Description and Objectives

The students attending this course will have already completed Calculus I (MATH 507/8) and Calculus II (MATH 527/8) and will be ready to look at multivariable calculus the calculus of vector-valued functions.  This course is similar to Math 241 at the University of Maryland.

We begin with the basics of vectors in two dimensions and in space.  (Chapter 11) Although for students having taken physics these topics are somewhat familiar, we nevertheless define the dot product, cross product and the triple product and learn how to write equations for lines and planes in space.

 Next we turn our attention to vector-valued functions and differentiation and integration of such functions. (Chapter 12) So here we are looking at functions   .  Then we look at functions of several variables so we look at or .  Partial derivatives and directional derivatives are discussed as well as the gradient of a function. (Chapter 13) Applications of partial derivatives such as Extrema and Tangent Planes and Lagrange multipliers are discussed.

We turn our attention next to multiple integrals: double integrals, triple integrals in rectangular and polar/cylindrical coordinates computing surface areas and volumes. (Chapter 14) Lastly we cover the calculus of vector fields, line integrals, Green’s Theorem and Stoke’s Theorem. (Chapter 15)

Textbooks

Calculus with Analytic Geometry 6th ed., Ellis and Gulick

Course Requirements

Students should have already completed Calculus I and Calculus II successfully as this course builds on that knowledge.

Successful Students

Students will have homework assigned after each class period and there will be several exams each semester.