Finite Mathematics and Calculus With Applications

by Lial, Margaret L.; Greenwell, Raymond N.; Ritchey, Nathan P.

• ISBN13: 9780321067159
• ISBN10: 0321067150
• Edition: 6th
• Format: Hardcover
• Copyright: 2001-07-01
• Publisher: Prentice Hall

Summary

Finite Mathematics and Calculus With Applications was written for the two-semester finite math and applied calculus course for students majoring in a variety of fieldsbusiness, economics, social science, and biological and physical science. Widely known for incorporating interesting, relevant, and realistic applications, this new edition now offers many more real applications citing current data sources. The new edition now offers more opportunities for use of technology, allowing for increased visualization and a better understanding of difficult concepts. A dedicated Web site rounds out the teaching and learning package, offering extended applications from the book, skill mastery quizzes, and graphing calculator programs tied to the text.

Table of Contents

Polynomials

Factoring

Rational Expressions

Equations

Inequalities

Exponents

Radicals

Linear Functions

Slopes and Equations of Lines

Linear Functions and Applications

The Least Squares Line

Systems of Linear Equations and Matrices

Solution of Linear Systems by the Echelon Method

Solution of Linear Systems by the Gauss-Jordan Method

Addition and Subtraction of Matrices

Multiplication of Matrices

Matrix Inverses

Input-Output Models

Linear Programming: The Graphical Method

Graphing Linear Inequalities

Solving Linear Programming Problems Graphically

Applications of Linear Programming

Linear Programming: The Simplex Method

Slack Variables and the Pivot

Maximization Problems

Minimization Problems

Duality

Nonstandard Problems

Mathematics of Finance

Simple and Compound Interest

Future Value of an Annuity

Present Value of an Annuity

Amortization

Logic

Statements and Quantifiers

Truth Tables and Equivalent Statements

The Conditional and Circuits

More on the Conditional

Analyzing Arguments with Euler Diagrams

Analyzing Arguments with Truth Tables

Sets and Probability

Sets

Applications of Venn Diagrams

Introduction to Probability

Basic Concepts of Probability

Conditional Probability

Independent Events

Bayes' Theorem

Counting Principles

Further Probability Topics

The Multiplication Principle

Permutations

Combinations

Probability Applications of Counting Principles

Binomial Probability

Probability Distributions

Expected Value

Statistics

Frequency Distributions

Measures of Central Tendency

Measures of Variation

The Normal Distribution

Normal Approximation to the Binomial Distribution

Nonlinear Functions

Properties of Functions

Quadratic Functions

Translation and Reflection

Polynomial and Rational Functions

Exponential Functions

Logarithmic Functions

Applications: Growth and Decay

Mathematics of Finance

The Derivative

Limits

Continuity

Rates of Change

Definition of the Derivative

Graphical Differentiation

Calculating the Derivative

Techniques for Finding Derivatives

Derivatives of Products and Quotients

The Chain Rule

Derivatives of Exponential Functions

Derivatives of Logarithmic Functions

Graphs and the Derivative

Increasing and Decreasing Functions

Relative Extrema

Higher Derivatives, Concavity, and the Second Derivative Test

Curve Sketching

Applications of the Derivative

Absolute Extrema

Applications of Extrema

Further Business Applications: Economic Lot Size, Economic Order Quantity

Elasticity of Demand

Implicit Differentiation

Related Rates

Differentials: Linear Approximation

Integration

Antiderivatives

Substitution

Area and the Definite Integral

The Fundamental Theorem of Calculus

The Area Between Two Curves

Numerical Integration

Further Techniques and Applications of Integration

Integration by Parts

Volume and Average Value

Continuous Money Flow

Improper Integrals

Solutions of Elementary and Separable Differential Equations

Multivariable Calculus

Functions of Several Variables

Partial Derivatives

Maxima and Minima

Lagrange Multipliers

Total Differentials and Approximations

Double Integrals

Probability and Calculus

Continuous Probability Models

Expected Value and Variance of Continuous Random Variables

Special Probability Density Functions

Tables

Formulas from Geometry

Area Under a Normal Curve

Integrals

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