# MATH 255 Syllabus

### Calculus II

Revised: January 2015

## Course Description

Derivatives and integrals of transcendental functions, techniques of integration, indeterminant forms, improper integrals, infinite series. Prerequisite: Math 153. Four semester hours.

## Student Learning Objectives

By the end of the course, the student will be able to:

• Calculate areas between curves.
• Compute volumes of solids by disks, washers, and cylindrical shells.
• Compute arc-length of a curve and surface area.
• Solve applied problems involving force and work.
• Evaluate anti-derivatives and definite integrals using u-substitution, integration by parts, trigonometric substitution, partial fractions, completing the square, and appropriate use of technology.
• Use simple approximation techniques for definite integrals, check the error bounds for each technique, and compare the strengths and weaknesses of each.
• Evaluate improper integrals.
• Compute areas of planar regions and arc-lengths of curves using polar coordinates.
• Determine whether a sequence converges or diverges.
• Determine whether a series converges conditionally, converges absolutely, or diverges using the appropriate methods, such as geometric series test, p-series test, the comparison test, the limit comparison test, the integral test, the ratio test, the root test, and the alternating series test.
• Determine the radius of convergence and the interval of convergence of a power series.
• Compute the Taylor and Maclaurin series of a function.

## Text

Steward, James. Calculus: Early Transcendentals, 6th edition, Thomson Brooks/Cole, 2008.

Grading procedures and factors influencing course grade are left to the discretion
of individual instructors, subject to general university policy.

## Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to
general university policy.

## Course Outline

• Review of Chapter 5 (1-2 days)
• CHAPTER 6 - Integrals (5 days)  Sections 6.2-6.5; Applications of the definite integral including volumes, work and average values of functions.
• CHAPTER 7 - Techniques of Integration (11 days)  Sections 7.1-7.5, 7.7, 7.8 essential, 7.6 optional. Methods of integration, approximate integration, and improper integrals.
• CHAPTER 8 - Further Applications of Integration (4 days)  Sections 8.1 and 8.2 essential, with selected topics from 8.3-8.5 (at instructor's discretion). Arc length, areas of surfaces of revolution, and selected applications from the sciences.
• CHAPTER 10 - Parametric Equations and Polar Coordinates (6 days)  Sections 10.1-10.4 essential. Derivatives, arc length, and areas in the parametric and polar settings.
• CHAPTER 11 – Infinite Sequences and Series (16 days)  Sections 11.1- 11.10 essential, 11.11 optional. Limits of sequences, tests for convergence of series, power series, and Taylor series.

Additional sections may be covered, if time permits, at the instructors discretion.