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 Procedure

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.

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