Calculus of Several Variables

MATH 4013


Time and Place: MWF 11:30-12:20 in HES 316
Professor: Igor E. Pritsker
Office: MSCS 524
Office Hours: MWF 10:30-11:30
Office Phone: 744-8220
E-mail: igor@math.okstate.edu
Web: http://www.math.okstate.edu/~igor/math4013/math4013_spring2008.html
Textbook: Vector Calculus, by J. E. Marsden and A. J. Tromba, W. H. Freeman and Co, 5th Ed.


Grading: There will be three semester tests and the Final Exam. The break up of your course grade is as follows:
Tests 1-3 60% (20% each)
Quizzes 10%
Final Exam 30%
Your grade will be determined according to the scale
A 90-100
B 80-89
C 70-79
D 60-69
F 59 and lower
Note that the above numbers are percentages of the highest possible score in the course.

Quizzes: Be prepared for short quizzes (1-2 problems, about 10 minutes).

Homework will be assigned on a daily basis (see the schedule) and may be collected periodically. It is required that you complete all homework.

Make-up Exams are given only in cases of serious illness or extreme emergency that prevents you from taking a test at the specified time. You have to contact me before the test and communicate all circumstances. Furthermore, you must appear in person, with supporting documents, to discuss the situation as soon as possible.

Technology: You will find that mathematical software is very useful for visualization and computations in this course. Any of the following packages is sufficient for our purposes: Maple, Mathematica or MATLAB.

Brief Schedule
Chapter 1 Chapter 3 Chapter 5 Chapter 7
Chapter 2 Chapter 4 Chapter 6 Chapter 8
Test 1 Test 2 Test 3 Final Exam

University Syllabus Attachment: Contains drop deadlines and procedures, as well as many other important dates and university policies.

Lecture Notes by Dr. Binegar

Catalog of Quadric Surfaces by Dr. Myers


Note: The homework problems below are to be assumed odd numbered, unless it is indicated otherwise.

Detailed Schedule
Week Date Sec Page Topic Homework
1 M, Jan 7 1.1 1 Vectors in 2 and 3 dimensional space 5-9, 13-23, 24
W, Jan 9 1.2 23 The inner product, length and distance 3-9, 15-21, 25
F, Jan 11 1.3 38 Matrices, determinants and the cross product 3-11, 15, 25-29
2 M, Jan 14 1.4 65 Cylindrical and spherical coordinates 1-9
W, Jan 16 1.5 74 n-Dimensional Euclidean space 5-13
F, Jan 18 2.1 94 The geometry of real-valued functions 7-17, 23-27
3 M, Jan 21 Martin Luther King Jr. Day
W, Jan 23 2.2 107 Limits and continuity 1, 5-17
F, Jan 25 2.3 127 Differentiation 3-17
4 M, Jan 28 2.4 141 Introduction to paths 5-9, 13-17
W, Jan 30 2.5 150 Properties of the derivative 1-9, 13-15
F, Feb 1 2.6 163 Gradients and directional derivatives 3-5, 9-15
5 M, Feb 4 Test 1
W, Feb 6 3.1 182 Iterated partial derivatives 1-11
F, Feb 8 3.2 193 Taylor's theorem 1-5
6 M, Feb 11 3.3 203 Extrema of real-valued functions 1-9, 17, 29-33
W, Feb 13 3.3 203 Extrema of real-valued functions 1-9, 17, 29-33
F, Feb 15 3.4 225 Constrained extrema and Lagrange multipliers 1-13, 21
7 M, Feb 18 3.4 225 Constrained extrema and Lagrange multipliers 1-13, 21
W, Feb 20 4.1 261 Acceleration and Newton's second law 1-7
F, Feb 22 4.2 274 Arc length 1-9
8 M, Feb 25 7.1 421 The path integral 1-7
W, Feb 27 4.3 285 Vector fields 5-15
F, Feb 29 4.4 294 Divergence and curl 7-17, 23-25
9 M, Mar 3 Test 2
W, Mar 5 5.1 317 Introduction 1-3, 7-11
F, Mar 7 5.2 327 The double integral over a rectangle 1-7, 11
10 M, Mar 10 5.3 341 The double integral over more general regions 1-11
W, Mar 12 5.4 349 Changing the order of integration 1-9
F, Mar 14 5.6 354 The triple integral 3-9, 13-17, 23-25
11 Mar 15-23 Spring Break
12 M, Mar 24 6.1 369 The geometry of maps from R^2 to R^2 1-9
W, Mar 26 6.2 376 The change of variables theorem 1-5, 13-19, 23, 31
F, Mar 28 6.3 393 Applications of double and triple integrals 1-5, 9-13
13 M, Mar 31 Test 3
W, Apr 2 7.2 429 Line integrals 1-11, 15
F, Apr 4 7.3 451 Parametrized surfaces 1-11
14 M, Apr 7 7.4 461 Area of a surface 1-5, 11-15
W, Apr 9 7.5 474 Integrals of scalar functions over surfaces 1-11
F, Apr 11 7.6 483 Surface integrals of vector fields 1-11
15 M, Apr 14 8.1 518 Green's theorem 3-13
W, Apr 16 8.2 532 Stokes' theorem 3-11
F, Apr 18 8.3 550 Conservative fields 1-9, 13, 15
16 M, Apr 21 8.4 561 Gauss' theorem 1-9
W, Apr 23 Final Review
F, Apr 25 Final Review
17 W, Apr 30 Final Exam (HES 316, 10-11:50 a.m.)