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Applied Calculus, 6e Deborah Hughes-Hallett (eBook PDF)

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Cover Title Page Copyright Dedication Preface Acknowledgments Applications Index 1 Functions and Change 1.1 What Is a Function? 1.2 Linear Functions 1.3 Average Rate of Change and Relative Change 1.4 Applications of Functions to Economics 1.5 Exponential Functions 1.6 The Natural Logarithm 1.7 Exponential Growth and Decay 1.8 New Functions from Old 1.9 Proportionality and Power Functions 1.10 Periodic Functions Chapter Summary Strengthen Your Understanding Projects for Chapter One 2 Rate of Change: The Derivative 2.1 Instantaneous Rate of Change 2.2 The Derivative Function 2.3 Interpretations of the Derivative 2.4 The Second Derivative 2.5 Marginal Cost and Revenue Chapter Summary Strengthen Your Understanding Projects for Chapter Two Focus on Theory 3 Shortcuts to Differentiation 3.1 Derivative Formulas for Powers and Polynomials 3.2 Exponential and Logarithmic Functions 3.3 The Chain Rule 3.4 The Product and Quotient Rules 3.5 Derivatives of Periodic Functions Chapter Summary Strengthen Your Understanding Projects for Chapter Three Focus on Theory Focus on Practice 4 Using The Derivative 4.1 Local Maxima and Minima 4.2 Inflection Points 4.3 Global Maxima and Minima 4.4 Profit, Cost, and Revenue 4.5 Average Cost 4.6 Elasticity of Demand 4.7 Logistic Growth 4.8 The Surge Function and Drug Concentration Chapter Summary Strengthen Your Understanding Projects for Chapter Four 5 Accumulated Change: The Definite Integral 5.1 Distance and Accumulated Change 5.2 The Definite Integral 5.3 The Definite Integral as Area 5.4 Interpretations of the Definite Integral 5.5 Total Change and the Fundamental Theorem of Calculus 5.6 Average Value Chapter Summary Strengthen Your Understanding Projects for Chapter Five Focus on Theory 6 Antiderivatives and Applications 6.1 Analyzing Antiderivatives Graphically and Numerically 6.2 Antiderivatives and the Indefinite Integral 6.3 Using the Fundamental Theorem to Find Definite Integrals 6.4 Application: Consumer and Producer Surplus 6.5 Application: Present and Future Value 6.6 Integration by Substitution 6.7 Integration by Parts Chapter Summary Strengthen Your Understanding Projects for Chapter Six Focus on Practice 7 Probability 7.1 Density Functions 7.2 Cumulative Distribution Functions and Probability 7.3 The Median and the Mean Chapter Summary Strengthen Your Understanding Projects for Chapter Seven 8 Functions of Several Variables 8.1 Understanding Functions of Two Variables 8.2 Contour Diagrams 8.3 Partial Derivatives 8.4 Computing Partial Derivatives Algebraically 8.5 Critical Points and Optimization 8.6 Constrained Optimization Chapter Summary Strengthen Your Understanding Projects for Chapter 8 Focus on Theory 9 Mathematical Modeling Using Differential Equations 9.1 Mathematical Modeling: Setting up a Differential Equation 9.2 Solutions of Differential Equations 9.3 Slope Fields 9.4 Exponential Growth and Decay 9.5 Applications and Modeling 9.6 Modeling the Interaction of Two Populations 9.7 Modeling the Spread of a Disease Chapter Summary Strengthen Your Understanding Projects for Chapter Nine Focus on Theory: Separation of Variables Problems on Separation of Variables 10 Geometric Series 10.1 Geometric Series 10.2 Applications to Business and Economics 10.3 Applications to the Natural Sciences Chapter Summary Strengthen Your Understanding Projects for Chapter 10 Appendices A Fitting Formulas to Data B Compound Interest and the Number e C Spreadsheet Projects Graphs of Families of Functions Index

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