College Mathematics for Business, Economics, Life Sciences and Social Sciences, Global Edition

Diagnostic Prerequisite Test

PART ONE: A LIBRARY OF ELEMENTARY FUNCTIONS

1. Linear Equations and Graphs

1.1 Linear Equations and Inequalities

1.2 Graphs and Lines

1.3 Linear Regression

Chapter 1 Review

Review Exercises

2. Functions and Graphs

2.1 Functions

2.2 Elementary Functions: Graphs and Transformations

2.3 Quadratic Functions

2.4 Polynomial and Rational Functions

2.5 Exponential Functions

2.6 Logarithmic Functions

Chapter 2 Review

Review Exercises

PART TWO: FINITE MATHEMATICS

3. Mathematics of Finance

3.1 Simple Interest

3.2 Compound and Continuous Compound Interest

3.3 Future Value of an Annuity; Sinking Funds

3.4 Present Value of an Annuity; Amortization

Chapter 3 Review

Review Exercises

4. Systems of Linear Equations; Matrices

4.1 Review: Systems of Linear Equations in Two Variables

4.2 Systems of Linear Equations and Augmented Matrices

4.3 Gauss-Jordan Elimination

4.4 Matrices: Basic Operations

4.5 Inverse of a Square Matrix

4.6 Matrix Equations and Systems of Linear Equations

4.7 Leontief Input-Output Analysis

Chapter 4 Review

Review Exercises

5. Linear Inequalities and Linear Programming

5.1 Linear Inequalities in Two Variables

5.2 Systems of Linear Inequalities in Two Variables

5.3 Linear Programming in Two Dimensions: A Geometric Approach

Chapter 5 Review

Review Exercises

6. Linear Programming: The Simplex Method

6.1 The Table Method: An Introduction to the Simplex Method

6.2 The Simplex Method: Maximization with Problem Constraints of the Form ≤

6.3 The Dual; Minimization with Problem Constraints of the form ≥

6.4 Maximization and Minimization with Mixed Problem Constraints

Chapter 6 Review

Review Exercises

7. Logic, Sets, and Counting

7.1 Logic

7.2 Sets

7.3 Basic Counting Principles

7.4 Permutations and Combinations

Chapter 7 Review

Review Exercises

8. Probability

8.1 Sample Spaces, Events, and Probability

8.2 Union, Intersection, and Complement of Events; Odds

8.3 Conditional Probability, Intersection, and Independence

8.4 Bayes' Formula

8.5 Random Variables, Probability Distribution, and Expected Value

Chapter 8 Review

Review Exercises

9. Markov Chains

9.1 Properties of Markov Chains

9.2 Regular Markov Chains

9.3 Absorbing Markov Chains

Chapter 9 Review

Review Exercises

PART THREE: CALCULUS

10. Limits and the Derivative

10.1 Introduction to Limits

10.2 Infinite Limits and Limits at Infinity

10.3 Continuity

10.4 The Derivative

10.5 Basic Differentiation Properties

10.6 Differentials

10.7 Marginal Analysis in Business and Economics

Chapter 10 Review

Review Exercises

11. Additional Derivative Topics

11.1 The Constant e and Continuous Compound Interest

11.2 Derivatives of Logarithmic and Exponential Functions

11.3 Derivatives of Products and Quotients

11.4 The Chain Rule

11.4 Implicit Differentiation

11.5 Related Rates

11.7 Elasticity of Demand

Chapter 11 Review

Review Exercises

12. Graphing and Optimization

12.1 First Derivative and Graphs

12.2 Second Derivative and Graphs

12.3 L'Hôpital's Rule

12.4 Curve Sketching Techniques

12.5 Absolute Maxima and Minima

12.6 Optimization

Chapter 12 Review

Review Exercises

13. Integration

13.1 Antiderivatives and Indefinite Integrals

13.2 Integration by Substitution

13.3 Differential Equations; Growth and Decay

13.4 The Definite Integral

13.5 The Fundamental Theorem of Calculus

Chapter 13 Review

Review Exercises

14. Additional Integration Topics

14.1 Area Between Curves

14.2 Applications in Business and Economics

14.3 Integration by Parts

14.4 Other Integration Methods

Chapter 14 Review

Review Exercises

15. Multivariable Calculus

15.1 Functions of Several Variables

15.2 Partial Derivatives

15.3 Maxima and Minima

15.4 Maxima and Minima Using Lagrange Multipliers

15.5 Method of Least Squares

15.6 Double Integrals Over Rectangular Regions

15.7 Double Integrals Over More General Regions

Chapter 15 Review

Review Exercises

APPENDICES

A. Basic Algebra Review

A.1 Algebra and Real Numbers

A.2 Operations on Polynomials

A.3 Factoring Polynomials

A.4 Operations on Rational Expressions

A.5 Integer Exponents and Scientific Notation

A.6 Rational Exponents and Radicals

A.7 Quadratic Equations

B. Special Topics

B.1 Sequences, Series, and Summation Notation

B.2 Arithmetic and Geometric Sequences

B.3 Binomial Theorem

C. Tables

Table I. Basic Geometric Formulas

Table II. Integration Formulas

Answers

Index

Applications Index

A Library of Elementary Functions

• Built-in guidance helps students help themselves learn the course content.
  • 483 worked examples, including many with several parts.
    • Examples are annotated and the problem-solving steps are clearly identified, which gives students extra assistance in understanding the solution.
    • Dashed boxes show the detailed algebraic steps that are normally not included in textbooks, giving students extra help in working through the examples.
    • A Matched Problem follows each example, providing students with an opportunity to reinforce and test understanding before moving on.
  • Conceptual Insight boxes, appearing in nearly every section, either make explicit connections to previously learned concepts or provide a broader, more conceptual explanation of the topic, helping students place this new information in context.
  • Explore & Discuss problems in every section encourage students to think about a relationship or process before a result is stated or to investigate additional consequences of a development in the text. These problems can help students of all levels gain better insight into the mathematical concepts and are effective in both small and large classroom settings. NEW! The author has provided Teaching Tips for less-experienced instructors on how to engage students in these discussions and the goals of the exploration.
• Flexible coverage allows instructors to use this text in a way that suits their syllabus and teaching style.
  • Topic selection, coverage, and organization reflect the course outlines of many major colleges and universities. The content is organized into three parts:
    • A Library of Elementary Functions (Chapters 1-2) provides optional material that can be covered in its entirety or referred to as needed.
    • Finite Mathematics (Chapters 3–9) coverage features a separate chapter on the simplex method and thorough coverage of Markov chains.
    • Calculus (Chapters 10-15) coverage features early treatment of exponential and logarithmic functions plus more in-depth coverage of calculus topics than other texts.
  • Emphasis on the construction of mathematical models, especially in linear systems and linear programming, gives students critical tools for solving application problems.
  • Technology coverage is optional, but discussions on using graphing calculators and spreadsheets are included where appropriate.
  • Mini-Lectures are included for most sections of the text and provide additional classroom examples, a summary of suggested learning objectives, and teaching notes for the material. These mini-lectures are ideal for instructors who do not teach this course frequently, or just need some additional guidance or resources.