Syllabus: Math 211 - Calculus II

Department of Mathematics

Millersville University

(Revised: May, 2005)

Description

Continuation of Math 161. Transcendental functions, techniques of integration, applications of definite integrals, improper integrals, polar coordinates, and infinite series. (4 credits)

Prerequisites

Math 161.

Objectives

The student will:

Apply the definite integral to finding plane areas, volumes and surface areas of solids, and lengths of curves, and to selected problems in physics.
Learn to differentiate and integrate inverse trigonometric functions.
Learn standard techniques of integration: Integration by parts, integration of powers of trigonometric functions, trigonometric substitution, partial fractions, and selected special substitutions.
Learn numerical techniques for the evaluation of integrals.
Evaluate improper integrals of both kinds, and use L'Hopital's Rule.
Learn about sequences and infinite series, and apply the standard tests for convergence of series (to numerical series, and to power series).
Construct Taylor and Maclaurin series for functions, and apply them in calculations.
Graph curves in polar coordinates, recognize standard forms in polar coordinates, and find areas in polar coordinates by integration.
Describe curves in parametric form, and apply the techniques of calculus to parametric curves.

Course Outline

Note: The course outline refers to the text by Smith and Minton.

Topic	Section (Smith/Minton)
Inverse trigonometric functions	6.7
Calculus of the inverse trig functions	6.8
Area between curves	5.1
Volume	5.2
Volumes by cylindrical shells	5.3
Arc length and surface area	5.4
Projectile motion	5.5
Work, moments and hydrostatic force	5.6
Integration by parts	7.2
Trigonometric integrals	7.3
Trig substitution	7.3
Partial fractions	7.4
L’Hopital’s Rule	7.6
Improper integrals	7.7
Sequences	8.1
Convergent or Divergent Series	8.2
Integral test and comparison tests	8.3
Alternating series	8.4
Absolute convergence and the Ratio Test	8.5
Power series	8.6
Taylor series	8.7
Plane curves and parametric equations	9.1
Calculus of parametric equations	9.2
Arc length and surface area	9.3
Polar coordinates	9.4
Calculus and polar coordinates	9.5

In sections 5.2 and 5.3, instructors must cover at least one of volumes by shells or volumes by cross-sections.
In Section 7.3, integrals containing a^2 + x^2, a^2 - x^2, and x^2 - a^2 must be covered.
In Section 7.4, rational functions with denominators that are products of linear terms are required. Rational functions with denominators that have irreducible quadratic factors are optional.
In section 9.5, area in polar coordinates is required; arc length in polar coordinates is optional.

Texts

Calculus, 2nd edition, Robert T. Smith and Roland B. Minton, McGraw-Hill, New York, 2002.

Students are required to purchase a graphing calculator (TI-82, TI-83, TI-84, TI-85, or TI-86).

General Education Credit

This course may be taken for general education credit (G2).

Page maintained by: Bob Buchanan and Bruce Ikenaga
To suggest changes or additions mail to math@marauder.millersv.edu

Last updated: October 7, 2004