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Applied Calculus for Business, Economics, and the Social and Life Sciences.
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Chapter 1: Functions, Graphs, and Limits 1.1 Functions 1.2 The Graph of a Function 1.3 Linear Functions 1.4 Functional Models 1.5 Limits 1.6 One-Sided Limits and Continuity Chapter 2: Differentiation: Basic Concepts 1.1 The Derivative 1.2 Techniques of Differentiation 1.3 Product and Quotient Rules; Higher-Order Derivatives 1.4 The Chain Rule 1.5 Marginal Analysis and Approximations Using Increments 1.6 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 Applications; Exponential Models Chapter 5: Integration 5.1 Antidifferentiation: The Indefinite Integral 5.2 Integration by Substitution 5.3 The Definite Integral and the Fundamental Theorem of Calculus 5.4 Applying Definite Integration: Area Between Curves 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 Improper Integrals 6.3 Numerical Integration 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: Differential Equations 8.1 Introduction to Differential Equations 8.2 First-Order Linear Differential Equations 8.3 Additional Applications of Differential Equations 8.4 Approximate Solutions of Differential Equations 8.5 Difference Equations; The Cobweb Model Chapter 9: Infinite Series and Taylor Series Approximations 9.1 Infinite Series; Geometric Series 9.2 Tests for Convergence 9.3 Functions as Power Series; Taylor Series Chapter 10: Probability and Calculus 10.1 Introduction to Probability; Discrete Random Variables 10.2 Continuous Random Variables 10.3 Expected Value and Variance of Continuous Random Variables 10.4 Normal and Poisson Probability Distributions Chapter 11: Trigonometric Functions 11.1 The Trigonometric Functions 11.2 Differentiation and Integration of Trigonometric Functions 11.3 Additional Applications Involving Trigonometric Function 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