Synopses & Reviews
This text is written for students preparing for a career in business, economics, psychology, sociology, architecture, or the life, social, environmental, or physical sciences. It is assumed that these students have completed high school algebra. This text's primary goal is to teach the techniques of differential and integral calculus that students are likely to encounter in undergraduate courses in their majors and in subsequent professional activities. The exposition is designed to provide a sound, intuitive understanding of the basic concepts of calculus without sacrificing mathematical accuracy. Thus, the main results are stated carefully and completely, and whenever possible, explanations are intuitive or geometric.
Table of Contents
Final Updated: 03/25/2003 April_southwood 1 FUNCTIONS, GRAPHS AND LIMITS 1 Functions 2 The Graph of a Function 3 Linear Functions 4 Functional Models 5 Limits 6 One-Sided Limits and Continuity 2 DIFFERENTIATION: BASIC CONCEPTS 1 The Derivative 2 Techniques of Differentiation 3 Product and Quotient Rules; Higher Order Derivatives 4 The Chain Rule 5 Marginal Analysis and Approximations Using Increments 6 Implicit Differentiation and Related Rates 3 ADDITIONAL APPLICATIONS OF THE DERIVATIVE1 Increasing and Decreasing Functions; Relative Extrema 2 Concavity and Points of Inflection 3 Curve Sketching 4 Optimization 5 Additional Applied Optimization 4 EXPONENTIAL AND LOGARITHMIC FUNCTIONS1 Exponential Functions 2 Logarithmic Functions 3 Differentiation of Logarithmic and Exponential Functions 4 Additional Exponential Models 5 INTEGRATION1 Antidifferentiation: The Indefinite Integral 2 Integration by Substitution 3 The Definite Integral and the Fundamental Theorem of Calculus 4 Applying Definite Integration: Area Between Curves and Average Value 5 Additional Applications to Business and Economics 6 Additional Applications to the Life and Social Sciences 6 ADDITIONAL TOPICS IN INTEGRATION1 Integration by Parts; Integral Tables 2 Introduction to Differential Equations 3 Improper Integrals; Continuous Probability 4 Numerical Integration 7 CALCULUS OF SEVERAL VARIABLES1 Functions of Several Variables 2 Partial Derivatives 3 Optimizing Functions of Two Variables 4 The Method of Least Squares 5 Constrained Optimization: The Method of Lagrange Multipliers 6 Double Integrals over Rectangular Regions Appendix A Algebra Review 1 A Brief Review of Algebra 2 Factoring Polynomials and Solving Systems of Equations Tables I Powers of e II The Natural Logarithm (Base e)