Table of Contents
(NOTE: Each chapter ends with a Review.)
0. Algebra Refresher.
Purpose. Sets and Real Numbers. Some Properties of Real Numbers. Operations with Real Numbers. Exponents and Radicals. Operations with Algebraic Expressions. Factoring. Fractions.
Linear Equations. Equations Leading to Linear Equations. Quadratic Equations. Supplement. Mathematical Snapshot: Real Growth of an Investment.
2. Applications of Equations and Inequalities.
Applications of Equations. Linear Inequalities. Applications of Inequalities. Absolute Value. Mathematical Snapshot: Quality VCR Recording.
3. Functions and Graphs.
Functions. Special Functions. Combinations of Functions. Graphs in Rectangular Coordinates. Symmetry. Translations and Reflections. Mathematical Snapshot: A Taxing Experience!
4. Lines, Parabolas, and Systems.
Lines. Applications and Linear Functions. Quadratic Functions. Systems of Linear Equations. Nonlinear Systems. Applications of Systems of Equations. Mathematical Snapshot: Anyone for Tennis?
5. Exponential and Logarithmic Functions.
Exponential Functions. Logarithmic Functions. Properties of Logarithms. Logarithmic and Exponential Equations. Mathematical Snapshot: Drug Dosages.
6. Matrix Algebra.
Matrices. MatrixAddition and Scalar Multiplication. Matrix Multiplication. Method of Reduction. Method of Reduction (Continued). Inverses. Determinants. Cramer's Rule. Input-Output Analysis with a Graphics Calculator. Mathematical Snapshot: Insulin Requirements as a Linear Process.
7. Linear Programming.
Linear Inequalities in Two Variables. Linear Programming. Multiple Optimum Solutions. The Simplex Method. Degeneracy, Unbounded Solutions, Multiple Optimum Solutions. Artificial Variables. Minimization. The Dual. Mathematical Snapshot: Drug and Radiation Therapies.
8. Mathematics of Finance.
Compound Interest. Present Value. Annuities. Amortization of Loans. Mathematical Snapshot: The Rule of 78's.
9. Introduction to Probability and Statistics.
Basic Counting Principles and Permutations. Combinations and Other Counting Principles. Sample Spaces and Events. Probability. Conditional Probability and Stochastic Processes. Independent Events. Bayes' Formula.
10. Additional Topics in Probability.
Discrete Random Variables and Expected Value. The Binomial Distribution. Markov Chains. Mathematical Snapshot: Is the Price Right?
11. Limits and Continuity.
Limits. Limits (Continued). Interest Compounded Continuously. Continuity. Continuity Applied to Inequalities. Mathematical Snapshot: National Debt.
The Derivative. Rules for Differentiation. The Derivative as a Rate of Change. Differentiability and Continuity. Product and Quotient Rules. The Chain Rule and Power Rule.
13. Additional Differentiation Topics.
Derivatives of Logarithmic Functions. Derivatives of Exponential Functions. Implicit Differentiation. Logarithmic Differentiation. Higher-Order Derivatives.
14. Curve Sketching.
Relative Extrema. Absolute Extrema on a Closed Interval. Concavity. The Second-Derivative Test. Asymptotes.
15. Applications of Differentiation.
Applied Maxima and Minima. Differentials. Elasticity of Demand. Newtons Method.
The Indefinite Integral. Integration with Initial Conditions. More Integration Formulas. Techniques of Integration. Summation. The Definite Integral. The Fundamental Theorem of Integral Calculus. Area. Area between Curves. Consumers' and Producers' Surplus. Mathematical Snapshot: Delivered Price.
17. Methods and Applications of Integration.
Integration by Parts. Integration by Partial Fractions. Integration by Tables. Average Value of a Function. Approximate Integration. Differential Equations. More Applications of Differential Equations. Improper Integrals. Mathematical Snapshot: Dieting.
18. Continuous Random Variables.
Continuous Random Variables. The Normal Distribution. The Normal Approximation to the Binomial Distribution.
19. Multivariable Calculus.
Functions of Several Variables. Partial Derivatives. Applications of Partial Derivatives. Implicit Partial Differentiation. Higher-Order Partial Derivatives. Chain Rule. Maxima and Minima for Functions of Two Variables. Lagrange Multipliers. Lines of Regression. A Comment on Homogeneous Functions. Multiple Integrals. Mathematical Snapshot: Data Analysis to Model Cooling.
Appendix A: Concepts for Calculus.
Appendix B: Compound Interest Tables.
Appendix C: Table of Selected Integrals.
Appendix D: Areas Under the Standard Normal Curve.
Answers to Odd-Numbered Problems.