MAT201

Brief Course Description: Third semester of the standard 3-semester calculus sequence. Gives a thorough introduction to multivariable calculus and mathematical methods needed to understand real world problems involving quantities changing over time in two and three dimensions. Topics include vectors, lines, planes, curves, and surfaces in 3-space; limits, continuity, and differentiation of multivariable functions; gradient, chain rule, linear approximation, optimization of multivariable functions; double and triple integrals in different coordinate systems; vector fields and vector calculus in 2- and 3-space, line integrals, flux integrals, and integration theorems generalizing the Fundamental Theorem of Calculus (Green's theorem, Stokes' theorem and Gauss's theorem, also known as the divergence theorem). 

Why take this course? It provides important mathematical foundations for advanced studies in life sciences, physical sciences, social sciences, computer science and engineering, building vocabulary and tools to describe and understand phenomena in the natural world, and improving analytic and problem-solving skills valuable in many disciplines.

Who takes this course? Most students in this course are first- or second-year students who consider majoring in one of the sciences or engineering.   More mathematically inclined economics majors will take this course along with 202 (instead of 175).  Although it is not a prerequisite, many students in the course will have had a more basic multivariable calculus course in high school.

Prerequisites:  104 or equivalent. A solid knowledge of single-variable calculus and precalculus is essential: how to analyze and graph functions, how to compute and interpret derivatives, how to interpret, set up, and calculate definite integrals with speed and accuracy. The very fast pace means that solid grasp of the prerequisite material is especially important.