed notes, and calculators are not permitted.
Homework: Weekly, due on Thursdays in section. Homework problems will appear on the exams and quizzes. No late homework will be accepted; the lowest score will be dropped. You are encouraged to work together, but you must each turn in your own work.
Quizzes: There will be 4 short quizzes in the discussion section, announced in advance. The lowest score will be dropped.
Grading: Section (homework, quizzes, participation) 20%, each midterm 20%, final 40%.
Other important dates: January 21 (last day to add or drop a course), February 11 (last day to withdraw from a course).
Students with disabilities: Come talk to me no later than the first week of classes.
Keys to success: Solve all the homework problems, well before the exams. Read the homework solutions, after working on the problems, to make sure you know how to do all of them. Spend more than six hours per week working on the problems. Form study groups to discuss the course material and homework problems. Read ahead in the text.