CALCULUS III MATH 1970

CALCULUS III
MATH 1970
Course Description:
This course presents vector functions, parametric equations, solid analytic geometry, partial
differentiation, multiple integration, and an introduction to vector calculus. A mathematical
software package is introduced with required assignments. 4 credits
Prerequisites:
MATH 1960 with a grade of C- or better, or MATH 1970 with a grade of F or better, or
permission of instructor.
Overview of Content and Purpose of the Course:
This is the third and final course of the Calculus sequence. The course builds on the calculus of
two-dimensions learned in MATH 1950 and MATH 1960 and applies calculus to threedimensions. This application is important to solving many real-world problems in engineering,
economics, and science, as well as higher mathematics.
Anticipated Audience/Demand:
This course is primarily intended for students in Math, Engineering, and Science, but is
appropriate for students in any discipline.
Major Topics:
1) Vectors and the Geometry of Space
a. Three-Dimensional Coordinate Systems
b. Vectors
c. The Dot Product
d. The Cross Product
e. Lines and Planes in Space
f. Cylinders and Quadratic Surfaces
2) Vector-Valued Functions and Motion in Space
a. Vector Functions and Their Derivatives
b. Integrals of Vector Functions
c. Arc Length in Space
d. Curvature of a Curve
e. Tangential and Normal Components of Acceleration
3) Partial Derivatives
a. Functions of Several Variables
b. Limits and Continuity in Higher Dimensions
c. Partial Derivatives
d. The Chain Rule
e. Directional Derivatives and Gradient Vectors
f. Tangent Planes and Differentials
g. Extreme Values and Saddle Points
h. Lagrange Multipliers
i. Taylor’s Formula for Two Variables
4) Multiple Integrals
a. Double and Iterated Integrals over Rectangles
b. Double Integrals over General Regions
c. Area by Double Integration
d. Double Integrals in Polar Form
e. Triple Integrals in Rectangular Coordinates
f. Moments and Centers of Mass
g. Triple Integrals in Cylindrical and Spherical Coordinates
h. Substitutions in Multiple Integrals
5) Integration in Vector Fields
a. Line Integrals
b. Vector Fields, Work, Circulation, and Flux
c. Path Independence, Potential Functions, and Conservative Fields
d. Green’s Theorem in the Plane
e. Surface’s and Area
f. Surface Integrals and Flux
g. Stokes’ Theorem
h. The Divergence Theorem and a United Theory
Methods:
This course will be presented in a lecture/discussion format.
Student Role:
Students must attend and participate in class, in addition to completing course requirements.
Textbook:
Hass, Joel, Maurice D. Weir, and George B. Thomas. University Calculus. Boston:
Addison Wesley, 2006.
February 2016