Faculty Syllabus

Prerequisites: Students must have completed MATH 2414 with a C or better.

Textbook: Calculus: Early Transcendentals, 3rd Edition by Briggs, Cochran, Gillette, & Schulz. Pearson Publishing (MyLab software) ISBN: 9780134763644

A standard third course in calculus. Topics include vectors and analytical geometry in three dimensions; vector-valued functions and curvature; components of acceleration; functions of several variables; limits and continuity in three-space; partial and directional derivatives; gradients, tangent planes, and extrema of functions of two variables; multiple integrals in rectangular, polar, spherical, and cylindrical coordinates; applications of multiple integrals to area, volume, moments, centroids, and surface area; line and surface integrals of functions and vector fields; Green's, Stoke's, and the Divergence Theorems.

Upon successful completion of the course, a student should be able to:

1. Demonstrate the ability to analyze and visualize curves, surfaces, and regions in 2 and 3 dimensions, in Cartesian, polar, cylindrical, and spherical coordinate systems.
2. Perform calculus operations on vector‐valued functions including limits, derivatives, integrals, curvature, and the description of motion in space.
3. Perform calculus operations on functions of several variables including limits, partial derivatives, directional derivatives, and multiple integrals.
4. Find and classify extrema and tangent planes of functions of two variables.
5. Apply some of the theorems of vector calculus, such as the Fundamental Theorem of Line Integrals, Green’s Theorem, the Divergence Theorem, and Stokes' Theorem, to simplify integration problems.
6. Apply the computational and conceptual principles of calculus to the solutions of various scientific and business applications.