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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