CATALOG DESCRIPTION:

Math 01.130 Calculus I                                                                                                                             4 s.h.

Prerequisites: Math #01122 or 60 on the CLM exam

This course begins with a discussion of functions, the limit concept and continuity.  The concept of a derivative is introduced and the student learns to differentiate algebraic functions, exponential, functions, logarithmic and trigonometric functions. Differentiation is applied to analysis of functions, extreme problems and to problems in related rates.  The integral as the unit of a sum is linked to the antiderivative by the Fundamental Theorem of Calculus and used to find areas. A graphing calculator is required for this course, and so is the use of a computer software, such as Mathematica.  Students are expected to have completed an equivalent of (Math 01.122) Precalculus.
 

OBJECTIVES:

Students will demonstrate the ability to: (i) compute limits; (ii) differentiate and integrate polynomial, rational, algebraic, exponential, logarithmic and trigonometric functions; (iii) use differentiation to solve extreme and related rate problems, and (iv) use integration to find areas and volumes.
 

CONTENTS:

1:   Prerequisites for Calculus

 A brief review of functions and their graphs.

2:  Limits and Continuity

 It is recommended that the emphasis here be on definitions and on intuitive understanding of concepts, though formal delta and epsilon proofs should be demonstrated.

3:  Derivatives

 The derivative definition and the rules for finding derivatives of polynomial, rational, exponential, logarithmic, trigonometric and algebraic functions.

4:  Logs and exponential functions

 Inverse functions, logs and exponential functions, derivatives of logs and exponential functions.
 Implicit differentiation, related rates.

5:  Analysis of functions and their graphs

 Increasing and decreasing functions, concavity, Relative extreme, First and 2nd derivative tests, Rolle's Theorem and the Mean Value Theorem.

6:  Applications of Derivatives

 Applications of the derivative to maxima and minima, the relationships between distance, velocity and acceleration.

7:  Integration

The definite integral is formally defined and the definition is used to evaluate the integral.  The Fundamental Theorem of        Calculus is proved and techniques for evaluation of both definite and indefinite integrals by means of the Fundamental Theorem is discussed. The process of integration by means of a change of variable is then introduced.

8:  Applications of Definite Integrals

Areas between two curves by the use of the definite integral.
 

REMARKS:  In each chapter we will be studying a little about the history of the development of Calculus through a brief study of the biographies of the great mathematicians who developed it.  In addition, we will begin to learn to use Mathematica as a tool.
 

Possible TEXT:

Rogawski, Jon, Calculus: Early Transcendentals Combo (Mathematica) & CalPortal, 2008, Freeman

Stewart, James, CALCULUS: CONCEPTS AND CONTEXTS, 3rd edition, Brooks, Cole, 2005.

Anton, H., CALCULUS, 6th edition, John Wiley and Sons, Inc., New York, 1998.

Larson, Hostetler & Edwards:  Calculus, 6th edition, D.C. Heath Company, Lexington, 1998.

(Note:  There are many suitable texts available that cover the same material at the same level. Among these are those by Finney/Thomas, Stein, Hunt and Leithold).