Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises. 1. Functions Application Preview: World Record Mile Runs 1.1 Real Numbers, Inequalities, and Lines 1.2 Exponents 1.3 Functions 1.4 Functions, Continued 1.5 Exponential Functions 1.6 Logarithmic Functions I. Finite Mathematics 2. Mathematics of Finance Application Preview: Musical Instruments as Investments 2.1 Simple Interest 2.2 Compound Interest 2.3 Annuities 2.4 Amortization 3. Systems of Equations and Matrices Application Preview: A "Taxing" Problem 3.1 Systems of Two Linear Equations in Two Variables 3.2 Matrices and Linear Equations in Two Variables 3.3 Systems of Linear Equations and the Gauss-Jordan Method 3.4 Matrix Arithmetic 3.5 Inverse Matrices and Systems of Linear Equations 3.6 Introduction to Modeling: Leontief Models and Least Squares 4. Linear Programming Application Preview: Managing an Investment Portfolio 4.1 Linear Inequalities 4.2 Two-Variable Linear Programming Problems 4.3 The Simplex Method for Standard Maximum Problems 4.4 Standard Minimum Problems and Duality 4.5* Nonstandard Problems: The Dual Pivot Element and the Two-Stage Method 4.6* Nonstandard Problems: Artificial Variables and the Big-M Method * These two sections provide alternate methods for solving the same types of problems. The choice of which to cover is left to the Instructor. 5. Probability Application Preview: The Chevalier de Mere 5.1 Sets, Counting, and Venn Diagrams 5.2 Permutations and Combinations 5.3 Probability Spaces 5.4 Conditional Probability and Independence 5.5 Bayes' Formula 5.6 Random Variables and Distributions 6. Statistics Application Preview: Household Income 6.1 Random Samples and Data Organization 6.2 Measures of Central Tendency 6.3 Measures of Variation 6.4 Normal Distributions and Binomial Approximation 7. Markov Chains Application Preview: Weather in Sri Lanka 7.1 States and Transitions 7.2 Regular Markov Chains 7.3 Absorbing Markov Chains II. Calculus 8. Derivatives and Their Uses Application Preview: Temperature, Superconductivity, and Limits 8.1 Limits and Continuity 8.2 Rates of Change, Slopes, and Derivatives 8.3 Some Differentiation Formulas 8.4 The Product and Quotient Rules 8.5 Higher-Order Derivatives 8.6 The Chain Rule and Generalized Power Rule 8.7 Nondifferentiable Functions 9. Further Applications of Derivatives Application Preview: Stevens' Law of Psychophysics 9.1 Graphing Using the First Derivative 9.2 Graphing Using the First and Second Derivatives 9.3 Optimization 9.4 Further Applications of Optimization 9.5 Optimizing Lot Size and Harvest Size 9.6 Implicit Differentiation and Related Rates Cumulative Review for Chapters 1, 8-9 10. Exponential and Logarithmic Functions Application Preview: Elasticity and Social Policy 10.1 Review of Exponential and Logarithmic Functions 10.2 Differentiation of Logarithmic and Exponential Functions 10.3 Two Applications to Economics: Related Rates and Elasticity of Demand 11. Integration and Its Applications Application Preview: Cigarette Smoking 11.1 Antiderivatives and Indefinite Integrals 11.2 Integration Using Logarithmic and Exponential Functions 11.3 Definite Integrals and Areas 11.4 Further Applications of Definite Integrals: Average Value and Area Between Curves 11.5 Two Applications to Economics: Consumers' Surplus and Income Distribution 11.6 Integration by Substitution 12. Integration Techniques and Differential Equations Application Preview: Improper Integrals and Eternal Recognition 12.1 Integration by Parts 12.2 Integration Using Tables 12.3 Improper Integrals 12.4 Numerical Integration 12.5 Differential Equations 12.6 Further Applications of Differential Equations: Three Models of Growth 13. Calculus of Several Variables Application Preview: Safe Cars, Unsafe Streets 13.1 Functions of Several Variables 13.2 Partial Derivatives 13.3 Optimizing Functions of Several Variables 13.4 Least Squares 13.5 Lagrange Multipliers and Constrained Optimization 13.6 Total Differentials and Approximate Changes 13.7 Multiple Integrals Cumulative Review for Chapters 1, 8-13 Appendix: Normal Probabilities Using Tables Answers to Selected Exercises Index Available on the Web G. Game Theory Application Preview: Sherlock Holmes and James Moriarty G.1 Two-Person Games and Saddle Points G.2 Mixed Strategies G.3 Games and Linear Programming Chapter L Logic L.1 Statements and Connectives Application Preview: Grammar, Logic, and Rhetoric L.2 Truth Tables Application Preview: Circuits L.3 Implications Application Preview: "If..., then..." as a Computer Instruction L.4 Valid Arguments Application Preview: Fuzzy Logic and Artificial Intelligence L.5 Quantifiers and Euler Diagrams Application Preview: The Dog Walking Ordinance Chapter Projects and Essays
