Calculus for Business, Economics, Life Sciences, and Social Sciences

(Each chapter concludes with Important Terms, Symbols, and Concepts Review Exercise and Group Activities.) PART ONE. A LIBRARY OF ELEMENTARY FUNCTIONS. CHAPTER 1. A Beginning Library of Elementary Functions. 1-1 Functions. 1-2 Elementary Functions: Graphs and Transformations. 1-3 Linear Functions and Straight Lines. 1-4 Quadratic Functions. Group Activity 1: Introduction to Regression Analysis. Group Activity 2: Mathematical Modeling in Business. CHAPTER 2. Additional Elementary Functions. 2-1 Polynomial and Rational Functions. 2-2 Exponential Functions. 2-3 Logarithmic Functions. Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions. Group Activity 2: Comparing Regression Models. PART TWO. CALCULUS. CHAPTER 3. The Derivative. 3-1 Introduction to Limits. 3-2 Limits and Continuity. 3-3 The Derivative. 3-4 Derivative of Constants, Power Forms, and Sums. 3-5 Derivatives of Products and Quotients. 3-6 Chain Rule: Power Form. 3-7 Marginal Analysis in Business and Economics. Group Activity 1: Minimal Average Cost. Group Activity 2: Numerical Differentiation on a Graphing Utility. CHAPTER 4. Graphing and Optimization. 4-1 First Derivative and Graphs. 4-2 Second Derivative and Graphs. 4-3 Curve Sketching Techniques Unified and Extended. 4-4 Optimization Absolute Maxima and Minima. Group Activity 1: Maximizing Profit. Group Activity 2: Minimizing Construction Costs. CHAPTER 5. Additional Derivative Topics. 5-1 The Constant e and Continuous Compound Interest. 5-2 Derivatives of Logarithmic and Exponential Functions. 5-3 Chain Rule: General Form. 5-4 Implicit Differentiation. 5-5 Related Rates. Group Activity 1: Elasticity of Demand. Group Activity 2: Point of Diminishing Returns. CHAPTER 6. Integration. 6-1 Antiderivatives and Indefinite Integrals. 6-2 Integration by Substitution. 6-3 Differential Equations Growth and Decay. 6-4 The Definite Integral. 6-5 The Fundamental Theorem of Calculus. Group Activity 1: Simpson's Rule. Group Activity 2: Bell-Shaped Curves. CHAPTER 7. Additional Integration Topics. 7-1 Area Between Curves. 7-2 Applications in Business and Economics. 7-3 Integration by Parts. 7-4 Integration Using Tables. Group Activity 1: Analysis of Income Concentration from Raw Data. Group Activity 2: Grain Exchange. CHAPTER 8. Multivariable Calculus. 8-1 Functions of Several Variables. 8-2 Partial Derivatives. 8-3 Maxima and Minima. 8-4 Maxima and Minima Using Lagrange Multipliers. 8-5 Method of Least Squares. 8-6 Double Integrals Over Rectangular Regions. Group Activity 1: City Planning. Group Activity 2: Numerical Integration of Multivariable Functions. CHAPTER 9. Trigonometric Functions. 9-1 Trigonometric Functions Review. 9-2 Derivatives of Trigonometric Functions. 9-3 Integrations of Trigonometric Functions. Group Activity 1: Seasonal Business Cycles. Group Activity 2: Heating Degree Days. APPENDIX A. Basic Algebra Review. APPENDIX B. Special Topics. APPENDIX C. Tables.