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Intended for a two-term applied calculus or finite mathematics and applied calculus course, Mathematical Applications, 8/e, presents concepts and skills in an approachable way for students of varying abilities and interests. The Eighth Edition retains the features that have made this text a popular choice, including applications covering diverse topics that are important to students in the management, life, and social sciences. This edition broadens the represented applications by adding a number of environmental science applications. The use of modeling has also been expanded, with modeling problems now clearly labeled in the examples.
Note: Each chapter concludes with Key Terms and Formulas, Review Exercises, a Chapter Test, and Extended Applications and Group Projects, and Chapters 1-14 also being with a Warm-up. 0. Algebraic Concepts 0.1 Sets 0.2 The Real Numbers 0.3 Integral Exponents 0.4 Radicals and Rational Exponents 0.5 Operations with Algebraic Expressions 0.6 Factoring 0.7 Algebraic Fractions 1. Linear Equations and Functions 1.1 Solution of Linear Equations and Inequalities in One Variable 1.2 Functions 1.3 Linear Functions 1.4 Graphs and Graphing Utilities 1.5 Solutions of Systems of Linear Equations 1.6 Applications of Functions in Business and Economics 2. Quadratic and Other Special Functions 2.1 Quadratic Equations 2.2 Quadratic Functions: Parabolas 2.3 Business Applications of Quadratic Functions 2.4 Special Functions and Their Graphs 2.5 Modeling; Fitting Curves to Data with Graphing Utilities (optional) 3. Matrices 3.1 Matrices 3.2 Multiplication of Matrices 3.3 Gauss-Jordan Elimination: Solving Systems of Equations 3.4 Inverse of a Square Matrix; Matrix Equations 3.5 Applications of Matrices: Leontief Input-Output Models 4. Inequalities and Linear Programming 4.1 Linear Inequalities in Two Variables 4.2 Linear Programming: Graphical Methods 4.3 The Simplex Method: Maximization 4.4 The Simplex Method: Duality and Minimization 4.5 The Simplex Method with Mixed Constraints 5. Exponential and Logarithmic Functions 5.1 Exponential Functions 5.2 Logarithmic Functions and Their Properties 5.3 Solution of Exponential Equations: Applications of Exponential and Logarithmic Functions 6. Mathematics of Finance 6.1 Simple Interest; Sequences 6.2 Compound Interest; Geometric Sequences 6.3 Future Value of Annuities 6.4 Present Value of Annuities 6.5 Loans and Amortization 7. Introduction to Probability 7.1 Probability: Odds 7.2 Unions and Intersections of Events: One-Trial Experiments 7.3 Conditional Probability: The Product Rule 7.4 Probability Trees and Bayes' Formula 7.5 Counting: Permutations and Combinations 7.6 Permutations, Combinations, and Probability 7.7 Markov Chains 8. Further Topics in Probability: Data Description 8.1 Binomial Probability Experiments 8.2 Data Description 8.3 Discrete Probability Distributions; The Binomial Distribution 8.4 Normal Probability Distribution 9. Derivatives 9.1 Limits 9.2 Continuous Functions; Limits at Infinity 9.3 Average and Instantaneous Rates of Change: The Derivative 9.4 Derivative Formulas 9.5 The Product Rule and the Quotient Rule 9.6 The Chain Rule and the Power Rule 9.7 Using Derivative Formulas 9.8 Higher-Order Derivatives 9.9 Applications of Derivatives in Business and Economics 10. Applications of Derivatives 10.1 Relative Maxima and Minima: Curve Sketching 10.2 Concavity: Points of Inflection 10.3 Optimization in Business and Economics 10.4 Applications of Maxima and Minima 10.5 Rational Functions: More Curve Sketching 11. Derivatives Continued 11.1 Derivatives of Logarithmic Functions 11.2 Derivatives of Exponential Functions 11.3 Implicit Differentiation 11.4 Related Rates 11.5 Applications in Business and Economics 12. Indefinite Integrals 12.1 The Indefinite Integral 12.2 The Power Rule 12.3 Integrals Involving Exponential and Logarithmic Functions 12.4 Applications of the Indefinite Integral in Business and Economics 12.5 Differential Equations 13. Definite Integrals: Techniques of Integration 13.1 Area Under a Curve 13.2 The Definite Integral: The Fundamental Theorem of Calculus 13.3 Area Between Two Curves 13.4 Applications of Definite Integrals in Business and Economics 13.5 Using Tables of Integrals 13.6 Integration by Parts 13.7 Improper Integrals and Their Applications 13.8 Numerical Integration Methods: Trapezoidal Rule and Simpson's Rule 14. Functions of Two or More Variables 14.1 Functions of Two or More Variables 14.2 Partial Differentiation 14.3 Applications of Functions of Two Variables in Business and Economics 14.4 Maxima and Minima 14.5 Maxima and Minima of Functions Subject to Constraints: Lagrange Multipliers