Each chapter concludes with a Review and a Mathematical Snapshot.
Chapter 0 Algebra Review 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 Linear Equations 0.8 Quadratic Equations Mathematical Snapshot Chapter 1 Applications of Equations and Inequalities 1.1 Applications of Equations
1.2 Linear Inequalities
1.3 Applications of Inequalities
1.4 Absolute Value
Chapter 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 Reflection
Chapter 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
Chapter 4 Exponential and Logarithmic Functions 4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Properties of Logarithms
4.4 Logarithmic and Exponential Equations
Chapter 5 Mathematics of Finance 5.1 Compound Interest
5.2 Present Value
5.3 Annuities
5.4 Amortization of Loans
Chapter 6 Matrix Algebra 6.1 Matrices
6.2 Matrix Addition and Scalar Multiplication
6.3 Matrix Multiplication
6.5 Solving Systems by Reducing Matrices
6.5 Method of Reduction (continued)
6.6 Inverses
6.6 Leontief's Input-Output Analysis
Chapter 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 Optimum Solutions
7.6 Artificial Variables
7.7 Minimization
7.8 The Dual
Chapter 8 Introduction to Probability 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' Formula
Chapter 9 Additional Topics in Probability 9.1 Discrete Random Variables
9.2 The Binomial Distribution
9.3 Markov Chains
Chapter 10 Limits and Continuity 10.1 Limits
10.2 Limits (Continued)
10.3 Interest Compounded Continuously
10.4 Continuity
10.5 Continuity Applied to Inequalities
Chapter 11 Differentiation 11.1 The Derivative
11.2 Rules for Differentiation
11.3 The Derivative as a Rate of Change
11.4 Differentiability and Continuity
11.5 Product and Quotient Rules
11.6 The Chain Rule and the Power Rule
Chapter 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
Chapter 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
Chapter 14 Integration 14.1 Differentials
14.2 The Indefinite Integral
14.3 Integration with Initial Conditions
14.4 Some Integration Formulas
14.5 Techniques of Integration
14.6 Summation
14.7 The Definite Integral
14.8 The Fundamental Theorem of Calculus
14.9 Approximate Integration
14.10 Area
14.11 Area Between Curves
14.12 Consumers' and Producers' Surplus
Chapter 15 Further 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
Chapter 16 Continuous Random Variables 16.1 Continuous Random Variables
16.2 The Normal Distribution
16.3 The Normal Approximation to the Binomial Distribution
Chapter 17 Multivariable Calculus 17.1 Functions of Several Variables
17.2 Partial Derivatives
17.3 Applications of Partial Derivatives
17.4 Implicit Partial Differentiation
17.5 Higher Order Partial Derivatives
17.6 The Chain Rule
17.7 Maxima and Minima for Functions of Two Variables
17.8 Lagrange Multipliers
17.9 Lines of Regression
17.10 A Comment on Homogeneous Functions
17.11 Multiple Integrals
Answers to Odd-Numbered Problems Index 