Mathematics with Applications in Business and Social Sciences

0.1 Real Numbers

0.2 The Arithmetic of Algebraic Expressions

0.3 Integer Exponents

0.4 Radicals

0.5 Rational Exponents

0.6 Polynomials and Factoring

1.1 Linear Equations in One Variable

1.2 Applications of Linear Equations in One Variable

1.3 Linear Inequalities in One Variable

1.4 Quadratic Equations in One Variable

1.5 Higher Degree Polynomial Equations

1.6 Rational and Radical Equations

2.1 The Cartesian Coordinate System

2.2 Linear Equations in Two Variables

2.3 Forms of Linear Equations

2.4 Parallel and Perpendicular Lines

2.5 Linear Regression

3.1 Introduction to Functions

3.2 Functions and Models

3.3 Linear and Quadratic Functions

3.4 Applications of Quadratic Functions

3.5 Other Common Functions

3.6 Transformations of Functions

3.7 Polynomial Functions

3.8 Rational Functions

3.9 Rational Inequalities

4.1 Exponential Functions and Their Graphs

4.2 Applications of Exponential Functions

4.3 Logarithmic Functions and Their Graphs

4.4 Applications of Logarithmic Functions

5.1 Basics of Personal Finance

5.2 Simple and Compound Interest

5.3 Annuities: Present and Future Value

5.4 Borrowing Money

6.1 Solving Systems of Linear Equations by Substitution and Elimination

6.2 Matrix Notation and Gauss-Jordan Elimination

6.3 Determinants and Cramer's Rule

6.4 Basic Matrix Operations

6.5 Inverses of Square Matrices

6.6 Leontief Input-Output Analysis

7.1 Linear Inequalities in Two Variables

7.2 Linear Programming: The Graphical Approach

7.3 The Simplex Method: Maximization

7.4 The Simplex Method: Duality and Minimization

7.5 The Simplex Method: Mixed Constraints

8.1 Set Notation

8.2 Operations with Sets

8.3 Introduction to Probability

8.4 Counting Principles: Combinations and Permutations

8.5 Counting Principles and Probability

8.6 Probability Rules and Bayes' Theorem

8.7 Expected Value

9.1 Collecting Data

9.2 Displaying Data

9.3 Describing and Analyzing Data

9.4 The Binomial Distribution

9.5 The Normal Distribution

9.6 Normal Approximation to the Binomial Distribution

10.1 One-Sided Limits

10.2 Limits

10.3 More about Limits

10.4 Continuity

10.5 Average Rate of Change

10.6 Instantaneous Rate of Change

10.7 Definition of the Derivative and the Power Rule

10.8 Techniques for Finding Derivatives

10.9 Applications: Marginal Analysis

11.1 The Product and Quotient Rules

11.2 The Chain Rule and the General Power Rule

11.3 Implicit Differentiation and Related Rates

11.4 Increasing and Decreasing Intervals

11.5 Critical Points and the First Derivative Test

11.6 Absolute Maximum and Minimum

12.1 Concavity and Points of Inflection

12.2 The Second Derivative Test

12.3 Curve Sketching: Polynomial Functions

12.4 Curve Sketching: Rational Functions

12.5 Business Applications

12.6 Other Applications: Optimization, Distance, and Velocity

13.1 Derivatives of Logarithmic Functions

13.2 Derivatives of Exponential Functions

13.3 Growth and Decay

13.4 Elasticity of Demand

13.5 L'Hôpital's Rule

13.6 Differentials

14.1 The Indefinite Integral

14.2 Integration by Substitution

14.3 Area and Riemann Sums

14.4 The Definite Integral and the Fundamental Theorem of Calculus

14.5 Area under a Curve (with Applications)

14.6 Area between Two Curves (with Applications)

14.7 Differential Equations

15.1 Integration by Parts

15.2 Annuities and Income Streams

15.3 Tables of Integrals

15.4 Numerical Integration

15.5 Improper Integrals

15.6 Volume

16.1 Functions of Several Variables

16.2 Partial Derivatives

16.3 Local Extrema for Functions of Two Variables

16.4 Lagrange Multipliers

16.5 The Method of Least Squares

16.6 Double Integrals