Introductory Calculus - 2nd Edition - ISBN: 9780125897563, 9781483263953

Introductory Calculus

2nd Edition

With Analytic Geometry and Linear Algebra

Authors: A. Wayne Roberts
eBook ISBN: 9781483263953
Imprint: Academic Press
Published Date: 1st January 1972
Page Count: 664
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Introductory Calculus: Second Edition, with Analytic Geometry and Linear Algebra is an introductory text on calculus and includes topics related to analytic geometry and linear algebra. Functions and graphs are discussed, along with derivatives and antiderivatives, curves in the plane, infinite series, and differential equations.

Comprised of 15 chapters, this book begins by considering vectors in the plane, the straight line, and conic sections. The next chapter presents some of the basic facts about functions, the formal definition of a function, and the notion of a graph of a function. Subsequent chapters examine the derivative as a linear transformation; higher derivatives and the mean value theorem; applications of graphs; and the definite integral. Transcendental functions and how to find an antiderivative are also discussed, together with the use of parametric equations to determine the curve in a plane; how to solve linear equations; functions of several variables and the derivative and integration of these functions; and problems that lead to differential equations.

This monograph is intended for students taking a two- or three-semester course in introductory calculus.

Table of Contents

Preface to the Second Edition


Chapter 1 Some Analytic Geometry

1.1 What Is Analytic Geometry?

1.2 Vectors in.the Plane

1.3 The Straight Line

1.4 The Conic Sections

Chapter 2 Functions

2.1 Number Machines

2.2 Functions

2.3 Graphs; Getting the Picture

2.4 This Is the Limit

2.5 Composition of Functions; the Inverse

2.6 Well-Behaved Functions

2.7 Approximation

Chapter 3 The Derivative

3.1 The Definition

3.2 Notation

3.3 The Speedometer Reading

3.4 Computational Rules

3.5 The Derivative as a Linear Transformation

Chapter 4 More About the Derivative

4.1 The Mean Value Theorem

4.2 Higher Derivatives

4.3 Taylor's Formula

Chapter 5 Applications

5.1 Graphs; Refining the Picture

5.2 Maxima-Minima Problems

5.3 Velocity and Acceleration; Related Rates

Chapter 6 The Definite Integral

6.1 The Area Under a Curve

6.2 The Integral Defined

6.3 Properties of the Integral

6.4 The Fundamental Theorem

6.5 Improper Integrals

Chapter 7 Transcendental Functions

7.1 Trigonometric Functions

7.2 Derivatives of the Trigonometric Functions

7.3 Derivatives of the Inverse Trigonometric Functions

7.4 The Logarithm and Its Inverse

7.5 The Hyperbolic Functions

7.6 A Tool for Finding Limits

Chapter 8 Finding Antiderivatives

8.1 A Summary

8.2 Trigonometric Substitutions

8.3 Integration by Parts

8.4 Rational Functions

8.5 Other Methods

Chapter 9 Curves in the Plane

9.1 Parametric Equations

9.2 Curves

9.3 Differentiation of Vector-Valued Functions

9.4 Acceleration and Curvature

9.5 Polar Coordinates

Chapter 10 Linear Algebra

10.1 Solving Linear Equations

10.2 More About Vectors

10.3 Linear Transformations

10.4 Determinants

10.5 Change of Basis

10.6 Bilinear Transformations and Quadratic Forms

10.7 Symmetric Matrices

Chapter 11 Functions of Several Variables

11.1 Vectors in R3

11.2 Lines and Planes in R3

11.3 Surfaces in R3

11.4 Functions

11.5 The Approximation Problem

Chapter 12 The Derivative of Functions of Several Variables

12.1 The Definition

12.2 Real-Valued Functions of Several Variables

12.3 Higher Derivatives

12.4 More About Extreme Values of Functions

Chapter 13 Integration of Functions of Several Variables

13.1 The Integral on a Rectangle

13.2 The Integral on a Nice Set

13.3 Change of Variables

Chapter 14 Infinite Series

14.1 Sequences and Series

14.2 Positive Series

14.3 Series with Some Negative Terms

14.4 Functions Defined by Infinite Series

Chapter 15 Differential Equations

15.1 Problems That Lead to Differential Equations

15.2 Families of Solutions

15.3 Linear Differential Equations with Constant Coefficients

15.4 First-Order Linear Differential Equations

15.5 Other First-Order, First-Degree Differential Equations

15.6 Approximating Solutions

What Next?


Table of Antiderivatives

Solutions to Problems

Answers to Odd Exercises



No. of pages:
© Academic Press 1972
Academic Press
eBook ISBN:

About the Author

A. Wayne Roberts

Affiliations and Expertise

Department of Mathematics, Macalester College, St. Paul, Minnesota