Introduction to Multivariable Calculus

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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.


MATH 1502 OR MATH 1512 OR MATH 1555 OR MATH 1504 ((MATH 1552 OR MATH 15X2 OR MATH 1X52) AND (MATH 1522 OR MATH 1553 OR MATH 1554 OR MATH 1564 OR MATH 1X53))

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