MA 128 Syllabus

Mathematics Department
Indiana University of Pennsylvania
Indiana, PA 15705



Course Number:		MA 128

Course Title:		Calculus II

Credits:		4 semester hours

Prerequisites:		Permission of the mathematics department

Textbook:		Calculus with Analytic Geometry (5th ed.)
			by Swokowski
			PWS-Kent

Revised:		9/92

Catalog Description:

The second in a three-course series of courses stresses the theory of calculus as well as the application in problem solving. Topics to be included are: definite integrals and application, logarithmic and exponential functions, trigonometric and inverse trigonometric functions, polar coordinates, hyperbolic functions, indeterminate forms, improper integrals, and Taylor's formula.

Course Outline/Time Schedule:

I.	Applications of the Definite Integral (11-12 days)
	A.	Area
	B.	Solids of Revolution
	C.	Volumes by Cylindrical Shells
	D.	Volumes by Cross Sections
	E.	Arc Length and Surfaces of Revolution
	F.	Work
	G.	Moments and Centers of Mass
	H.	Other Applications (optional)

II.	Logarithmic and Exponential Functions (8-9 days)
	A.	Inverse Functions
	B.	The Natural Logarithmic Function
	C.	The Natural Exponential Function
	D.	Integration
	E.	General Exponential and Logarithmic Functions
	F.	Laws of Growth and Decay

III.	Inverse Trigonometric and Hyperbolic Functions (5-6 days)
	A.	Inverse Trigonometric Functions
	B.	Derivatives and Integrals of a Function
	C.	Hyperbolic Functions
	D.	Inverse Hyperbolic Functions 
	
IV.	Techniques of Integration (10-11 days)
	A.	Integration by Parts
	B.	Trigonometric Integrals
	C.	Trigonometric Substitutions
	D.	Integrals of Rational Functions
	E.	Integrals involving Quadratic Expressions
	F.	Miscellaneous Substitutions
	G.	Tables of Integrals

V.	Indeterminate Forms and Improper Integrals (4-5 days)
	A.	The Indeterminate Form 0/0 and °/°
	B.	Other Indeterminate Forms
	C.	Integrals with Infinite Limits of Integration
	D.	Integrals with Discontinuous Integrands

VI.	Infinite Series (14-15 days)
	A.	Sequences
	B.	Convergent or Divergent Series
	C.	Positive-Term Series
	D.	The Ratio and Root Tests
	E.	Alternating Series and Absolute Convergence
	F.	Power Series
	G.	Power Series Representations of Functions

References:

1.	The Calculus with Analytic Geometry, by Louis Leithold.
2.	Calculus with Analytic Geometry, by Robert Ellis and Denny Gulick.
3.	Calculus and Analytic Geometry, by Abe Mizrahi and Michael Sullivan.
4.	Calculus with Analytic Geometry, by Harley Flanders and Justin Price.
5.	Calculus, by M.A. Munem and D.J. Foulis.
6.	Theory and Problems of Differential and Integral Calculus (Schaum's Outline Series), by Frank Ayres.