# Technical Calculus with Analytic Geometry, 4th edition

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## Overview

- NEW - NEW! The graphing calculator is now used throughout the text in examples and exercises to help develop and reinforce the coverage of many important topics.

- NEW - NEW! Special Caution and Note indicators are used in the margins when appropriate to identify areas where students commonly make errors and to add emphasis to material that is of particular importance in developing a solid understanding of the topic at hand.

- NEW - NEW! Writing exercises are now included throughout the text to help students learn to express themselves mathematically. There is one specific writing exercise included at the end of each chapter, as well as over 110 additional exercises throughout the book (at least 5 in each chapter) that require at least a sentence or two of explanation along with the answer.

- NEW - NEW! All new chapter openers introduce the topic to be discussed through an application that is illustrated with a drawing. A problem related to this application is solved in an example later in the chapter.

- NEW - NEW! New and updated applications bring students a wealth of realistic examples and problems with which to develop their understanding. There are now about 4,400 exercises (an increase of about 20%), including about 2,000 that are new to this edition. Technical applications are illustrated in about 1,000 of these exercises, including 650 that are new to this edition. The inclusion of business-related examples and exercises appeal to the increasing number of information technology students in this course.

- NEW - NEW!
**Page Layout**Special attention has been given to the page layout in this 4th edition. Nearly all examples are started and completed on the same page and all figures are shown immediately adjacent to the material in which they are discussed.

- NEW - NEW! There are 620 figures in the 4th edition. This is
**200**more than in the previous edition! In addition, a new design and trim size make this a more attractive and practical text for students who are visually motivated.

- NEW - NEW! The AW Math Tutor Center is staffed by qualified mathematics instructors who provide students with tutoring on text examples and odd-numbered problems. Tutoring is provided by toll-free telephone, fax, and e-mail. White Board technology allows tutors and students to actually see problems worked while they talk live during the tutoring sessions.

## Table of contents

(Each Chapter ends with Chapter Equations, Review Exercises, and a Practice Test).

**1. Functions and Graphs.**

Introduction to Functions.

Algebraic Functions.

Rectangular Coordinates.

The Graph of a Function.

**2. Plane Analytic Geometry.**

Basic Definitions.

The Straight Line.

The Circle.

The Parabola.

The Ellipse.

The Hyperbola.

Translation of Axes.

The Second Degree Equation.

**3. The Derivative.**

Limits.

The Slope of a Tangent to a Curve.

The Derivative.

The Derivative as an Instantaneous Rate of Change.

Derivatives of Polynomials.

Derivatives of Products and Quotients of Functions.

The Derivative of a Power of a Function.

Differentiation of Implicit Functions.

Higher Derivatives.

**4. Applications of the Derivative.**

Tangents and Normals.

Newton's Method for Solving Equations.

Curvilinear Motion.

Related Rates.

Using Derivatives in Curve Sketching.

More on Curve Sketching.

Applied Maximum and Minimum Problems.

Differentials and Linear Approximations.

**5. Integration.**

Antiderivatives.

The Indefinite Integral.

The Area Under a Curve.

The Definite Integral.

Numerical Integration; The Trapezoidal Rule.

Simpson's Rule.

**6. Applications of Integration.**

Applications of the Indefinite Integral.

Areas by Integration.

Volumes by Integration.

Centroids.

Moments of Inertia.

Work by a Variable Force.

Force Due to Liquid Pressure.

Other Applications.

**7. Differentiation of the Trigonometric and Inverse Trigonometric Functions.**

The Trigonometric Functions.

Basic Trigonometric Relations.

Derivatives of the Sine and Cosine Functions.

Derivatives of Other Trigonometric Functions.

The Inverse Trigonometric Functions.

Derivatives of the Inverse Trigonometric Functions.

Applications.

**8. Derivatives of the Exponential and Logarithmic Functions.**

Exponential and Logarithmic Functions.

Derivative of the Logarithmic Function.

Derivative of the Exponential Function.

Applications.

**9. Integration by Standard Forms.**

The General Power Formula.

The Basic Logarithmic Form.

The Exponential Form.

Basic Trigonometric Forms.

Other Trigonometric Forms.

Inverse Trigonometric Forms.

**10. Methods of Integration.**

Integration by Parts.

Integration by Substitution.

Integration by Trigonometric Substitution.

Integration by Partial Fractions: Nonrepeated Linear Factors.

Integration by Partial Fractions: Other Cases.

Integration by Use of Tables.

Improper Integrals.

**11. Introduction to Partial Derivatives and Double Integrals.**

Functions of Two Variables.

Curves and Surfaces in Three Dimensions.

Partial Derivatives.

Certain Applications of Partial Derivatives.

Double Integrals.

Centroids and Moments of Inertia by Double Integration.

**12. Polar and Cylindrical Coordinates.**

Polar Coordinates.

Curves in Polar Coordinates.

Applications of Differentiation and Integration in Polar Coordinates.

Cylindrical Coordinates.

**13. Expansion of Functions in Series.**

Infinite Series.

Maclaurin Series.

Certain Operations with Series.

Computations by Use of Series Expansions.

Taylor Series.

Introduction to Fourier Series.

More About Fourier Series.

**14. First-Order Differential Equations.**

Solutions of Differential Equations.

Separation of Variables.

Integrating Combinations.

The Linear Differential Equation of the First Order.

Elementary Applications.

**15. Higher-Order Differential Equations.**

Higher-Order Homogeneous Equations.

Auxiliary Equation with Repeated or Complex Roots.

Solutions of Nonhomogeneous Equations.

Applications of Higher Order Equations.

**16. Other Methods of Solving Differential Equations.**

Numerical Solutions.

A Method of Successive Approximations.

Laplace Transforms.

Solving Differential Equations by Laplace Tansforms.

**Appendix A. Supplementary Topics.**

Rotations of Axes.

Regression.

**Appendix B. Units of Measurement.****Appendix C. Introduction.**

The Graphing Calculator.

Graphing Calculator Programs.

**Appendix D. Newton's Method.****Appendix E. A Table of Integrals.****Answers to Odd-Numbered Exercises.****Solutions to Practice Test Problems.****Index of Applications.****Index of Writing Exercises.****Index.**## For teachers

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