Introductory Mathematical Analysis for Business, Economics and the Life and Social Sciences, 9/e
Ernest F. Haeussler, The Pennsylvania State University
Richard S. Paul, The Pennsylvania State University
Published August, 1998 by Prentice Hall Engineering/Science/Mathematics
Copyright 1999, 982 pp.
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Mathematics for Business-Mathematics
Mathematical Methods in Business-Decision Science
For courses in Mathematics for Business and Mathematical
Methods in Business.
This acclaimed text provides a solid mathematical foundation
in business, economics, and the life and social sciences. Beginning
with precalculus and finite math topics such as equations, functions,
matrix algebra, linear programming, mathematics of finance, and probability,
it then progresses through single and multivariable calculus. An abundance
and variety of applications appear throughout, enabling students to
continually see how the mathematics being taught can be put into practice.
NEWPrinciples in Practice
Additional applied exercises located in text margins.
NEWConcepts for Calculus AppendixIncludes
Slopes and Equations of Lines; Secant Lines and Average Rate of Change;
and Slope of a Curve: Derivative.
- Demonstrates real-world applications so that students
have more opportunities to see chapter material put to practical use.
NEWRevised and updated Mathematical SnapshotsIncludes
many chapter-end exercises.
- Supplies students with additional precalculus concepts
Various relevant and meaningful ApplicationsIn
exercises and examples, with background content integrated.
- Offers stimulating and often novel applications involving
chapter concepts, reinforcing the text's strong emphasis on hands-on
Graphing calculatorMaterial appears throughout
the text in the exposition and exercises.
- Shows students the practical function of math outside
the classroomand in the fields of business, economics, biology,
medicine, sociology, psychology, ecology, earth science, archeology,
Step-by-step examples and solved problems.
- Provides students with a tool to assist comprehension
and understanding when appropriate.
A wealth of exercisesIncludes basic mechanical-drill
type and more interesting thought-provoking problems with real data.
- Enables students to easily follow solution techniques
and then solve other problems.
Review section in each chapter.
- Helps students avoid commonly made errors.
Boxed rules and formulas, displayed definitions and key
- Presents students with a list of important terms and
symbols, chapter summary, and numerous review problems for convenient
Answers to odd-numbered problems.
- Highlights the most important points for student focus.
(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
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. Matrix Addition 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.
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:
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.
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.