We also travel whenever we get a chance and especially enjoy cruising. My wife, Jaqui, and I are active supporters of recording textbooks for the blind and dyslexic. I love to write, and in addition to this text have written published texts on engineering calculus and linear algebra. in mathematics from the University of Wisconsin.Īfter receiving my undergraduate degree at Harvey Mudd College and my PhD from Caltech, I joined the Mathematics Department at Claremont McKenna College, where I have continued to teach, specializing in calculus, linear algebra, and differential equations. Long ago, I received by BA in mathematics from Brown University and my Ph.D. I am an avid (but average) tennis player, am addicted to the Sunday Puzzle on NPR, and have been trying for several years to become fluent in Italian. My wife, Janice, and I love to travel, enjoy music and the arts, have two grown sons, three grandchildren and two Maltese dogs. In addition to my current profession and my ongoing involvement with this text, I serve on the Strategic Planning committee of the Claremont Community foundation and on the Investment Committee of the Rancho Santa Ana Botanic Gardens in Claremont. Before assuming my current position as a Senior Investment Management Consultant with Morgan Stanley Smith Barney, I was a tenured professor of mathematics at Claremont McKenna College, where, on three occasions, I was honored to be the recipient of the Huntoon Award for Excellence in Teaching, a “best-teacher” award determined by a vote of the students. I consider myself to be a writer and expositor as well as a mathematician, and these traits led to the original version of this text published in 1975. Chapter 1: Functions, Graphs, and Limits 1.1ğunctions 1.2 The Graph of a Function 1.3 Lines and Linear Functions 1.4ğunctional Models 1.5 Limits 1.6 One-Sided Limits and Continuity Chapter 2: Differentiation: Basic Concepts 2.1 The Derivative 2.2 Techniques of Differentiation 2.3 Product and Quotient Rules Higher-Order Derivatives 2.4 The Chain Rule 2.5 Marginal Analysis and Approximations Using Increments 2.6 Implicit Differentiation and Related Rates Chapter 3: Additional Applications of the Derivative 3.1 Increasing and Decreasing Functions Relative Extrema 3.2 Concavity and Points of Inflection 3.3 Curve Sketching 3.4 Optimization Elasticity of Demand 3.5 Additional Applied Optimization Chapter 4: Exponential and Logarithmic Functions 4.1 Exponential Functions Continuous Compounding 4.2 Logarithmic Functions 4.3 Differentiation of Exponential and Logarithmic Functions 4.4 Additional Applications Exponential Models Chapter 5: Integration 5.1 Indefinite Integration and Differential Equations 5.2 Integration by Substitution 5.3 The Definite Integral and the Fundamental Theorem of Calculus 5.4 Applying Definite Integration: Distribution of Wealth and Average Value 5.5 Additional Applications to Business and Economics 5.6 Additional Applications to the Life and Social Sciences Chapter 6: Additional Topics in Integration 6.1 Integration by Parts Integral Tables 6.2 Numerical Integration 6.3 Improper Integrals Chapter 7: Calculus of Several Variables 7.1 Functions of Several Variables 7.2 Partial Derivatives 7.3 Optimizing Functions of Two Variables 7.4 The Method of Least-Squares 7.5 Constrained Optimization: The Method of Lagrange Multipliers 7.6 Double Integrals Chapter 8: Trigonometric Functions 8.1 Angle Measurement Trigonometric Functions 8.2 Trigonometric Applications Involving Differentiation 8.3 Trigonometric Applications Involving Integration Chapter 9: Differential Equations 9.1 Modeling with Differential Equations 9.2 First-Order Linear Differential Equations 9.3 Additional Applications of Differential Equations 9.4 Approximate Solutions of Differential Equations 9.5 Difference Equations The Cobweb Model Chapter 10: Infinite Series and Taylor Series Approximations 10.1 Infinite Series Geometric Series 10.2 Tests for Convergence 10.3 Functions as Power Series Taylor Series Chapter 11: Probability and Calculus 11.1 Introduction to Probability Discrete Random Variables 11.2 Continuous Probability Distributions 11.3 Expected Value and Variance of Continuous Random Variables 10.4 Normal and Poisson Probability Distributions Appendix A: Algebra Review A.1 A Brief Review of AlgebraĪ.2 Factoring Polynomials and Solving Systems of EquationsĪ.3 Evaluating Limits with L’Hopital’s Rule
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