Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences

Part I. ALGEBRA

0. Review of Algebra

0.1 Sets of Real Numbers

0.2 Some Properties of Real Numbers

0.3 Exponents and Radicals

0.4 Operations with Algebraic Expressions

0.5 Factoring

0.6 Fractions

0.7 Equations, in Particular Linear, Equations

0.8 Quadratic Equations

1. Applications and More Algebra

1.1 Applications of Equations

1.2 Linear Inequalities

1.3 Applications of Inequalities

1.4 Absolute Value

1.5 Summation Notation

1.6 Sequences

2. Functions and Graphs

2.1 Functions

2.2 Special Functions

2.3 Combinations of Functions

2.4 Inverse Functions

2.5 Graphs in Rectangular Coordinates

2.6 Symmetry

2.7 Translations and Reflections

2.8 Functions of Several Variables

3. Lines, Parabolas, and Systems

3.1 Lines

3.2 Applications and Linear Functions

3.3 Quadratic Functions

3.4 Systems of Linear Equations

3.5 Nonlinear Systems

3.6 Applications of Systems of Equations

4. Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

4.4 Logarithmic and Exponential Equations

Part II. FINITE MATHEMATICS

5. Mathematics of Finance

5.1 Compound Interest

5.2 Present Value

5.3 Interest Compounded Continuously

5.4 Annuities

5.5 Amortization of Loans

5.6 Perpetuities

6. Matrix Algebra

6.1 Matrices

6.2 Matrix Addition and Scalar Multiplication

6.3 Matrix Multiplication

6.4 Solving Systems by Reducing Matrices

6.5 Solving Systems by Reducing Matrices (continued)

6.6 Inverses

6.7 Leontief's Input-Output Analysis

7. Linear Programming

7.1 Linear Inequalities in Two Variables

7.2 Linear Programming

7.3 Multiple Optimum Solutions

7.4 The Simplex Method

7.5 Degeneracy, Unbounded Solutions, and Multiple Solutions

7.6 Artificial Variables

7.7 Minimization

7.8 The Dual

8. Introduction to Probability and Statistics

8.1 Basic Counting Principle and Permutations

8.2 Combinations and Other Counting Principles

8.3 Sample Spaces and Events

8.4 Probability

8.5 Conditional Probability and Stochastic Processes

8.6 Independent Events

8.7 Bayes's Formula

9. Additional Topics in Probability

9.1 Discrete Random Variables and Expected Value

9.2 The Binomial Distribution

9.3 Markov Chains

Part III. CALCULUS

10. Limits and Continuity

10.1 Limits

10.2 Limits (Continued)

10.3 Continuity

10.4 Continuity Applied to Inequalities

11. Differentiation

11.1 The Derivative

11.2 Rules for Differentiation

11.3 The Derivative as a Rate of Change

11.4 The Product Rule and the Quotient Rule

11.5 The Chain Rule

12. Additional Differentiation Topics

12.1 Derivatives of Logarithmic Functions

12.2 Derivatives of Exponential Functions

12.3 Elasticity of Demand

12.4 Implicit Differentiation

12.5 Logarithmic Differentiation

12.6 Newton's Method

12.7 Higher-Order Derivatives

13. Curve Sketching

13.1 Relative Extrema

13.2 Absolute Extrema on a Closed Interval

13.3 Concavity

13.4 The Second-Derivative Test

13.5 Asymptotes

13.6 Applied Maxima and Minima

14. Integration

14.1 Differentials

14.2 The Indefinite Integral

14.3 Integration with Initial Conditions

14.4 More Integration Formulas

14.5 Techniques of Integration

14.6 The Definite Integral

14.7 The Fundamental Theorem of Integral Calculus

14.8 Approximate Integration

14.9 Area between Curves

14.10 Consumers' and Producers' Surplus

15. Methods and Applications of Integration

15.1 Integration by Parts

15.2 Integration by Partial Fractions

15.3 Integration by Tables

15.4 Average Value of a Function

15.5 Differential Equations

15.6 More Applications of Differential Equations

15.7 Improper Integrals

16. Continuous Random Variables

16.1 Continuous Random Variables

16.2 The Normal Distribution

16.3 The Normal Approximation to the Binomial Distribution

17. Multivariable Calculus

17.1 Partial Derivatives

17.2 Applications of Partial Derivatives

17.3 Implicit Partial Differentiation

17.4 Higher-Order Partial Derivatives

17.5 Chain Rule

17.6 Maxima and Minima for Functions of Two Variables

17.7 Lagrange Multipliers

17.8 Lines of Regression

17.9 Multiple Integrals

• Diverse applications both in the exercises and the examples help students see how mathematics is applied to everyday and work-related situations. Many use real-world data to increase their relevance to students’ lives.
• More than 5,000 exercises provide a wide variety of quality problems that are sorted in increasing order of difficulty, starting with basic skills and applications and progressing to increasingly challenging exercises.
• More than 850 examples are worked out in detail. Many examples include strategies that are specifically designed to guide students through the logistics of the solution before finding the solution.
  • “Now Work” exercises follow every example, suggesting an end-of-section exercise that is similar in style and concept to the example. This gives the student the opportunity to test and confirm their understanding. Answers to the “Now Work” exercises are found in the Answers section in the back of the text.
  • Apply It exercises (formerly titled Principles in Practice) are located in the margins next to examples to provide an opportunity for students to apply and check their understanding of the mathematics in the corresponding example.
  • Explore & Extend exercises (formerly titled Mathematical Snapshot) at the end of each chapter offer stimulating, relevant, and often novel applications involving chapter concepts, reinforcing the text’s strong emphasis on hands-on practice.
• More than 500 diagrams illustrate and clarify concepts for students.
• Optional graphing calculator tutorials appear throughout the text in both the exposition and the exercises, providing students with a tool to assist comprehension and understanding when appropriate.
• End-of-chapter review provides a list of important terms and symbols, chapter summary, and numerous review problems for students to practice and reinforce their understanding of the concepts.

Very good

3 Oct 2011

By Yousef

Haeussler, Paul, and Wood establish a strong algebraic foundation that sets this text apart from other applied mathematics texts, paving the way for readers to solve real-world problems that use calculus. Emphasis on developing algebraic skills is extended to the exercises-including both drill problems and applications. The authors work through examples and explanations with a blend of rigor and accessibility. In addition, they have refined the flow, transitions, organization, and portioning of the content over many editions to optimize learning for readers. The table of contents covers a wide range of topics efficiently, enabling readers to gain a diverse understanding.