Introduction to Multivariable Calculus

Department: 
MATH
Course Number: 
2550
Hours - Lecture: 
2
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
2
Typical Scheduling: 
Every Semester

An introduction to multivariable calculus through vectors in 3D, curves, functions of several variables, partial derivatives, min/max problems, multiple integration. Vector Calculus not covered.

Prerequisites: 

(MATH 1552 or MATH 1X52) and (MATH 1553 or MATH 1554 or MATH 1564 or MATH 1X53 or MATH 1X54)

Course Text: 

At the level of Thomas, Calculus: Early Transcendentals, (14th ed.) Pearson.

Flow chart describing textbook choices for Fall 2019.

Topic Outline: 
Topic Text Sections Lectures
Vectors and geometry of space: dot and cross product, lines and planes, cylinders and quadric surfaces 12.1-12.6 3
Vector functions and curves: limits, continuity, tangent vector and motion, integrals, arc length, curvature 13.1-13.4 5
Functions of several variables: domain, graphs and level sets, limits and continuity, partial derivatives, chain rule, directional derivatives and gradients, tangent planes, extreme values and saddle points, Lagrange multipliers, Taylor's theorem 14.1-14.9 12
Multiple integrals: double and triple integrals over rectangles and general regions, area by double integration, integrals in polar, cylindrical and spherical coordinates, substitutions in multiple integrals. 15.1-15.8 10