Calculus III
Spring 2000
MATH 261.01 (4 credits), MTu_ThF, 10:00AM-10:50AM, Wickersham 105

Textbook:

Calculus, 6th edition, Swokowski, Olinick, and Pence PWS Publishing Company, 1994.

Instructor:

Dr. Buchanan
Office: Wickersham 113, Phone: 872-3659, FAX: 871-2320
Office Hours: 2:00PM-3:00PM (MTu_ThF), 10:00AM-11:00AM (W), or by appointment
Email: Robert.Buchanan@millersville.edu
URL: http://banach.millersville.edu/~bob

Coverage:
• Vectors and Surfaces (Chap. 10)
• Vector-valued Functions (Chap. 11)
• Partial Differentiation (Chap. 12)
• Multiple Integrals (Chap. 13)
• Vector Calculus (Chap. 14)

Objectives:

The student will:

• Understand the algebra and geometry of vectors in 2 and 3 dimensions.
• Understand the calculus of curves in , the unit tangent and unit normals vectors, curvature, and motion along a trajectory.
• Learn the three-dimensional vector algebra required by linear algebra courses: Dot and cross products, projections, and equations of line and planes in .
• Understand spherical coordinates and cylindrical coordinates.
• Understand partial differentiation, and will apply partial derivatives to the computation of gradients, directional derivatives, tangent planes, and differentials.
• Understand differentiable functions of several variables.
• Locate and classify critical points of functions of several variables, and will solve applied optimization problems.
• Understand definite integrals in higher dimensions. The student will set up and evaluate multiple integrals, and will be able to interchange the order of integration.
• Understand line and surface integrals, potential functions, and path independence. The student will apply Green's theorem in the plane, and Gauss's and Stokes' theorems in .

Prerequisites:

A grade of C- or better in MATH 162 ( Calculus II) is a prerequisite for this course.

Attendance:

Students are expected to attend all class meetings. If you must be absent from class you are expected to complete class requirements (tests and/or homework assignments) prior to the absence. Students who miss a test should provide a valid excuse, otherwise you will not be allowed to make up the test. Tests should be made up within one week of their scheduled date. No final exam exemptions.

Homework:

Students are expected to do their homework and participate in class. Occasionally homework assignments will be collected and graded. The homework is your opportunity to determine if you understand the material covered in class. The homework assignments will also reinforce and extend the classroom material covered. The student solutions manual for this course will be placed on reserve in the Ganser Library. You may check out the solutions for a maximum of three hours at a time by asking for the ``Buchanan MATH 261 Solutions Manual'' at the reserve desk.

Students should expect to spend a minimum of twelve hours per week reviewing notes taken during class and working assigned homework exercises. Preparation for the tests and final exam will require additional hours of study. Students will find it beneficial to review all lecture notes and other relevant material collected from the beginning of the semester until the present time at least once per week.

Assignments by Section

• Sec. 10.1, pp. 855-857; 1-55 odd
• Sec. 10.2, pp. 863-864; 1-45 odd
• Sec. 10.3, pp. 874-876; 1-51 odd
• Sec. 10.4, pp. 884; 1-37 odd
• Sec. 10.5, pp. 896-898; 1-65 odd
• Sec. 10.6, pp. 915-917; 1-7 odd, 9-20, 23-43 odd, 57
• Chap. 10 Review, pp. 918-919; 1-49 odd
• Sec. 11.1, pp. 928; 1-23 odd, 27, 28, 29
• Sec. 11.2, pp. 935-937; 1-49 odd
• Sec. 11.3, pp. 944-945; 1-25 odd, 26, 27-33 odd
• Sec. 11.4, pp. 957-958; 1-49 odd
• Chap. 11 Review, pp. 970-971; 1-19 odd
• Sec. 12.1, pp. 982-986; 1-39 odd, 40-44, 45-57 odd, 58, 59, 61
• Sec. 12.2, pp. 995-996; 1-41 odd
• Sec. 12.3, pp. 1004-1007; 1-18, 19-57 odd, 58, 59-63 odd
• Sec. 12.4, pp. 1019-1021; 1-37 odd, 39-42
• Sec. 12.5, pp. 1028-1030; 1-35 odd, 37-41, 45
• Sec. 12.6, pp. 1040-1042; 1-31 odd, 39-44
• Sec. 12.7, pp. 1049-1050; 1-29 odd
• Sec. 12.8, pp. 1058-1062; 1-45 odd, 51
• Sec. 12.9, pp. 1070-1071; 1-21 odd
• Chap. 12 Review, pp. 1071-1073; 1-43 odd
• Sec. 13.1, pp. 1088-1090; 1-10, 11-49 odd
• Sec. 13.2, pp. 1099-1101; 1-31 odd
• Sec. 13.3, pp. 1109-1111; 1-31 odd
• Sec. 13.4, pp. 1114-1115; 1-13 odd
• Sec. 13.5, pp. 1125-1127; 1-33 odd
• Sec. 13.7, pp. 1143-1144; 1-35 odd, 39, 40
• Sec. 13.8, pp. 1150-1151; 1-35 odd, 39, 40, 41
• Chap. 13 Review, pp. 1163-1165; 1-51 odd
• Sec. 14.1, pp. 1175-1176; 1-11 odd, 13-16, 17-35 odd, 36
• Sec. 14.2, pp. 1186-1188; 1, 2, 5-8, 11-19 odd, 20, 21-33 odd
• Sec. 14.3, pp. 1196-1197; 1-29 odd
• Sec. 14.4, pp. 1205-1206; 1-23 odd, 24, 25, 27
• Sec. 14.5, pp. 1214-1215; 1-21 odd
• Sec. 14.6, pp. 1221-1222; 1-17 odd, 18, 19-27 odd
• Sec. 14.7, pp. 1231; 1-13 odd, 14, 15-19 odd, 20
• Chap. 14 Review, pp. 1232; 1, 3, 5, 9-17 odd, 23-29 odd

Tests:

Three 50-minute tests (tentatively scheduled for 02/21/2000, 03/17/2000, and 04/25/2000) and a comprehensive final exam (Wednesday, May 10, 2000, 2:45PM-4:45PM). The Mathematics Department's calculus assessment exam will be given during class on 02/10/2000.

If you feel that an error was made in the grading of a test, you should explain the error on a separate sheet of paper and return both it and the test to me within three class periods after the test is returned to you.

Course grade will be calculated as follows.

 Core Calculus Test 5% Tests 55% Exam 25% Homework 15%

The course letter grades will be calculated as follows.

 90-100 A 80-89 B 70-79 C 60-69 D 0-59 F

Final Word:

Math is not a spectator sport. What you learn from this course and your final grade depend mainly on the amount of work you put forth. Daily contact with the material through homework assignments and review of notes taken during lectures is extremely important.

Page maintained by: Robert.Buchanan
Robert.Buchanan@millersville.edu

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