MATH 241 -- CALCULUS III

An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss. All sections of the course will use the software package MATLAB. Math 141 is a prerequisite for this course.

Here is some more basic information about Math 241:

Time & Place: MWF 11-11:50 am, ARM 0135

Instructor:

Professor Richard A. Wentworth
Office: 3109 Mathematics Building
Phone: (301) 405-5130
Office Hours: MWF 10-11 and by appointment
Email: raw@umd.edu
Web: www.math.umd.edu/~raw
TA's:

Mickey Salins, secs. 0211, 0221
Tyler Drombosky, secs. 0212, 0222
Bin Han, secs. secs. 0231, 0241
Alex Cloninger, secs. 0232, 0242
Texts:

Calculus, 6th Edition, by R. Ellis and D. Gulick. Thomson Publishing, 2003. ISBN: 0759313792.
A Guide to MATLAB: For Beginners and Experienced Users, 2nd Edition, by B. Hunt, R. Lipsman, and J. Rosenberg. Cambridge Univ. Press, 2006. ISBN: 0521615658.
Homework: Suggested homework problems will be assigned every week. It is essential that you also try on your own as many similar problems from the book as possible. While homework from the book will not count towards your grade, the periodic quizzes in section will. Quizzes will consist of selected problems from the homework.
Quizzes:

There will be short quizzes periodically (approximately every other week). These will be given in section. The lowest quiz grade will be dropped from the average.

Exams: There will be exams on Sept. 27, Oct. 25, Nov. 17, and Dec. 8. These will be given during the regular lecture period in the regular lecture hall. In addition, there will be a comprehensive final exam. Check the exam schedule for time and room. FINAL EXAM INFO.
Makeups:

There will be no makeups for quizzes or midterms. If you miss a quiz or a midterm, then that will be the midterm or section quiz you will drop. Don't decide an earlier midterm or quiz is going to be your bad score -- if you miss a later one, then that is going to be your bad score. When you have compelling reasons for missing an exam, share them with me or your TA. In particular, if you know before an exam that you have a conflict contact me in advance. In this case, it may be possible to arrange an early exam.
Grading: The final grade will depend on your performance on the exams and quizzes, and completion of the MATLAB exercises. The relative weights I will use are: Best three midterm exams = 60%, Final exam = 25%, Quizzes = 10%, MATLAB exercises = 5%.
Expectations:

You are expected to come to class, do the homework, and most important of all be actively engaged in trying to understand. Two tips for success: (1) Don't fall behind -- try to do a little homework every day; and (2) Make friends -- ask questions and help each other (especially after trying alone first).

Help: You can find information about tutoring and other useful resources here.
Academic Integrity : You should be familiar with the University's policies on Academic Integrity, including the Honor Pledge.
Students with disabilities : If you have some disability related to testing under the usual timed, in-class conditions, you may contact the office of Disabled Students Services (DSS) in Shoemaker. If they assess you as meriting private conditions and/or extra time, then you may arrange to take your tests at DSS, with extra time as they indicate. You must arrange this well in advance of a test (in particular: no retakes). Click to Disability Support Services for further information.
Religious observances : If your religion dictates that you cannot take an exam or hand in assigned work on a particular date, then contact me at the beginning of the semester to discuss alternatives. You are responsible for making these arrangements at the beginning of the semester.
Detailed Syllabus: Below is an outline of the material I hope to cover and when. This will undoubtedly change as the semester progresses, so check here often for updates. The reading selections and homework are from Ellis and Gulick.

WEEK

DATE

TOPICS

READING

 HOMEWORK

1

Aug 30

Vectors; dot products, cross products

11.1-11.4

 11.1: # 4,7,9,10,14,21; 11.2: 4,9,10,13,16,19, 23, 27; 11.3: # 2,5,7,10,11,15,19,28,33

2

Sep 6

Lines and planes

11.5-11.6

 11.4: # 2,5,10,11,13; 11.5: # 2,5,8,9,12,13,18; 11.6: # 1,5,6,7,8,9,13,17,21,27,31

3

Sep 13

Vector valued functions and their derivatives

12.1-12.3

 12.1: # 15,21,23,32; 12.2: # 4,6,9; 12.3: # 1,5,17,19,23,31,33,39

4

Sep 20

Curves and curvature

12.4-12.6

 12.4: # 7,11,14,21,25,28,31; 12.5: # 2,5,9,11,14,19,22,30; 12.6: # 2,5,9,11,18,21,27

5

Sep 27

Functions of several variables

13.1-13.2

 13.1: # 4,9,15,17,19,27,31,43,45,55,61,68; 13.2: # 11,13,14,16,29

6

Oct 4

Partial and directional derivatives

13.3-13.5

 13.3: # 4,5,7,11,19,23,29,33,34,45,53; 13.4: # 1,7,11,15,23,25,35; 13.5: # 1,3,7,9,13,16

7

Oct 11

Gradients and tangent planes

13.5-13.7

 13.6: # 1,5,7,11,15,21,24,39; 13.7: # 1,4,9,11,13,21,24

8

Oct 18

Extrema; Lagrange multipliers

13.8-13.9

 13.8: # 1,3,7,12,17,29,40; 13.9: # 1,5,7,9,11,13,15,24,28

9

Oct 25

Double integrals

14.1-14.2

 14.1: # 5,7,9,15,21,23,24,30,34,37,39,47,54,58,62; 14.2: # 3,4,9,12,15,25

10

Nov 1

Surface area; triple integrals

14.3-14.5

 14.3: # 1,3,7,10; 14.4: # 1,5,11,15,23,29; 14.5: # 5,7,9,15,16,19,23,29,33

11

Nov 8

Change of variables

14.6-14.8

 14.6: # 1,2,5,9,11,16,19,25; 14.7: # 1,6,9,11,14,17,19,20; 14.8: # 17,19,21,26

12

Nov 15

Vector fields and line integrals

15.1-15.3

 15.1: # 3,7,15,17,19,24,25,27; 15.2: # 1,3,8,9,11,19,25; 15.3: # 1,3,5,7,8

13

Nov 22

Green's Theorem, surface integrals

15.4-5

 15.4: # 4,7,9,13,16,20; 15.5: # 2,3,5,7,12,14

14

Nov 29

Surface integrals, Stokes's theorem

15.6-15.7

 15.6: # 5,7,10,12,13,15; 15.7: # 5,7,9,11,15,19
15
Dec 6
Divergence Theorem
15.8
 15.8: # 11,13,15,17,19,21,23

Richard A. Wentworth