Applied Calculus for the Managerial, Life, and Social Sciences

by Tan, Soo T.

• ISBN13: 9780495383123
• ISBN10: 0495383120
• Edition: 7th
• Format: Hardcover
• Copyright: 2006-12-29
• Publisher: Brooks Cole

Summary

This text helps you succeed in applied calculus by using clear explanations, real-life examples, and up-to-date technology. Real-life applications-such as satellite radio subscriptions, Google's revenue, job outsourcing, and the effects of smoking bans-are drawn from the areas of business and the behavioral, life, and social sciences. Portfolio profiles give you a firsthand look at how real-world professionals use applied calculus in their work. You can also take advantage of extensive online support to enhance your learning, including video instruction and interactive tutorials that walk you step by step through examples and problems in the text.

Table of Contents

Preliminaries

Precalculus Review

Precalculus Review II

The Cartesian Coordinate System

Straight Lines

Functions, Limits, and the Derivative

Functions and Their Graphs

The Algebra of Functions

Functions and Mathematical Models

Limits

One-Sided Limits and Continuity

Derivative

Differentiation

Basic Rules of Differentiation

The Product and Quotient Rules

The Chain Rule

Marginal Functions in Economics

Higher-Order Derivatives

Implicit Differentiation and Related Rates

Differentials

Applications of the Derivative

Applications of the First Derivative

Applications of the Second Derivative

Curve Sketching

Optimization

Optimization II

Exponential and Logarithmic Functions

Exponential Functions

Logarithmic Functions

Compound Interest

Differentiation of Exponential Functions

Differentiation of Logarithmic Functions

Exponential Functions as Mathematical Models

Integration

Antiderivatives and the Rules of Integration

Integration by Substitution

Area and the Definite Integral

The Fundamental Theorem of Calculus

Evaluating Definite Integrals

Area Between Two Curves

Applications of the Definite Integral to Business and Economics

Volumes of Solids of Revolution

Additional Topics in Integration

Integration by Parts

Integration Using Tables of Integrals

Numerical Integration

Improper Integrals

Calculus of Several Variables

Functions of Several Variables

Partial Derivatives

Maxima and Minima of Functions of Several Variables

The Method of Least Squares

Constrained Maxima and Minima and the Method of Lagrange Multipliers

Total Differentials

Double Integrals

Applications of Double Integrals

Differential Equations

Differential Equations

Separation of Variables

Applications of Separable Differential Equations

Approximate Solutions of Differential Equations

Probability and Calculus

Probability Distributions of Random Variables

Expected Value and Standard Deviation

Normal Distributions

Taylor Polynomials and Infinite Series

Taylor Polynomials

Infinite Sequences

Infinite Series

Series with Positive Terms

Power Series and Taylor Series

More on Taylor Series

The Newton's Method

Trigonometric Functions

Measurement of Angles

The Trigonometric Functions

Differentiation of Trigonometric Functions

Integration of Trigonometric Functions

Inverse Functions

Table

Answers to Odd-Numbered Exercises

Index

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