Syllabus: Math 161 - Calculus I

Department of Mathematics

Millersville University

(Revised: May, 2005)

Description

An introduction to the concepts and techniques of calculus, beginning with limits; theory and applications of derivatives, antiderivatives, and definite integrals; calculus of trigonometric, exponential, and logarithmic functions. (4 credits)

Prerequisites

A C- or better in Math 160 or Math Placement or Testing before registration.

Objectives

The student will:

Learn about the derivative, relationship to limits, and its application to finding slopes of curves and rates of change.
Learn the fundamental formulas and techniques of differential calculus.
Learn about the definite integral, its relationship to limits, and its application to finding areas.
Learn to differentiate and integrate simple trigonometric functions, exponential functions, and logarithmic functions.
Develop some applications of the theoretical underpinnings of calculus: The notions of limits and continuity, derivations of the key formulas of calculus, and proofs of some major theorems.
Become competent in applying the techniques of calculus to problem-solving situations.

Course Outline

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

	Topic	Section (Smith/Minton)
	The Concept of Limit	1.1
	Computation of limits	1.2
	Continuity and its consequences	1.3
	Limits involving infinity	1.4
	Tangent lines and velocity	2.1
	Definition of derivative	2.2
	Computation of derivatives	2.3
	The Product and Quotient Rules	2.4
	Derivatives of trig functions	2.5
	Derivatives of Exponential and Logarithms	2.6
	The Chain Rule	2.7
	Implicit differentiation and Related Rates	2.8
	The Mean Value Theorem	2.9
	Linear Approximations and Differentials	3.1
	Newton's method	3.2
	Maximum and Minimum Values	3.3
	Increasing and decreasing functions	3.4
	Concavity	3.5
	Curve Sketching	3.6
	Optimization problems	3.7
	Antiderivatives	4.1
	Sums and sigma notation	4.2
	Area	4.3
	The Definite integral	4.4
	The Fundamental Theorem of Calculus	4.5
	Integration by substitution	4.6
	Numerical integration*	4.7
	The natural logarithm as an integral	6.1
	Inverse functions	6.2
	The exponential function	6.3
	Growth and decay problems	6.4

* Coverage of Simpson’s Rule is not required.

Text

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