MATH2081 — Multivariable Calculus
MATH 2081 - Multivariable Calculus MATH 2081 - Multivariable Calculus Hours/Week: Lecture 5 Lab 0 Course Description: This is a first course in Multivariable Calculus. Topics include vectors in 3D-space, vector functions, functions of two or more variables, partial derivatives, gradients, and the chain rule; applications to max/min problems, Lagrange multipliers; double and triple integrals, change of variable, polar and spherical coordinates; line and surface integrals, vector fields and the fundamental theorem of line integrals; curl and divergence, theorems of Green and Stokes, and the Divergence theorem. Use of a 3-D graphing calculator, such as a TI-Nspire CX CAS, is required. Limited use of a computer algebra system will be made. This course is intended for students majoring in chemistry, engineering, physics, science, mathematics, mathematics education, or computer science. MnTC Goals None Major Content 1. Vectors a. Introduction to vectors b. Vectors in the plane and basic operations c. Vectors in space and basic operations d. Dot product and cross product e. Lines, planes, spheres, and quadric surfaces f. Vector-valued functions, space curves, and tangent vectors g. Differentiation and integration of vector functions h. Applications, including arc length and curvature 2. Differential Calculus of Functions of Several Variables a. Definition of a function of more than one variable b. Limits and continuity c. Partial derivatives d. Tangent planes and linear approximatio
Prerequisites: MATH1082