Math 3            Multivariable Calculus (4 credits) & Linear Algebra (1 credit)

Pre-Requisite:        Single-Variable Calculus, Introduction to Linear Algebra (or Math 1 and 2)

Course Description:

This course is an extension of single-variable calculus and an introduction to more formal linear algebra. It focuses on vectors, parametric equations, linear transformations, surfaces, partial differentiation, optimization, multiple integrals, vector fields with line and surface integrals, and Taylor and Fourier series. There is heavy emphasis on applications, mathematical modeling, and problem solving techniques.The class meets once week in the computer laboratory. The primary software used is Mathematica . It is a required course for all mathematics majors and minors and all engineering majors.

Course Objectives:   Students Will

• Understand how and why vectors are used in both the geometric and analytical sense
• Use vectors to find projections and to derive equations of lines and planes
• Extend vector projections to linear transformations
• Relate taking the derivative to the application of the vector del operator and extend the notion of the slope of a curve to the gradient of a surface
• Apply the gradient to find the directional derivative and to solve constrained and unconstrained optimization problems for functions of two or more variables
• Understand the geometric and physical interpretations for multiple integrals
• Apply the concepts of vectors and integrals to find line integrals
• Understand Green’s Theorem as an extension of the Fundamental Theorem of the Integral Calculus
• Be able to model and solve applications involving partial derivatives and multiple integrals
• Expand the idea of  linearizing functions using the gradient to approximating functions using the Taylor Series
• Understand how the Fourier Series can be used to approximate periodic data or functions of a single variable over an interval

Required Text: 

Thomas' Calculus  (The standard version and the Early Transcendentals version are the same for the chapters covered in this course.) (10^th edition), by Finney, Weir, Giordano, © 2001, Addison Wesley

Grading Policies:

Exams are given every two to three weeks. Labs are done every week.

Relative weights:            Exams (65%), Homework (10%), Projects/Labs (25%)

                                    Projects are computer intensive and students are encouraged to work in pairs.

                                    Some project results will be presented orally as well as in written form.

                                    Computer printouts without comments and a summary sheet will never be accepted.

Course Outline

Meeting 5 Days Per Week for 14 Weeks