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Calculus III for Science and Mathematics


Course Description

Calculus of functions of two and three variables: Parametric curves and applications to planetary motion. Derivatives, the gradient, Lagrange multipliers. Multiple integration, area, volume, and physical applications, polar, cylindrical, and spherical coordinates. Line and surface integrals, Green's, Stokes's, and Divergence theorems, with applications to physics.


Athena Title

Calc III Science and Math


Equivalent Courses

Not open to students with credit in MATH 2270H, MATH 2500, MATH 2500E


Prerequisite

MATH 2260 or MATH 2310H or MATH 2410 or MATH 2410H


Semester Course Offered

Offered fall, spring and summer


Grading System

A - F (Traditional)


Course Objectives

Students should be able to calculate partial derivatives, directional derivatives and gradients. Students should be able to solve maximum and minimum problems using Lagrange multipliers. They should learn to calculate area, volume, center of mass, and moment of inertia using multiple integrals. They are expected to understand integrals along curves and surfaces, culminating in various generalizations of the Fundamental Theorem of Calculus. Students should be able to apply the tools learned in this course to areas such as planetary motion, gravitation, data fitting, Gauss's Law, and fluid dynamics.


Topical Outline

1. Review of vector algebra. 2. Parametric curves; Kepler's laws. 3. Partial differentiation: directional derivatives, gradients, tangent planes, chain rule, maximum/minimum problems, and Lagrange multipliers. 4. Multiple integration: double and triple integrals, change of order of integration, applications to computations of areas, volumes, center of mass and moments of inertia. Polar, cylindrical, and spherical coordinates. 5. Line integrals, work, path-independence, and Green's Theorem. 6. Surface integrals and flux. Curl, divergence, Stokes's and Divergence Theorems and their applications.


General Education Core

CORE III: Quantitative Reasoning

Syllabus