Calculus of Functions of Several Variables

University credit, 15 assignments, 3 exams, $684 tuition, $75 administration fee, Prerequisites: see below. This is course U600-234.

This is the third course in the calculus sequence. It continues the studies begun in Math 221 and 222, and covers the last three modules of a 13-module sequence on the fundamental ideas of calculus. Each module contains five lessons and a module exam. Math 234 covers vector-valued functions of a real variable, real-valued functions of 2 and 3 variables, tangent vectors, directional derivatives and the gradient, applications of double and triple integrals, change of variables, cylindrical and spherical coordinates, line integrals, and a brief treatment of vector fields and Green's Theorem.

Prerequisite: Successful completion of a two-term calculus sequence including techniques of integration, transcendental functions, parametric equations, and an introduction to vectors in the plane and in space. See the prerequisite page for more details.

Course Materials

• Calculus and Analytic Geometry, 9th ed., Thomas and Finney, Addison-Wesley 1996, ISBN: 0-201-53174-7. This book has also been reissued as Thomas's Calculus, Alternate Edition 9/e, with new ISBN: 0-321-11771-9. The content of the two versions is identical; students may use either one. The reissued text is available through the MBS bookstore, or you can search for available copies of the 1996 printing.
• Course Guide for Mathematics U600-234, Wilson, UW-Extension Independent Learning, available through MBS at direct.mbsbooks.com/uwlearning.htm (choose "Buy Materials", then "Independent Learning") or 800-325-3252.
• Student Handbook, available at learn.wisconsin.edu/il/studenthandbook/studenthandbook.pdf, or on paper by request to Learner Services, toll-free 1-877-UW-LEARN (877-895-3276).

Format of Course

The course consists of 15 lessons and 3 module exams. Each lesson consists of:

• A reading assignment from the text.
• Exercises to test your understanding of the material. (Solutions to these self-test problems are provided in the course guide.)
• A written assignment, from the text, to submit for grading and feedback.

At the end of each module is a sample exam, with solutions provided. The actual exam is mailed to a proctor selected by the student in accordance with Independent Learning's guidelines.

Grading

Score	Letter Grade
NOTE: The grading scale was revised on Nov 13, 2003. This grading scale applies to all students who complete the course after that date.
93-100	A
90-92	AB
83-89	B
80-82	BC
73-79	C
65-72	D
0-64	F

Each lesson and each exam is graded on a 100-point scale. The final score is computed as a weighted average, with the average of the lessons counting for 40%, and the average of the exams counting 60%. The exam average must be at least 65 for a passing grade. Assuming this is the case, the average of all your work is converted to a letter grade as shown in the table.

Course Outline

Module 271: Vector Functions and Partial Derivatives

• Lesson 1: Paths in Space
• Lesson 2: Tangents and Normals
• Lesson 3: Functions of Several Variables
• Lesson 4: Partial Derivatives
• Lesson 5: Linearization and the Chain Rule

Module 272: Directional Derivatives and Multiple Integrals

• Lesson 6: Directional Derivatives
• Lesson 7: Extreme Values
• Lesson 8: Double Integrals
• Lesson 9: Applications of Double Integrals
• Lesson 10: Triple Integrals

Module 273: Integral Applications and Extensions

• Lesson 11: Triple Integrals in Other Coordinate Systems
• Lesson 12: Substitution in Multiple Integrals
• Lesson 13: Line Integrals
• Lesson 14: Vector Fields
• Lesson 15: Path Independence and Green's Theorem