Course Number: MATH 1413

Course Title: Survey of Calculus

Hours Credit: 3 hours

Prerequisites: MATH 1111 or MATH 1113

Course Description: This course will provide a survey of the differential and integral calculus of polynomial, rational, exponential, and logarithmic functions with an emphasis on applications to problems from business, economics and life sciences.

Text: Bittinger, Calculus and Its Applications, Eighth Edition, Addison Wesley, 2004.

Learning Outcomes:

1. The student will be able to compute limits.
2. The student will be able to differentiate polynomial, rational, exponential, and logarithmic functions.
3. The student will be able to apply differential calculus to problems from business, economics, and life science.
4. The student will be able to integrate polynomial, rational, exponential, and logarithmic functions and to apply the Fundamental Theorem of Calculus.
5. The student will be able to apply integral calculus to problems from business, economics, and life science.
6. The student will understand the basic techniques of integration.

Topics: The following sections of the textbook will be covered:

Section

2.1       Limits and Continuity: Numerically and Graphically

2.2       Limits: Algebraically

2.3       Average Rates of Change

2.4       Differentiation Using Limits of Difference Quotients

2.5       Differentiation Techniques: The Power and Sum-Difference Rules

2.6       Instantaneous Rates of Change

2.7       Differentiation Techniques: The Product and Quotient Rules

2.8       The Chain Rule

2.9       Higher-Order Derivatives

3.1       Using First Derivative to Find Maximum and Minimum Values and Sketch Graphs

3.2       Using Second Derivative to Find Maximum and Minimum Values and Sketch Graphs

3.4       Using Derivatives to Find Absolute Maximum and Minimum Values

3.5       Maximum-Minimum Problems: Business and Economic Applications

3.6       Differentials

3.7       Implicit Differentiation and Related Rates

4.1       Exponential Functions

4.2       Logarithmic Functions

4.3       Applications: The Uninhibited Grwoth Model dp/dt=kP

4.6       An Economics Application: Elasticity of Demand

5.1       Integration

5.2       Area and Definite Integrals

5.4       Properties of Definite Integrals

5.5       Integration Techniques: Substitution

6.1       An Economics Application: Consumer Surplus and Producer Surplus

Grading Method: To be determined by instructor. The final exam should be given during the time as scheduled by the RegistrarŐs Office and should count between 20% and 35% of the overall grade.