Mathematics 251: Multivariable Calculus

Rutgers University, Fall 2008

Anders Buch (asbuch at math dot rutgers period edu)

TTh5, Tuesday and Thursday 3:20 PM - 4:40 PM in Hill-116

Course web site:

http://sites.math.rutgers.edu/~asbuch/calc251_f08/

Watch this page for announcements!

Text:

Rogawski, Calculus Early Transcendentals, W. H. Freeman, 2008, ISBN-10: 0-7167-7267-1.

This book has been augmented with some Rutgers "local matter," which is also available at http://sites.math.rutgers.edu/courses/151-152/lm.pdf.

Office Hours:

Tuesday and Thursday 4:20 - 5:20 in Hill Center 234.

Grading:

Weekly quizzes: 10%

Maple assignments: 10%

Midterm 1, Thursday, October 9 in class: 20%

Midterm 2, Thursday, November 13 in class: 20%

Final exam, Monday, December 22, 12:00-3:00 PM in Hill-116: 40%

Note: The duration of the final may be less than 3 hours.

Recitation classes:

Instructor: Amit Priyadarshi

Section 07: W2, 10:20 AM - 11:40 AM in SEC-202

Section 08: W3, 12:00 PM - 1:20 PM in ARC-108

Section 09: W4, 1:40 PM - 3:00 PM in SEC-206

Note: Each recitation class will have a 10 minute quiz.

Maple Assignments

There will be 4 graded Maple Labs during this course.

Details can be found on Amit Priyadarshi's 251 page.

Maple Lab 1: Due Wednesday, October 1, in recitation.

Maple Lab 2: Due Wednesday, October 22, in recitation.

Maple Lab 3: Due Wednesday, November 5, in recitation.

Maple Lab 4: Due Wednesday, December 3, in recitation.

Syllabus:

Lecture	Text sections	Homework problems
1	12.1 Vectors in the Plane 12.2 Vectors in Three Dimensions	12.1: 5, 9, 11, 15, 21, 40, 47 12.2: 11, 13, 19, 25, 27, 31, 51
2	12.3 Dot Product and the Angle Between Two Vectors 12.4 The Cross Product	12.3: 1, 13, 21, 29, 31, 52, 57, 63 12.4: 1, 5, 13, 20, 25, 26, 43, 44
3	12.5 Planes in Three-Space	12.5: 1, 9, 11, 15, 25, 31, 53
4	13.1 Vector-Valued Functions 13.2 Calculus of Vector-Valued Functions	13.1: 5, 13, 15, 18 13.2: 4, 14, 30, 31, 33, 41, 49
5	13.3 Arc Length and Speed 13.4 Curvature 13.5 Motion in Three-Space	13.3: 3, 9, 13, 14 13.4: 1, 7, 17, 21 13.5: 3, 6, 32
6	14.1 Functions of Two or More Variables 14.2 Limits and Continuity in Several Variables	14.1: 7, 20, 23, 27, 36, 40 14.2: 5, 15, 27, 35
7	14.3 Partial Derivatives 14.4 Differentiability, Linear Approximation and Tangent Planes	14.3: 3, 19, 21, 39, 47, 50, 53 14.4: 3, 4, 7, 15, 27, 33
8	14.5 The Gradient and Directional Derivatives	14.5: 7, 13, 27, 31, 33, 37, 39, 43
9	14.6 The Chain Rule	14.6: 1, 5, 7, 17, 20, 23, 27, 30
10	14.7 Optimization in Several Variables	14.7: 1, 3, 7, 17, 19, 24, 25, 27, 29
11	14.8 Lagrange Multipliers: Optimizing with a Constraint	14.8: 2, 7, 11, 13, 15
12	Midterm 1 (October 9)
13	15.1 Integration in Several Variables	15.1: 10, 15, 23, 25, 33, 37, 44
14	15.5 Double Integrals over More General Regions	15.2: 3, 5, 11, 25, 32, 37, 43, 45, 49, 59
15	15.3 Triple Integrals	15.3: 3, 5, 11, 15, 17, 25, 33
16	12.7 Cylindrical and Spherical Coordinates 15.4 Integration in Polar, Cylindrical, and Spherical Coordinates	12.7: 1, 5, 23, 31, 41, 43, 48, 53 15.4: 1, 5, 9, 19, 23, 27, 31, 37, 39, 42, 47, 51, 59
17
18	15.5 Change of Variables	15.5: 1, 5, 14, 15, 21, 29, 33, 37
19	16.1 Vector Fields	16.1: 1, 3, 10, 17, 23, 27
20	16.2 Line Integrals	16.2: 3, 9, 13, 21, 27, 35, 39, 40
21	16.3 Conservative Vector Fields	16.3: 1, 5, 9, 13, 17, 19, 21
22	Midterm 2 (November 13)
23	16.4 Parameterized Surfaces and Surface Integrals	16.4: 1, 5, 8, 11, 19, 21, 37
24	16.5 Surface Integrals of Vector Fields	16.5: 1, 6, 9, 12, 15, 17, 23
25	17.1 Green's Theorem	17.1: 1, 3, 6, 9, 12, 23, 27
26	17.2 Stokes' Theorem	17.2: 1, 5, 9, 11, 19, 23
27	17.3 Divergence Theorem	17.3: 1, 5, 7, 11, 14, 15, 18
28	Review