Synopses & Reviews
Intended for a two-semester applied calculus course or a two-term course of finite mathematics and applied calculus, Mathematical Applications, 7/e, presents concepts and skills in an approachable way for students of varying abilities and interests. Applications cover diverse topics that are important to students in the management, life, and social sciences.New! A greater variety of exercises include more critical-thinking questions, challenging new Examples, and Checkpoint Exercises. In addition to enhanced variety, the improved grading of drill and application exercises offers appropriate problems for students of all abilities and skill levels.New! Numerous data-driven examples and exercises have been updated throughout the text and the number of modeling problems has increased.New! More graphical interpretations have been added to the exposition, especially during calculus discussions.New! Enhanced optional technology coverage includes the addition of Excel information, as necessary, and expanded discussion of calculator capabilities to clarify presentation of algebraic topics.New! New margin labels and example labels have been added to help readers quickly identify where concepts are presented and when new topics are introduced.Chapter Warm Ups appear at the beginning of each chapter, with the exception of Chapter 0, allowing instructors and students to easily assess whether the student is prepared to begin the new material or needs to review prerequisite concepts before continuing.Check Points pose questions and problems that allow students to check their own understanding of the skills and concepts under discussion before proceeding. Solutions are conveniently locatedbefore the section exercises.Application Previews begin each section and establish the context and direction for the concepts to be presented. They are revisited in complete worked-out examples that appear later in the lesson.Application contexts are clearly labeled and identified, enabling instructors to tailor their assignments to their students' majors. More than 2,000 of the 5,500 exercises in the book are applied problems, and most chapters include a section or sections devoted exclusively to applications of the mathematical topics presented in the chapter.
Synopsis
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.
About the Author
Ron Harshbarger and Jim Reynolds have worked together as co-authors on MATHEMATICAL APPLICATIONS, Nineth Edition since the book's inception. They have both taught for over 20 years, at all levels of undergraduate mathematics. Harshbarger is a professor at the University of South Carolina, and Reynolds is a professor at Clarion University in Pennsylvania.Ron Harshbarger and Jim Reynolds have worked together as co-authors on MATHEMATICAL APPLICATIONS since the book's inception. They have both taught for over 20 years, at all levels of undergraduate mathematics. Harshbarger is a professor at the University of South Carolina, and Reynolds is a professor at Clarion University in Pennsylvania.
Table of Contents
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