Finite Mathematics with Calculus : A Modeling Approach

by Bronson, Richard; Bronson, Gary J.

• ISBN13: 9780534356521
• ISBN10: 0534356524
• Format: Hardcover
• Copyright: 1999-12-13
• Publisher: Cengage Learning

Summary

This text uses a modeling approach to unify the traditional topics of finite mathematics and calculus. Use of graphing calculators is carefully integrated to support the modeling approach. The authors apply graphical, numerical, and symbolic techniques to motivate understanding.

Table of Contents

Mathematical Models	1	(79)
The Modeling Process	2	(6)
Modeling with Equalities	8	(12)
Modeling with Proportionality	20	(9)
Modeling with Graphs	29	(18)
Linear Equations and Straight Lines	47	(16)
Graphing Systems of Equations	63	(17)
Keys	75	(5)
Linear Models	80	(82)
Elementary Row Operations	81	(13)
Gaussian Elimination	94	(15)
Modeling Data with Straight Lines	109	(15)
Matrices	124	(15)
Matrix Inversion	139	(23)
Keys	155	(7)
Linear Programming Models	162	(93)
Modeling with Inequalities	163	(9)
Graphing Linear Inequalities	172	(10)
Optimizing with Graphs	182	(17)
Initializing the Simplex Method	199	(13)
The Basic Simplex Algorithm	212	(19)
The Enhanced Simplex Algorithm	231	(24)
Keys	247	(8)
Financial Models	255	(50)
Interest	256	(12)
Present Value	268	(10)
Annuities	278	(12)
Present Value of an Annuity	290	(15)
Keys	301	(4)
Presentation Models	305	(60)
Sets and Venn Diagrams	306	(13)
Pie Charts and Bar Graphs	319	(14)
Standard Measures for Numerical Data	333	(14)
Tree Diagrams	347	(18)
Keys	359	(6)
Probability Models	365	(104)
Equally Likely Outcomes	366	(12)
The Laws of Probability	378	(18)
Conditional Probability and Independent Events	396	(16)
The Bayesean Method	412	(10)
Combinatorics	422	(15)
Bernoulli Trials	437	(8)
Expected Value	445	(24)
Keys	462	(7)
Markov Chain Models	469	(51)
Markov Chain	470	(15)
Distribution Vectors	485	(18)
Absorbing States	503	(17)
Keys	516	(4)
Probability Distribution Models	520	(89)
Random Number Generators	521	(12)
Uniform Distributions	533	(14)
Sampling	547	(21)
Normal Distributions	568	(21)
Exponential Distributions	589	(20)
Keys	604	(5)
Modeling with Functions	609	(66)
Functions	610	(12)
Polynomial, Rational, and Power Functions	622	(11)
Exponential Functions	633	(11)
The Natural Logarithm	644	(12)
Trigonometric Functions	656	(19)
Keys	671	(4)
Modeling Change	675	(102)
Rates of Change	676	(18)
Limits and Continuity	694	(17)
The Derivative	711	(14)
More Rules of Differentiation	725	(13)
The Chain Rule	738	(16)
Differentiable Functions	754	(23)
Keys	771	(6)
Optimization Models	777	(67)
Critical Points	778	(14)
Design Problems	792	(12)
Production Problems	804	(13)
Related Rates	817	(7)
Second Derivatives and Local Optima	824	(20)
Keys	838	(6)
Modeling with Integrals	844	(96)
Antiderivatives and Indefinite Integrals	845	(12)
Applications of the Indefinite Integral	857	(12)
Substitution of Variables	869	(10)
The Definite Integral	879	(20)
Applications of the Definite Integral	899	(19)
Probability Density Functions	918	(22)
Keys	932	(8)
Multivariable Models	940	(57)
Functions of Many Variables	941	(13)
Partial Derivatives	954	(10)
Optimization	964	(14)
Iterated Integrals	978	(19)
Keys	993	(4)
APPENDICES	997	(30)
A Exponents	998	(6)
B Polynomials	1004	(3)
C Factoring	1007	(6)
D Roots and the Quadratic Formula	1013	(4)
E Common Logarithms	1017	(5)
F Sigma Notation	1022	(5)
G Leontief Models (available from the publisher)
Answers to Selected Problems	1027	(90)
Index	1117	(6)
Photo Credits	1123