Fall-2013. Math 53. Multivariable Calculus (ccn: 53913)

Lectures: by Alexander Givental, TuTh 8-9:30, in 155 Dwinelle
Office hours: Th 3:30-5 pm in 701 Evans
Grading: Final exam (40%)+Midterm I (10%)+Midterm II (20%)+Discussion section grade (30%)
Textbook: James Stewart, Multivariable Calculus. Early Transcendentals for UC Berkeley. Seventh Edition.
ISBN-13: 978-1-285-13239-6
This is a reprint of chapters 10, 12-16 from the 7th edition of Stewart's "Calculus. Early Transcendentals",
tailored for UC Berkeley multivariable calculus courses.
Homework: Exercises to solve are posted here by weeks.
Written solutions are due on Fri of the next week at the discussion section.
Enrollment issues: Contact Thomas Brown thomasbrown_at_berkeley_dot_edu
Midterm I: Tuesday, September 24 (Chapter 12 + Section 10.5)
Midterm II: Tuesday, October 29 (Chapters 13, 14)
Final Exam: Wednesday, December 18, 2013, 3-6 pm
All exams are "closed books, closed notes, no calculators"

Practice problems for Midterm I
Practice problems for MIdterm II
Practice problems for the final

Syllabus

Week 1 (Th, Aug. 28) Introduction. Vectors. Dot-product.
Read: 12.1-12.3
Solve (due 09.06): 12.2(3,8,29,38,39,44,46,51), 12.3(1,12,26,29, 50,62, 63,64)

Week 2: Cross-product. Applications
Read: 12.4-12.5
Solve (due 09.13): 12.4(2,7,20,31,33,38) 12.5(5,7,12,19,27,34.43,51)

Week 3: Quadratic functions, curves, surfaces.
Read: 12.6, 10.5
Solve (due 09.20): 10.5(16,25,26,27,34) 12.6(6,8,21-28)

Week 4: Vector functions.
Read: 13.1, 13.2, 13.3 (arc length)
Solve (due 09.27): 13.1(21-26,48) 13.2(23,45) 13.3(3,11,13)

Week 5: Scalar functions of several variables. Midterm I (Ch. 12, Sect. 10.5), Tue, Sep. 24
Read: 14.1, 14,2, 14.4
Solve (due 10.04): 14.1(51,52,59-64) 14.2(10,16,36) 14.4(17,35,45,46)

Week 6: The chain rule.
Read: 14.3, 14.5
Solve (due 10.11): 14.3(67,69,80,95,101abcde) 14.5(7,13,24,28,34,53,55,58)

Week 7: Gradient. Maximum and minimum values
Read: 14.6-14.7
Solve (due 10.18): 14.6(20,21,29,41,45,56), 14.7(9,12,15,29,30,50,55)

Week 8: Constraint extrema (Lagrange multipliers)
Read: 14.8
Solve (due 10.25): 14.8(7,11,19,25,26,38,41,45)

Week 9: Multiple integrals
Read: 15.1-15.3,15.7,15.10
Solve (due 11.01): 15.2(7,17,27) 15.3(9,15,29,32,,43,52) 15.7(33-36) 15.10(5,9,24)

Week 10: Change of variables. Applications / Midterm II (Ch. 13,14), Tuesday, Oct. 29
Read: 15.4, 15.5, 15.7-15.9
Solve (due 11.08): 15.4(7,11,22,41) 15.5(13,14,15,19) 15.8(15,16,29,30) 15.9(17,18,39,40)

Week 11: Vector fields. Line integrals.
Read: 16.1-16.3
Solve (due 11.15): 16.1(6,11-14,26,29-32) 16.2(3,14,22,27,37,39) 16.3(6,16,23,29,31-34)

Week 12: Green's Theorem. Curl and divergence.
Read: 16.4, 16.5
Solve (due 11.22): 16.4(2,4,12,21,22,24,27) 16.5(4,5,9-11,15,27,29,30,32,37)

Week 13: Surface integrals
Read: 16.6, 16.7
Solve (due Wed, 11.27): 16.6(3-6,13-18,35,48) 16.7(8,20,23,37,39,46)

Weeks 14-15 Stokes' and Gauss' Theorems (11.28, Th=Thanksgiving)
Read: 16.8, 16.9
Solve (due 12.11): 16.8(2,6,13,15,18,19) 16.9(4,6,13,23,26,28,31)

Dec. 9-13: RRR week