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-valued functions in the plane and space, quadric surfaces, and an introduction to spherical and cylindrical coordinates. Graphing technology required.

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

Natural Sciences Distribution Requirement
Quantitative

Meets FQE Requirement: No
Elective Requirements: Fulfills Academic Electives
Integrative Experience Requirement: No

Student Learning Outcomes

Determine the convergence or divergence of sequences.
Determine the convergence or divergence of infinite series using a variety of methods: Geometric. Partial sums. Integral test. Comparison tests. Alternating series. Ratio and root tests.
Find power series for functions, including Taylor and Maclaurin series.
Calculate and apply derivatives and integrals of parametric equations.
Find the equations of lines and planes in space using vectors.
Determine velocity and acceleration using vector-valued functions.
Solve applications involving geometry and science using the dot product and cross product.
Calculate the arclength and curvature of vector-valued functions.
Calculate and apply derivatives and integrals of polar equations.
Produce 3-dimensional graphs, including quadric surfaces and points in cylindrical and spherical coordinates.

Course Contents

Sequences: Finding a formula for the nth term of a sequence. Convergence of sequences. Squeeze theorem (optional).
Series: Finding a closed form for a series. Divergence theorem. Geometric series. Integral test. Comparison tests. Alternating series. Absolute convergence. Ratio and root test. Telescoping series (optional). Binomial series (optional).
Power series: Taylor and Maclaurin series. Error estimation.
Parametric Equations: Find derivatives and tangent lines for parametric equations. Calculate parametric integrals and apply them to find area and arclength
Vectors and Vector-Valued Functions: Equations of lines and planes in space. Space curves. The dot and cross products. Differentiate and integrate vector-valued functions. Velocity and acceleration in space. Tangent and unit tangent vectors to a smooth curve at a point. Unit normal and unit binormal completing the trihedral vectors: T, N, B (optional). Arclength and curvature.
Non-rectangular Systems: Find derivatives and tangent lines for polar equations. Calculate polar integrals and apply them to find area and arclength. Plot points in cylindrical and spherical coordinates. Convert points and equations from rectangular coordinates to cylindrical and spherical coordinates and vice versa.
Graph Quadric Surfaces.

Instructional Units: 5