# SYLLABUS

## Vector Calculus (Math 241, Section 1) Fall 2000, USC

Lecture
M W F 9:05-9:55 am LC 405.
Instructor
Check the course web site periodically for revised versions of this syllabus, and to obtain homework assignments and copies of old tests and quizzes.

Course Description
We will study derivatives and integrals of functions of several variables with a view towards studying geometry of curves and surfaces in 3-space, together with a host of other applications in Physics and Engineering.

Prerequisites
Math 142--a sound understanding of derivatives and integrals of functions of one variable.

Textbook
Calculus, by J. Varberg, Pursell, and Rigdon, Seventh Edition.

Homework and Quizzes
There will be weekly homework assignments due each week. Late homeworks will not be accepted.

Also, there will be some practice quizzes. You should save copies of these quizzes as they are a very good source for preparing for the final and midterms.

Doing the homework problems is the most important part of this class. You may work with a group of your classmates if you are all at about the same level; however, you should definitely try to do many problems on your own. Further, try to practice doing at least some of the problems in settings which resemble that of the test and quizzes, i.e., without using your calculator or constantly referring to the textbook.

You should make a sincere effort to keep up with your reading assignments; otherwise, you may significantly compromise your ability to benefit from the lectures.
 Dates Lectures Aug 25 F 13.1 Parametric curves in the plane 2830 MW 13.213.3 Vectors in the planeVectors in the plane Sep 1 F 13.4 Vector Functions 468 MWF .13.514.1 Labor day-no classesCurvature and AccelerationCoordinates in 3-Space 111315 MWF 14.214.2, 14.314.3 Vectors in 3-SpaceDot ProductCross Product 182022 MWF 14.4.. Lines and Curves in 3-SpaceReviewMidterm 1(covers up to and including 14.2) 252729 MWF 14.514.614.7 Velocity and AccelerationSurfaces in Three-SpaceCylindrical and Spherical Coordinates Oct 257 MWF 15.115.1, 15.215.2 Functions of several variablesGraphsPartial Derivatives 91113 MWF 15.415.515.6 GradientsDirectional DerivativesThe Chain Rule 161820 MWF ... Fall Break-no classesReviewMidterm 2(covers up to and including 15.5) 232527 MWF 15.715.815.9 Tangent Planes and ApproximationsMaxima and MinimaLagrange's Method 30 M 16.1 Double Integrals over Rectangles Nov 14 WF 16.216.3 Iterated IntegralsDouble Integrals over Nonrectangular Regions 6810 MWF 16.316.416.5 More Double IntegralsDouble Integrals in Polar CoordinatesApplications of Double Integrals 131517 MWF 16.5.. Applications of Double IntegralsReviewMidterm 3 (covers up to and including 16.4) 202224 MWF 16.7.. Triple Integrals (rectangular coordinates)Thanksgiving Recess-no classesThanksgiving Recess-no classes 2729 MW 16.716.8 Triple Integrals (rectangular coordinates)Triple Integrals (spherical and cylindrical coordinates) Dec 1 F 16.8 Triple Integrals (spherical and cylindrical coordinates) 468 MWF ... Applications of Triple IntegralsReviewReview 13 W . Final Exam(Comprehensive)

Assignments
You should plan to work on these problems over a period of several days. Getting a head start on each assignment is perhaps the most critical factor determining your success in this class.
 Homework # Due Date Problems 1 Sep 4 13.1)2, 8, 17, 26, 44, 57; 13.2) 2, 4, 6, 14; 13.3) 2, 4, 10, 12, 14, 16, 26, 30. 2 Sep 11 13.4)14(a), 18, 24, 32, 36, 38; 13.5) 2, 13, 29. 3 Sep 18 14.1) 7, 11(a), 12, 14, 25, 29; 14.2) 6, 8, 12, 13, 23, 25(a), 28; 4 Sep 25 14.3) 4, 6, 10, 12, 18, 26; 14.4) 2, 6, 14, 24, 28, 29. 5 Oct 2 14.5) 7, 14, 15, 40, 58; 14.6) 2, 9, 10, 16, 21. 6 Oct 9 14.7) 2, 3, 4, 8, 17, 18, 30; 15.1) 2, 8, 14, 18, 23. 7 Oct 16 15.2)4, 18, 30, 33; 15.4)2, 6, 12; 15.5)4, 10, 16, 18, 20, 23. 8 Oct 23 15.6) 2, 14, 17, 18, 20. 9 Oct 30 15.7) 2, 14, 22, 23; 15.8) 2, 5, 12, 14, 16, 18, 19. 10 Nov 6 15.9) 2, 7, 8, 10; 16.1) 2, 6, 10, 15; 16.2) 6, 8, 14, 20. 11 Nov 13 16.3) 2, 10, 14, 24, 38, 39; 16.4) 4, 5, 11, 14. 12 Nov 27 16.5) 2, 5, 6, 8; 16.7) 2,4, 16, 19, 20, 22. 13 Dec 4 16.8) 1, 2, 5, 7, 12, 17, 22, 23.

Tests and Exams
There will be three midterms on Fridays Sep 22, Oct 20, and Nov 17. The final exam will be on Wednesday, Dec 13, 9 am. No calculators, or notes will be allowed during the exams. Note: bring a bluebook to the exams.

The final grade is based on homeworks and quizzes, 15%, midterms, 15% each, and the final exam, 40%.

A Few More Study Hints and Guidelines
Learning Mathematics is a demanding affair. It requires a good deal of self discipline and hard work to appreciate the power and beauty of the subject. Further, solving Calculus problems, much like playing a musical instrument, is a skill, which can be developed only through persistent practice. You should plan to work on your exercises everyday, and for a total of at least 10 hours each week. Also, it is very important that you faithfully attend all lectures.

A good deal of class time shall be devoted to working through problems. Do not get into the habit of sitting passively and expect the professor to make you understand. Rather, you should take out your paper and pencil and try to do the problems at the same time with your instructor. If something is unclear to you, feel free to ask questions, and if you need more help, go see your instructor and/or the TA during the office hours. If you cannot come during the office hours, you are welcome to knock on the professor's door at another time, or send an email for an appointment.

Calculus is one of the greatest accomplishments of the human mind. Having the opportunity to study it is a true privilege, and an excellent chance to practice the art of thinking in a clear and organized way. I hope that this class will be a rewarding experience for you.