Provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, economics, and the life and social sciences. In this book, the author applies real-world orientation to concepts, problem-solving approach, straight forward and concise writing style, and comprehensive exercise sets.
Provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, economics, and the life and social sciences. In this book, the author applies real-world orientation to concepts, problem-solving approach, straight forward and concise writing style, and comprehensive exercise sets.
Laurence D. Hoffmann November 2011 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. 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. 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. My wife, Janice, and I love to travel, enjoy music and the arts, have two grown sons, three grandchildren and two Maltese dogs. 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. Long ago, I received by BA in mathematics from Brown University and my Ph.D. in mathematics from the University of Wisconsin.
Inhaltsangabe
Chapter 1: Functions, Graphs, and Limits 1.1Functions 1.2The Graph of a Function 1.3Lines and Linear Functions 1.4Functional Models 1.5Limits 1.6One-Sided Limits and Continuity Chapter 2: Differentiation: Basic Concepts 2.1The Derivative 2.2Techniques of Differentiation 2.3Product and Quotient Rules; Higher-Order Derivatives 2.4The Chain Rule 2.5Marginal Analysis and Approximations Using Increments 2.6Implicit 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 6.4 Introduction to Continuous Probability 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 Appendix A: Algebra Review A.1 A Brief Review of Algebra A.2 Factoring Polynomials and Solving Systems of Equations A.3 Evaluating Limits with L'Hopital's Rule A.4 The Summation Notation
Chapter 1: Functions, Graphs, and Limits 1.1Functions 1.2The Graph of a Function 1.3Lines and Linear Functions 1.4Functional Models 1.5Limits 1.6One-Sided Limits and Continuity Chapter 2: Differentiation: Basic Concepts 2.1The Derivative 2.2Techniques of Differentiation 2.3Product and Quotient Rules; Higher-Order Derivatives 2.4The Chain Rule 2.5Marginal Analysis and Approximations Using Increments 2.6Implicit 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 6.4 Introduction to Continuous Probability 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 Appendix A: Algebra Review A.1 A Brief Review of Algebra A.2 Factoring Polynomials and Solving Systems of Equations A.3 Evaluating Limits with L'Hopital's Rule A.4 The Summation Notation
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