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Created through a "student-tested, faculty-approved" review process, MATH APPS is an engaging and accessible solution to accommodate the diverse lifestyles of today's learners at a value-based price. The book's concept-based approach, multiple presentation methods, and interesting and relevant applications keep students who typically take the course—business, economics, life sciences, and social sciences majors—engaged in the material. An innovative combination of content delivery both in print and online provides a core text and a wealth of comprehensive multimedia teaching and learning assets, including end-of-chapter review cards, downloadable flashcards and practice problems, online video tutorials, solutions to exercises aimed at supplementing learning outside of the classroom. Also available is Cengage Learning's Enhanced WebAssign®—a complete online homework management system for students and professors.
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- Detachable Review Cards for each chapter provide students a portable study tool containing information to prepare for class and for tests, including objectives, keywords, formulas, and practice tests.
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1.1. Solutions of Linear Equations and Inequalities in One Variable.
Relations and Functions.
Graphs of Functions.
Domains and Ranges.
Operations with Functions.
1.3. Linear Functions.
Rate of Change; Slope of a Line.
Writing Equations of Lines.
1.4. Solutions of Systems of Linear Equations.
Solution by Substitution.
Solution by Elimination.
Three Equations in Three Variables.
1.5. Applications of Functions in Business and Economics.
Total Cost, Total Revenue, and Profit.
Supply, Demand, and Market Equilibrium.
Supply, Demand, and Taxation.
2. Quadratic and Other Special Functions.
2.1. Quadratic Equations.
The Quadratic Formula.
2.2 Quadratic Functions: Parabolas.
2.3. Business Applications of Quadratic Functions.
Supply, Demand, and Market Equilibrium.
Break-Even Points and Maximization.
2.4. Special Functions and Their Graphs.
Polynomial and Rational Functions.
Piecewise Defined Functions.
2.5. Modeling Data with Graphing Utilities (optional).
Chapter 3 Matrices.
3.1. Operations with Matrices.
Addition and Subtraction of Matrices.
3.2. Multiplication of Matrices.
Product of Two Matrices.
3.3. Gauss-Jordan Elimination: Solving Systems of Equations.
Systems with Unique Solutions.
Systems with Nonunique Solutions.
3.4. Inverse of a Square Matrix.
4. Inequalities and Linear Programming.
4.1 Linear Inequalities in Two Variables.
One Linear Inequality in Two Variables.
Systems of Linear Inequalities.
4.2. Linear Programming: Graphical Methods.
4.3. The Simplex Method: Maximization.
The Simplex Method.
Tasks and Procedure.
Nonunique Solutions: Multiple Solutions and No Solution.
4.4. The Simplex Method: Duality and Minimization.
Duality and Solving.
4.5. The Simplex Method with Mixed Constraints.
Mixed Constraints and Maximization.
Mixed Constraints and Minimization.
5. Exponential and Logarithmic Functions.
5.1. Exponential Functions.
Modeling with Exponential Functions.
5.2. Logarithmic Functions and Their Properties.
Logarithmic Functions and Graphs.
Modeling with Logarithmic Functions.
Properties of Logarithms.
Change of Base.
5.3. Applications of Exponential and Logarithmic Functions.
Solving Exponential Equations Using Logarithmic.
Growth and Decay.
Economic and Management Applications.
6. Mathematics of Finance.
6.1. Simple Interest and Arithmetic Sequences.
6.2 Compound Interest and Geometric Sequences.
6.3. Future Values of Annuities.
6.4. Present Values of Annuities.
6.5. Loans and Amortization.
Unpaid Balance of a Loan.
7. Introduction to Probability.
7.1. Probability and Odds.
Sample Spaces and Single Events.
7.2. Unions, Intersections, and Complements of Events.
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.
8. Probability and Data Description.
8.1. Binomial Probability Experiments.
8.2. Describing Data.
Types of Averages.
Variance and Standard Deviation.
8.3. Discrete Probability Distributions.
Discrete Probability Distributions.
Measures of Dispersion.
The Binomial Distribution.
8.4. Normal Probability Distribution.
Notion of a Limit.
Properties of Limits, Algebraic Evaluation.
Limits of Piecewise Defined Functions.
9.2. Continuous Functions; Limits at Infinity.
Limits at Infinity.
9.3. Average and Instantaneous Rates of Change: The Derivative.
Instantaneous Rates of Change: Velocity.
Tangent to a Curve.
Differentiability and Continuity.
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. Derivatives in Business and Economics.
10. Applications of Derivatives.
10.1. Relative Maxima and Minima: Curve Sketching.
10.2. Concavity: Points of Inflection.
Points of Inflection.
10.3. Optimization in Business and Economics.
Minimizing Average Cost.
10.4. Applications of Maxima and Minima.
10.5. Rational Functions: More Curve Sketching.
More Curve Sketching.
11. Derivatives Continued.
11.1. Derivatives of Logarithmic Functions.
Using Properties of Logarithms.
11.2. Derivatives of Exponential Functions.
11.3. Implicit Differentiation.
11.4. Related Rates.
Percent Rates of Change.
Solving Related-Rates Problems.
11.5. Applications in Business and Economics.
Elasticity of Demand.
Taxation in a Competitive Market.
12. Indefinite Integrals.
12.1. The Indefinite Integral.
12.2. The Power Rule.
12.3. Integrals Involving Exponential and Logarithmic Functions.
Integrals Involving Exponential Functions.
Integrals Involving Logarithmic Functions.
12.4. The Indefinite Integral in Business and Economics.
Total Cost and Profit.
National Consumption and Savings.
12.5. Differential Equations.
Solution of Differential Equations.
Separable Differential Equations.
Applications of Differential Equations.
13. Definite Integrals: Techniques of Integration.
13.1. The Definite Integral: The Fundamental Theorem of Calculus.
Estimating the Area under a Curve.
13.2. Area between Two Curves.
13.3. Definite Integrals in Business and Economics.
Continuous Income Streams.
13.4. Using Tables of Integrals.
13.5. Integration by Parts.
13.6. Improper Integrals and Their Applications.
14. Functions of Two or More Variables.
14.1. Functions of Two or More Variables.
14.2. Partial Differentiation.
First-Order Partial Derivatives.
Higher-Order Partial Derivatives.
14.3. Functions of Two Variables in Business and Economics.
Joint Cost and Marginal Cost.
14.4. Maxima and Minima.
14.5. Constrained Optimization and Lagrange Multipliers.
Answers to Odd-Numbered Exercises.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Solutions Builder for Harshbarger's MATH APPS
MATH APPS: PowerLecture CD-ROM with ExamView Test Generator
This CD-ROM provides the instructor with dynamic media tools for teaching. Create, deliver, and customize tests (both print and online) in minutes with ExamView® Computerized Testing Featuring Algorithmic Equations. Easily build solution sets for homework or exams using Solution Builder's online solutions manual. Microsoft® PowerPoint® slides with art, including numbered tables and figures from the book, are also included on this CD-ROM.
Online Student Solutions Manual for Harshbarger's MATH APPS