Calculus II

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Syllabus

Catalog Description
4 credits, 4 hours
Prerequisite: MAT201

This is a course designed to provide students with an appreciation of the usefulness and power of calculus. Emphasis will be placed on the application of calculus to various disciplines. Among the topics studied are the definite integral, area, formal integration, applications of integration, and series.

Instructional Objectives

1. Intermediate integration techniques, substitution, integration by parts, method of partial fractions.
2. Applications to volume and surface area of solids of revolutions and arc length.
3. Representation of trig, exponential, and log functions as "infinite" polynomials.
4. Elementary theory of, and solution techniques for 1st- and 2nd-order linear ODE's.
Performance Objectives
1. Integration by substitution, by parts, by partial fraction decomposition.
2. Calculate volume, surface area and arc length.
3. Obtain power series expansions of appropriate functions, and determine their radii of convergence.
4. Solve elementary ODE's by separation of variables, or manipulation of the characteristic equation.
Text:
Calculus (Harvard) 3rd Edition
by Hughes-Hallett, et al.
Published by John Wiley & Sons, Inc.
Grading: Quizzes, tests, Final Exam
Attendance: Mandatory

Calculus II – MAT202 Syllabus
Topics

Section #	Topic
7.1	Integration by Substitution
7.2	Integration by Parts
7.3	Tables of Integrals
7.4	Algebraic Identity and Trigonometric Substitution
7.5	Approximating Definite Integrals
7.6	Approximation Methods and Simpson’s Rule
7.7	Improper Integrals
7.8	Comparison of Improper Integrals
	Review
	Test
8.1	Areas and Volumes
8.2	Applications to Geometry
8.3	Density and Center of Mass
8.4	Applications to Physics
	Review
	Test
9.1	Geometric Series
9.2	Convergence of sequences and series
9.3	Tests for Convergence
9.4	Power series
10.1	Taylor Polynomials
10.2	Taylor Series
10.3	Finding and Using Taylor Series
10.4	The Error in Taylor Polynomials
	Review
	Test
11.1	What is a Differential Equation?
11.2	Slope Fields
11.3	Euler’s Method
11.4	Separation of Variables
11.11	Linear Second Order Differential Equations
	ODE’s and Power series, recursive formula for coefficients
	Final Review