College Mathematics for Business, Economics, Life Sciences and Social Sciences

For freshman/sophomore, 2 semester/2-3 quarter courses covering finite mathematics and calculus for students in business, economics, social sciences, or life sciences departments. This accessible text is designed to help students help themselves excel in the course. The content is organized into three parts: (1) A Library of Elementary Functions (Chapters 1-2), (2) Finite Mathematics (Chapters 3-9), and (3) Calculus (Chapters 10-15). The book's overall approach, refined by the authors' experience with large sections of college freshmen, addresses the challenges of teaching and learning when your students' prerequisite knowledge varies greatly. Student-friendly features such as Matched Problems, Explore & Discuss questions, and Conceptual Insights, together with the motivating and ample applications, make this text a popular choice for today's students and instructors. The MyMathLab course for the text features thousands of homework exercises plus instructional videos for nearly every example in the book.Part One: A Library of Elementary Functions Chapter 1: Linear Equations and Graphs 1-1 Linear Equations and Inequalities 1-2 Graphs and Lines 1-3 Linear Regression Chapter 1 Review Review Exercise Chapter 2: Functions and Graphs 2-1 Functions 2-2 Elementary Functions: Graphs and Transformations 2-3 Quadratic Functions 2-4 Polynomial and Rational Functions 2-5 Exponential Functions 2-6 Logarithmic Functions Chapter 2 Review Review Exercise Part Two: Finite Mathematics Chapter 3: Mathematics of Finance 3-1 Simple Interest 3-2 Compound and Continuous Compound Interest 3-3 Future Value of an Annuity; Sinking Funds 3-4 Present Value of an Annuity; Amortization Chapter 3 Review Review Exercise Chapter 4: Systems of Linear Equations; Matrices 4-1 Review: Systems of Linear Equations in Two Variables 4-2 Systems of Linear Equations and Augmented Matrices 4-3 Gauss-Jordan Elimination 4-4 Matrices: Basic Operations 4-5 Inverse of a Square Matrix 4-6 Matrix Equations and Systems of Linear Equations 4-7 Leontief Input-Output Analysis Chapter 4 Review Review Exercise Chapter 5: Linear Inequalities and Linear Programming 5-1 Inequalities in Two Variables 5-2 Systems of Linear Inequalities in Two Variables 5-3 Linear Programming in Two Dimensions: A Geometric Approach Chapter 5 Review Review Exercise Chapter 6: Linear Programming: Simplex Method 6-1 A Geometric Introduction to the Simplex Method 6-2 The Simplex Method: Maximization with Problem Constraints of the Form = 6-3 The Dual; Minimization with Problem Constraints of the form = 6-4 Maximization and Minimization with Mixed Problem Constraints Chapter 6 Review Review Exercise Chapter 7: Logic, Sets, and Counting 7-1 Logic 7-2 Sets 7-3 Basic Counting Principles 7-4 Permutations and Combinations Chapter 7 Review Review Exercise Chapter 8: Probability 8-1 Sample Spaces, Events, and Probability 8-2 Union, Intersection, and Complement of Events; Odds 8-3 Conditional Probability, Intersection, and Independence 8-4 Bayes' Formula 8-5 Random Variables, Probability Distribution, and Expected Value Chapter 8 Review Review Exercise Chapter 9: Markov Chains 9-1 Properties of Markov Chains 9-2 Regular Markov Chains 9-3 Absorbing Markov Chains Chapter 9 Review Review Exercise Part Three: Calculus Chapter 10: Limits and the Derivative 10-1 Introduction to Limits 10-2 Infinite Limits and Limits at Infinity 10-3 Continuity 10-4 The Derivative 10-5 Basic Differentiation Properties 10-6 Differentials 10-7 Marginal Analysis in Business and Economics Chapter 10 Review Review Exercise Chapter 11: Additional Derivative Topics 11-1 The Constant e and Continuous Compound Interest 11-2 Derivatives of Logarithmic and Exponential Functions 11-3 Derivatives of Products and Quotients 11-4 The Chain Rule 11-4 Implicit Differentiation 11-5 Related Rates 11-7 Elasticity of Demand Chapter 11 Review Review Exercise Chapter 12: Graphing and Optimization 12-1 First Derivative and Graphs 12-2 Second Derivative and Graphs 12-3 L'Hopitals's Rule 12-4 Curve Sketching Techniques 12-5 Absolute Maxima and Minima 12-6 Optimization Chapter 12 Review Review Exercise Chapter 13: Integration 13-1 Antiderivatives and Indefinite Integrals 13-2 Integration by Substitution 13-3 Differential Equations; Growth and Decay 13-4 The Definite Integral 13-5 The Fundamental Theorem of Calculus Chapter 13 Review Review Exercise Chapter 14: Additional Integration Topics 14-1 Area Between Curves 14-2 Applications in Business and Economics 14-3 Integration by Parts 14-4 Integration Using Tables Chapter 14 Review Review Exercise Appendixes Appendix A: Basic Algebra Review Self-Test on Basic Algebra A-1 Algebra and Real Numbers A-2 Operations on Polynomials A-3 Factoring Polynomials A-4 Operations on Rational Expressions A-5 Integer Exponents and Scientific Notation A-6 Rational Exponents and Radicals A-7 Quadratic Equations Appendix B: Special Topics B-1 Sequences, Series, and Summation Notation B-2 Arithmetic and Geometric Sequences B-3 Binomial Theorem Appendix C: Tables Table I Area Under the Standard Normal Curve Table II Basic Geometric Formulas Answers Index Applications Index A Library of Elementary Functions