Course
Objectives for MAT 1236: Calculus III
This third course in calculus continues the study of differential and
integral calculus begun in MAT 1234 and 1235. The course includes
parametric equations, polar coordinates, vectors, sequences, series, and
Taylor expansions. It also introduces multivariable calculus, including
partial derivatives, double integrals, and triple integrals. The primary aims of the course are to help
students develop new problem solving and critical reasoning skills and to
prepare them for further study in mathematics, the physical sciences, or
engineering. By the end of the course, students should be able to

sketch and analyze
curves given parametrically;

graph curves in polar
coordinates;

compute areas and arc
lengths using rectangular and polar coordinates;

recognize and apply algebraic and geometric
properties of
vectors in two and three dimensions;

compute dot products and cross products and
recognize their geometric meaning;

visualize and sketch surfaces in
threedimensional space;

compute and interpret partial derivatives of functions of
several variables;

set up and evaluate double
and triple
integrals using a variety of coordinate systems, including rectangular, polar,
cylindrical, and spherical;

use Maple effectively to explore and solve calculus problems;

analyze and solve complex problems;

write short proofs using the ideas and
techniques listed above; and

provide
clear written explanations of the ideas behind key concepts from the
course.
Students should also gain an increased
appreciation of mathematics as part of the language of science and as a
study in itself.
Course
Content
The standard
material to be covered in Calculus III from the 6th edition of Stewart's
Calculus is listed below. Individual instructors may make minor
modifications to this list.

11.1 Curves Defined by Parametric
Equations

11.2 Calculus with Parametric Curves

11.3 Polar Coordinates

11.4 Areas and Lengths in Polar
Coordinates

12.1 Sequences

12.2 Series.

12.3 The Integral Test and Estimates of
Sums.

12.4 The Comparison Tests.

12.5 Alternating Series.

12.6 Absolute Convergence and the Ratio
and Root Tests.

12.7 Strategy for Testing Series.

12.8 Power Series.

12.9 Representation of Functions as
Power Series.

12.10 Taylor and Maclaurin Series.

12.11 Applications of Taylor Polynomials

13.1 Threedimensional Coordinate
Systems

13.2 Vectors

13.3 The Dot Product

13.4 The Cross Product

13.5 Equations of Lines and Planes

13.6 Quadric Surfaces

15.1 Functions of Several Variables

15.2 Limits and Continuity

15.3 Partial Derivatives

15.5 The Chain Rule

16.1 Double Integrals over Rectangles

16.2 Iterated Integrals

16.3 Double Integrals over General
Regions

16.4 Double Integrals in Polar
Coordinates

16.5 Applications of Double Integrals

16.6 Triple Integrals

16.7 Triple Integrals in Cylindrical
Coordinates

16.8 Triple Integrals in Spherical Coordinates
