An Introduction to Analytic Geometry and Calculus
- 1st Edition - January 1, 1973
- Imprint: Academic Press
- Author: A. C. Burdette
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 6 7 5 - 9
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 5 2 2 - 3
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… Read more
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Request a sales quoteAn 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.
Preface1. 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 Lines2. 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 Lines3. 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 Parabola4. 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 Functions5. 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 Derivatives6. 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 Differential7. 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 Integral8. 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 Integrals9. 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 Growth10. 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 Tables11. 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 Pressure12. 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 Coordinates13. 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 Differentiation14. 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 SeriesAppendix A Table of IntegralsAppendix B Some Function ValuesAppendix C Logarithm TablesAnswers to Odd-Numbered ProblemsIndex
- Edition: 1
- Published: January 1, 1973
- No. of pages (eBook): 448
- Imprint: Academic Press
- Language: English
- Paperback ISBN: 9781483236759
- eBook ISBN: 9781483265223
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