MATH& 153 - Calculus III

Credits: 5
Variable Credit Course: No

Lecture Hours: 55
Lab Hours: 0
Worksite/Clinical Hours: 0
Other Hours (LIA/Internships): 0

Course Description: This is the third in a sequence of four calculus courses for students who are planning to major in engineering, mathematics, or the sciences. Topics include infinite sequences and series, parametric equations, vectors and vector-values functions in the plane and space, spherical and cylindrical coordinates. Graphing technology required.

Prerequisite: MATH& 152 with a grade of C or higher.
Distribution Requirements:

Natural Sciences Distribution Requirement

Meets FQE Requirement: No
Integrative Experience Requirement: No

Student Learning Outcomes

Calculate and apply derivatives and integrals using polar coordinates.
Calculate and apply derivatives and integrals using parametric equations.
Determine the convergence or divergence of sequences.
Determine the convergence or divergence of infinite series using a variety of tests: Integral test. Comparison test. Alternating series. Ratio and root tests.
Determine power series for common functions.
Approximate functions using Taylor and Maclaurin series.
Solve applications involving geometry and science using the dot product and cross product.
Find the equations of lines and planes in space using vectors.
Determine velocity and acceleration using vector valued functions.
Calculate the arc-length and curvature of vector valued functions.

Course Contents

Analytic Geometry. Calculus with parametric equations. Cylinders and quadric surfaces. Polar coordinates: areas and lengths.
Sequences and Series. Sequences and series. Integral test. The comparison test. Alternating series. Absolute convergence. Ratio and root test. Power series. Taylor and Maclaurin series. Binomial series (optional).
Vectors and Vector Valued Functions. The dot and cross products. Equations of lines and planes in space. Space curves. Differentiate and integrate vector valued functions. Arclength and curvature. Tangent and unit tangent vectors to a smooth curve at a point. Unit normal and unit binormal completing the trihedral vectors: T, N, B. Velocity and acceleration in space.

Instructional Units: 5