Calculus and its Applications

by Goldstein, Larry J.; Schneider, David I.; Lay, David C.; Asmar, Nakhle H.

• ISBN13: 9780131919631
• ISBN10: 0131919636
• Edition: 11th
• Format: Hardcover
• Copyright: 2010-01-01
• Publisher: Pearson College Div

Summary

Normal 0 false false false MicrosoftInternetExplorer4 This extremely readable, highly regarded, and widely adopted text presents innovative ways for applying calculus to real-world situations in the business, economics, life science, and social science disciplines. The texts'straightforward, engaging approach fosters the growth of both the student's mathematical maturity and his/her appreciation for the usefulness of mathematics. The authors'tried and true formula pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exercises has proven to be tremendously successful with both students and instructors. Functions; The Derivative; Applications of the Derivative; Techniques of Differentiation; Logarithm Functions; Applications of the Exponential and Natural Logarithm Functions; The Definite Integral; Functions of Several Variables; The Trigonometric Functions; Techniques of Integration; Differential Equations; Taylor Polynomials and Infinite Series; Probability and Calculus For all readers interested in applied calculus.

Table of Contents

Preface

Introduction

Functions

Functions and Their Graphs

Some Important Functions

The Algebra of Functions

Zeros of Functions-The Quadratic Formula and Factoring

Exponents and Power Functions

Functions and Graphs in Applications

The Derivative

The Slope of a Straight Line

The Slope of a Curve at a Point

The Derivative

Limits and the Derivative

Differentiability and Continuity

Some Rules for Differentiation

More About Derivatives

The Derivative as a Rate of Change

Applications of the Derivative

Describing Graphs of Functions

The First and Second Derivative Rules

The First and Second Derivative Tests and Curve Sketching

Curve Sketching (Conclusion)

Optimization Problems

Further Optimization Problems

Applications of Derivatives to Business and Economics

Techniques of Differentiation

The Product and Quotient Rules

The Chain Rule and the General Power Rule

Implicit Differentiation and Related Rates

Logarithm Functions

Exponential Functions

The Exponential Function ex

Differentiation of Exponential Functions

The Natural Logarithm Function

The Derivative of ln x

Properties of the Natural Logarithm Function

Applications of the Exponential and Natural Logarithm Functions

Exponential Growth and Decay

Compound Interest

Applications of the Natural Logarithm Function to Economics

Further Exponential Models

The Definite Integral

Antidifferentiation

Areas and Riemann Sums

Definite Integrals and the Fundamental Theorem

Areas in the xy-Plane

Applications of the Definite Integral

Functions of Several Variables

Examples of Functions of Several Variables

Partial Derivatives

Maxima and Minima of Functions of Several Variables

Lagrange Multipliers and Constrained Optimization

The Method of Least Squares

Double Integrals

The Trigonometric Functions

Radian Measure of Angles

The Sine and the Cosine

Differentiation and Integration of sin t and cos t

The Tangent and Other Trigonometric Functions

Techniques of Integration

Integration by Substitution

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