Calculus with Applications, Brief Version

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

• ISBN13: 9780321228291
• ISBN10: 0321228294
• Edition: 8th
• Format: Hardcover
• Copyright: 2005-01-01
• Publisher: Addison Wesley

Summary

Widely known for incorporating interesting, relevant, and realistic applications, this text offers many real applications citing current data sources. There are a wide variety of opportunities for use of technology, allowing for increased visualization and a better understanding of difficult concepts. MyMathLab, a complete online course, will be available with this text. For the first time, a comprehensive series of lectures on video will be available.

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

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

Multivariable Calculus

Functions of Several Variables

Partial Derivatives

Maxima and Minima

Lagrange Multipliers

Total Differentials and Approximations

Double Integrals

Differential Equations

Solutions of Elementary and Separable Differential Equations

Linear First-Order Differential Equations

Euler's Method

Applications of Differential Equations

Probability and Calculus

Continuous Probability Models

Expected Value and Variance of Continuous Random Variables

Special Probability Density Functions

Sequences and Series

Geometric Sequences

Annuities: An Application of Sequences

Taylor Polynomials at 0

Infinite Series

Taylor Series

Newton's Method

L'Hôpital's Rule

The Trigonometric Functions

Definitions of the Trigonometric Functions

Derivatives of Trigonometric Functions

Integrals of Trigonometric Functions

Tables

Table

Formulas from Geometry

Table

Area Under a Normal Curve

Table

Integrals

Table

Integrals Involving Trigonometric Functions

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