An Introduction to Analytic Geometry and Calculus - 1st Edition - ISBN: 9780121422523, 9781483265223

An Introduction to Analytic Geometry and Calculus

1st Edition

Authors: A. C. Burdette
eBook ISBN: 9781483265223
Imprint: Academic Press
Published Date: 1st January 1973
Page Count: 448
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An Introduction to Analytic Geometry and Calculus covers the basic concepts of analytic geometry and the elementary operations of calculus.

This book is composed of 14 chapters and begins with an overview of the fundamental relations of the coordinate system. The next chapters deal with the fundamentals of straight line, nonlinear equations and graphs, functions and limits, and derivatives. These topics are followed by a discussion of some applications of previously covered mathematical subjects. This text also considers the fundamentals of the integrals, trigonometric functions, exponential and logarithm functions, and methods of integration. The final chapters look into the concepts of parametric equations, polar coordinates, and infinite series.

This book will prove useful to mathematicians and undergraduate and graduate mathematics students.

Table of Contents


1. The Coordinate System—Fundamental Relations

1-1 Introduction

1-2 Directed Lines

1-3 Cartesian Coordinates

1-4 Projections of a Line Segment on Horizontal and Vertical Lines

1-5 Midpoint of a Line Segment

1-6 Distance between Two Points

1-7 Slope of a Line

1-8 Parallel and Perpendicular Lines

1-9 Angle Formed by Intersecting Lines

2. The Straight Line

2-1 Equation and Locus

2-2 The Graph of an Equation

2-3 The Graph of a Linear Equation

2-4 The Point-Slope Equation

2-5 The Two-Point Equation

2-6 The Slope-Intercept Equation

2-7 The First-Degree Equation

2-8 Intersection of Lines

3. Nonlinear Equations and Graphs

3-1 Introduction

3-2 Intercepts

3-3 Symmetry

3-4 Extent

3-5 Graphing Equations

3-6 The Circle

3-7 The Parabola

4. Functions and Limits

4-1 Introduction

4-2 Function

4-3 Tangent to a Curve

4-4 Limit of a Sequence

4-5 Limit of a Function

4-6 Continuous Functions

5. The Derivative

5-1 Introduction

5-2 The Derivative

5-3 Some Additional Interpretations of the Derivative

5-4 Some Basic Theorems

5-5 Derivatives of Products and Quotients

5-6 The Chain Rule

5-7 Functions Defined Implicitly and Their Derivatives

5-8 Higher Derivatives

6. Some Applications

6-1 The Mean Value Theorem

6-2 Sign of the First Derivative

6-3 Sign of the Second Derivative

6-4 Maxima and Minima

6-5 Applications of Maxima and Minima

6-6 Related Rates

6-7 The Differential

6-8 Applications of the Differential

7. The Integral

7-1 Introduction

7-2 The Summation Notation

7-3 An Area Problem

7-4 The Definite Integral

7-5 Properties and Definitions

7-6 The Indefinite Integral

7-7 Evaluation of Indefinite Integrals

7-8 Areas of Plane Figures

7-9 More General Plane Areas

7-10 A Product Theorem

7-11 Work

7-12 Applications of the Indefinite Integral

8. The Trigonometric Functions

8-1 Formulas and Definitions

8-2 An Important Limit

8-3 Derivatives of Trigonometric Functions

8-4 Inverse Trigonometric Functions

8-5 Differentiation of the Inverse Trigonometric Functions

8-6 Some Integrals

9. The Exponential and Logarithm Functions

9-1 The Exponential Function

9-2 The Logarithm Function

9-3 The Number e

9-4 Derivative of the Logarithm Function

9-5 Derivative of the Exponential Function

9-6 More Integrals

9-7 Logarithmic Differentiation

9-8 Exponential Growth

10. Methods of Integration

10-1 Introduction

10-2 Integration by Parts

10-3 Integrals Involving Trigonometric Functions

10-4 Algebraic Substitution

10-5 Trigonometric Substitution

10-6 Partial Fractions

10-7 Integral Tables

11. More Applications

11-1 Volumes of Solids

11-2 Volumes of Solids of Revolution—Disks and Washers

11-3 Volumes of Solids of Revolution—Hollow Cylinders

11-4 Arc Length

11-5 Area of Surfaces of Revolution

11-6 Fluid Pressure

12. Parametric Equations—Polar Coordinates

12-1 Parametric Representation

12-2 Derivative of a Function Defined by Parametric Equations

12-3 Polar Coordinates

12-4 Sketching Polar Curves

12-5 Intersection of Polar Curves

12-6 Plane Areas

12-7 Arc Length

12-8 Tangent Lines to Curves in Polar Coordinates

13. Functions of Several Variables

13-1 Fundamental Concepts

13-2 Three-Dimensional Geometry

13-3 Partial Differentiation

13-4 Fundamental Increment Formula

13-5 Total Differential

13-6 The Chain Rule

13-7 Higher Derivatives

13-8 Implicit Differentiation

14. Infinite Series

14-1 Introduction

14-2 Fundamental Concepts

14-3 General Tests

14-4 The Geometric Series

14-5 The p-Series

14-6 The Comparison Test

14-7 The Ratio Test

14-8 Alternating Series

Appendix A Table of Integrals

Appendix B Some Function Values

Appendix C Logarithm Tables

Answers to Odd-Numbered Problems



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Academic Press
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About the Author

A. C. Burdette

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