Introductory Calculus
Revised: November 2006
Course Description
Main topics include derivatives of functions of one variable; an introduction to integration of functions of one variable; and applications of derivatives and integrals. Calculator: A TI-83 or TI-83+ graphing calculator is required for this course.
Objectives
1. To provide students with a working knowledge of the fundamental concepts and
techniques of differential and integral calculus of algebraic functions of one variable.
2. To provide students experience with applications of these techniques and use
of technology in solving real world problems.
3. To enhance student's problem solving skills;
4. To emphasize algebraic, numerical, geometric, and verbal approaches to calculus
concepts.
Text
Hughes-Hallett, Gleason, Lock, Flath, et al. Applied Calculus: Third Edition. John Wiley & Sons, 2006.
Grading Procedure
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Course Outline
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Chapter 1: Functions and Change
Sections 1 - 10 - What is a function, Linear functions, Rates of change, Applications of functions to economics, Exponential functions, The natural logarithm, Exponential growth and decay, New functions from old, Proportionality power functions and polynomials, periodic functions. -
Chapter 2: Rate of Change: The Derivative
Sections 1 - 5 - Instantaneous rare of change, The derivative function, Interpretations of the derivative, Marginal cost and revenue. -
Chapter 3: Short-Cuts to Differentiation
Sections 1 - 5 - Derivative formulas for powers and polynomials, Exponential and logarithmic functions, The chain rule, The product and quotient rules, Derivatives of periodic functions. -
Chapter 4: Using the Derivative
Sections 1 - 8 (skip section 6) - Local maxima and minima, Inflection points, Global maxima and minima, Profit cost and revenue, Average cost, Logistic growth, The surge function and drug concentration. -
Chapter 5: Accumulated Change: The Definite Integral
Sections 1 - 5 - Distance and accumulated change, The definite integral as area, Interpretations of the definite integral, The fundamental thermo of calculus. -
Chapter 6: Using the Definite Integral
Sections 1 - 4 - Average value, Consumer and producer surplus, Present and future value, Integrating relative growth rates. -
Chapter 7: Antiderivatives
Sections 1 - 4 - Constructing antiderivatives analytically, Integration by substitution, Using the fundamental theorem to find definite integrals, Analyzing antiderivatives graphically and numerically.