# Mathematics 251: Multivariable Calculus

### Course web site:

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

### 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.

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:

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 Plane12.2 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 Vectors12.4 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 Functions13.2 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 Curvature13.5 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 Derivatives14.4 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 Coordinates15.4 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