CALCULUS III
MATH 361 SPRING 2011
Instructor: Dr. R. P. Webber
Office and hours: East Ruffner 332, MF 2 – 3:30, T 2 - 3, and by appointment or coincidence. I am not normally on campus on Thursdays.
Telephone: 395-2192
email: webberrp@longwood.edu
Course description: Topics in multivariable calculus and vector analysis. Prerequisite: MATH 262. Students who do not make C or better in 262 should have consent of the chair before enrolling. 4 credits.
Course objectives: The student will be able to calculate partial derivatives and multiple integrals. The student will be able to calculate gradients and directional derivatives. The student will be able to apply various derivatives to concepts involved in graphing functions in more than two variables. The student will understand what a vector is and be able to graph vectors. The student will be able to add, subtract, and find dot and cross products of vectors. The student will be able to calculate basic line integrals.
Text: Rogawski, Multivariable Calculus Early Transcendentals, W.H. Freeman, 2008.
Computer algebra system: We will use Maple, which is available in the Ruffner computer lab. Maple is a commercial product. You may purchase it for your PC if you like, although it is not required.
Course requirements and grading: There will be three tests and a class participation grade, of which you may drop one. The resulting three marks, counted equally, will comprise 40% of your course grade. Your composite lab grade will count 35% of your course grade, and the final exam will count the remaining 25%. The grading scale goes by tens: 90 - 100, A; 80 - 90, B; 70 - 80, C; 60 - 70, D; below 60, F.
Homework: Problems will be assigned regularly, and everyone is expected to do them. They will not be collected without warning, and it is your responsibility to do all of the assigned problems. Feel free to work with others on the homework problems.
Labs: These problems will be done in groups. They will be computationally challenging (and thus best done on a computer) or intellectually challenging (and thus best done in cooperation with others), or occasionally both! You will be expected to begin work on these problems in the lab class meeting and to complete them out of class if necessary. You will hand in one solution to each problem from the group, and every member of the group will receive the same grade. Each lab assignment will have a due date, and failure to hand it in by the start of class on the due date will result in a penalty of 25% per class day late.
Class participation: Often you will be asked to work in groups in class. Working in small groups of three or four (which need not be the same groups as in the lab), you will be asked to solve a problem and present your results to the class. Missed class participation sessions cannot be made up, but you will be allowed one absence from a class participation session without penalty. You will receive a grade of 0 for each additional missed session.
Attendance: Your attendance is expected at all classes. Makeup tests will be given reluctantly, and then only upon presentation of a doctor's excuse. Makeup tests are always more difficult than regular tests, regardless of the reason for absence. You may not make up missed class participation sessions.
Honor code: I subscribe to the Longwood University honor system, which, among other things, assumes you do not cheat and that you take responsibility to see that others do not. Infractions will be dealt with harshly. A student who is convicted of an Honor Code offense involving this class will receive a course grade of F, in addition to any penalties imposed by the Honor Board.
Course schedule:
Week 1 Jan 19 - 21 | 11.1: Parametric representation |
Week 2 Jan 24 - 28 | 11.2 - 11.4: Arc length; polar coordinates |
Week 3 Jan 31 - Feb 4 | 11.5 - 12.2: Conic sections; vectors in 2 and 3 space |
Week 4 Feb 7 - 11 | 12.3 - 12.6: Dot and cross products; planes and surfaces |
Week 5 Feb 14 - 18 | Review; TEST; 12.7: Cylindrical and spherical coordinates |
Week 6 Feb 21 - 25 | 13.1 - 13.4: Vector-valued functions; curvature |
Week 7 Feb 28 - Mar 4 | 14.1-14.4: Partial derivatives |
Week 8 Mar 7 - 11 | 14.5 - 14.7: Gradient; optimization |
SPRING BREAK | |
Week 9 Mar 21-25 | 15.1 - 15.3: Multiple integrals |
Week 10 Mar 28 - Apr 1 | Review; TEST; 16.1: Vector fields |
Week 11 Apr 4 - 8 | 16.2 - 16.3: Line integrals |
Week 12 Apr 11 - 15 | 16.3 - 16.5: Conservative fields; surface integrals |
Week 13 April 18 - 22 | 17.2 - 17.2: Green's and Stokes' theorems |
Week 14 Apr 25 - 29 | Review; TEST; review |
TBA | FINAL EXAM Computer lab room (at the regularly scheduled time for 12:30 TR classes) |