# C-ID Descriptor Single Variable Calculus II Early Transcendentals

## Submission Information

• Final
• Mathematics
• March 31, 2011

## Descriptor Details

• Single Variable Calculus II Early Transcendentals
• Single Variable Calculus II Late Transcendentals MATH 221
• 220
• 4.0

## General Description

A second course in differential and integral calculus of a single variable: integration; techniques of integration; infinite sequences and series; polar and parametric equations; applications of integration.  Primarily for Science, Technology, Engineering & Math Majors.

## Prerequisites

Single Variable Calculus I Early Transcendentals (Math 210, CAN 18).

## Content

1. Areas between curves;
2. Volume, volume of a solid of revolution;
3. Additional techniques of integration including integration by parts and trigonometric substitution;
4. Numerical integration; trapezoidal and Simpson's rule;
5. Improper integrals;
6. Applications of integration to areas and volumes;
7. Additional applications such as work,  arc length, area of a surface of revolution, moments and centers of mass, separable differential equations, growth and decay;
8. Introduction to sequences and series;
9. Multiple tests for convergence of sequences and series;
10. Power series, radius of convergence, interval of convergence;
11. Differentiation and integration of power series;
12. Taylor series expansion of functions;
13. Parametric equations and calculus with parametric curves; and
14. Polar curves and calculus in polar coordinates;

## Objectives

Upon successful completion of the course, students will be able to:

1. Evaluate definite and indefinite integrals using a variety of integration formulas and techniques;
2. Apply integration to areas and volumes, and other applications such as work or length of a curve;
3. Evaluate improper integrals;
4. Apply convergence tests to sequences and series;
5. Represent functions as power series; and
6. Graph, differentiate and integrate functions in polar and parametric form.

## Evaluation Methods

Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.

## Textbooks

A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course.