Fall-07. Math 53. Multivariable Calculus (ccn: 54499)

Lectures: by Alexander Givental, TuTh 12:30 - 2, in 100 Lewis
Office hours: TuTh 5:10 - 6, in 701 Evans
Grading: Final (40%)+Midterm I (20%)+Midterm II (20%)+Quizzes (20%)
Final Exam: Wednesday, December 19, 2007, 12:30-3:30
Enrollment: For all enrollment issues visit the website of the be handled by the head TA Aubrey Clayton at http://math.berkeley.edu/~aclayton/math53

Rules for Midterms: They are 80 minute exams during Thursday's lecture time. Closed books, closed notes, no "cheat sheets", no calculators. You don't need "blue books" but may bring scratch paper. Pen or pencil - either is OK. Here is a practice exam for your convenience. And another one, for Midterm II.

Syllabus Text: Multivariable Essential Calculus by Stewart, UC Berkeley custom edition (ISBN: 0495439460).

Week 1: Vectors, dot-product, cross-product
Read: 10.1-10.4
Solve: 10.2(23,26,33) 10.3(19,27,32,37) 10.4(2,7,14,31,33,45)

Week 2: Geometry of linear and quadratic functions
Read: 10.5, 10.6
Solve: 10.5(5,7,12,19,27,34.43,51) 10.6(13,14,17,19,30,32)

Week 3: Quadratic curves and surfaces / Polar, cylindrical and spherical coordinates
Read: part of 9.5, 10.6, part of 12.6,12.7
Solve: 10.6(16,25,26,27,34) 12.6(7,8,9,10) 12.7(9,10,13,14)

Week 4: Vector-functions and parametric curves
Read: 9.1,9.2, 10.7-10.9
Midterm I: Thursday, September 20; covers 10.1-10.6, 9.3,9.5, partly 12.6,12.7
Solve: 10.7(17-22,51,62,75,77) 10.8(2,8)

Week 5: Kepler's laws / Functions of several variables
Read: 10.9, 11.1-11.3
Solve: 10.9(15,18,32), 11.1(13,19,20,29,32,34), 11.2(13,15,26,28,30) 11.3(51-56)

Week 6: Differentiability, Clairaut's Theorem / The chain rule
Read: 11.4, 11.5
Solve: 11.4(5,13,19,26,36) 11.5(4,20,24,28,37,42,47)

Week 7: Gradient / Extrema, classification of critical points
Read: 11.6, 11.7
Solve: 11.6(19,27,29,39,40,47) 11.7(2,12,16,23,35,45)

Week 8: Constraint extrema / Finding maximum and minimum values
Read: 11.8
Solve: 11.8(5,10,16,23,24,29,37,38,39,43,44)

Week 9: Double integrals, Fubini's Theorem
Read: 12.1,12.2
Midterm II: Thursday, October 25; covers 10.7-10.9, 11.1-11.8
Solve: 12.1(16,18,28,38) 12.2(9,13,21,28,33,42,48).

Week 10: Triple integrals / Change of variables
Read: 12.5, 12.8
Solve: 12.5(6,9,18,25,29,32,33), 12.8(4,5,9,15,19,23)

Week 11: Applications of integration
Read: 12.3,12.4,12.6,12.7
Solve: 12.3(8,13,22,24,31b) 12.4(12,16) 12.6(15,22,29b) 12.7(24,30.40)

Week 12: Vector fields. Newton-Leibnitz's Theorem
Read: 13.1-13.3
Solve: 13.1(6,14,25,27,31) 13.2(3,14,22,27,37,39) 13.3(6,16,21,25,31,32)

Week 13: Green's Theorem
Read: 13.4
Solve: 13.4(2,4,15,21,22,24,27)

Week 14: Curl and divergence / Parametric surfaces & surface integrals
Read: 13.5, 13.6, 13.7
Solve: 13.5(4,10,27,29,30,32) 13.6(31,36,58ac) 13.7(8,11,18)

Week 15: Stokes' and Gauss' Theorems and their applications
Read: 13.7-13.9
Solve: 13.7(20,25,32,33,35) 13.8(2,6,13,15,16c) 13.9(4,6,13,18,20,23,28)