MTH 264 Calculus II
Course Title: MTH 264 Calculus II
Course Description
Continues the study of calculus of algebraic and transcendental functions including rectangular, polar and parametric graphing, indefinite and definite integrals, methods of integration and power series along with applications. Features instruction designed for mathematical, physical and engineering science programs. Lecture 3 hours per week. 3 credits.
General Course Purpose
The general purpose of this second course in a three course sequence is to prepare students for further study in calculus with analytic geometry as well as topics such as linear algebra and differential equations so that they meet the necessary competencies in integration, algebraic and transcendental functions, graphing, power series and their applications.
Course Prerequisites/Corequisites
Prerequisite: Completion of MTH 263 or equivalent with a grade of C or better.
Course Objectives
Upon completing the course, the student will be able to:
Applications of Integration

Compute Volumes by crosssection

Compute Volumes by diskwasher

Compute Volumes by shells

Compute Work (spring, rope)

Compute Arc length

Compute Areas of surfaces of revolution

Compute Application (center of mass)
Techniques of Integration

Integrate by parts

Calculate trigonometric integrals

Calculate integrals by trigonometric substitution

Define the indeterminate form and apply L’Hopital’s Rule.

Calculate improper integrals

Integrate by partial fractions

Integrate using Tables and Software

Approximate integrals (Trapezoidal, Simpson) with error estimation.
Infinite Sequences and Series

Write definition of and understand Sequences

Write definition of and understand Series (intro)

Determine convergence by integral test

Determine convergence by comparison test

Determine convergence of alternating series

Determine absolute convergence (ratio, root tests)

Apply strategies for testing series

Work with power series

Represent functions as power series

Find Taylor, Maclaurin series & polynomials

Calculate Taylor and Maclaurin series
Parametric Curves and Polar Coordinates

Represent curves by parametric equations

Perform calculus with parametric curves

Use and graph with polar system

Calculate areas and lengths in polar coordinates

Define the conic forms in polar form
Major Topics to be Included
Applications of Integration
Techniques of Integration
Infinite Sequences and Series
Parametric Curves and Polar Coordinates