Elementary Functions and Analytic Geometry - 1st Edition - ISBN: 9780122596551, 9781483271965

Elementary Functions and Analytic Geometry

1st Edition

Authors: Harley Flanders
eBook ISBN: 9781483271965
Imprint: Academic Press
Published Date: 1st January 1973
Page Count: 402
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Elementary Functions and Analytic Geometry is an introduction to college mathematics, with emphasis on elementary functions and analytic geometry. It aims to provide a working knowledge of basic functions (polynomial, rational, exponential, logarithmic, and trigonometric); graphing techniques and the numerical aspects and applications of functions; two- and three-dimensional vector methods; and complex numbers, mathematical induction, and the binomial theorem.

Comprised of 13 chapters, this book begins with a discussion on functions and graphs, paying particular attention to quantities measured in the real number system. The next chapter deals with linear and quadratic functions as well as some of their applications. Tips on graphing are offered. Subsequent chapters focus on polynomial functions, along with graphs of factored polynomials; rational functions; exponential and logarithm functions; and trigonometric functions. Identities and inverse functions, vectors, and trigonometry are also explored, together with complex numbers and solid analytic geometry. The book concludes by considering mathematical induction, binomial coefficients, and the binomial theorem.

This monograph will be a useful resource for undergraduate students of mathematics and algebra.

Table of Contents


Chapter 1 Functions and Graphs

1. Introduction

2. Real Numbers

3. Coordinates on the Line and Plane

4. Functions

5. Construction of Functions


Chapter 2 Linear and Quadratic Functions

1. Linear Functions

2. Quadratic Functions

3. Some Applications

4. Tips on Graphing


Chapter 3 Polynomial Functions

1. Algebra of Polynomials

2. Graphs of Polynomials

3. Zeros and Roots

4. Zeros of Higher Degree Polynomials

5. Graphs of Factored Polynomials


Chapter 4 Rational Functions

1. Basic Properties

2. Algebraic Operations

3. Graphs of Rational Functions

4. Division with Remainder

5. Partial Fractions


Chapter 5 Exponential and Logarithm Functions

1. Review of Exponents

2. Exponential Functions

3. Logarithm Functions

4. Accuracy and Tables [Optional]

5. Log Tables [Optional]

6. Computations with Logarithms [Optional]

7. Power Functions


Chapter 6 Trigonometric Functions

1. Introduction

2. Distances and Angles

3. Sine and Cosine

4. Other Trigonometric Functions

5. Graphs of Sine and Cosine

6. Graphs of the Other Functions


Chapter 7 Identities and Inverse Functions

1. Identities

2. Further Identities

3. Inverse Functions

4. Trigonometric Equations


Chapter 8 Trigonometry

1. Right Triangles

2. Laws of Cosines and Sines

3. Oblique Triangles [Optional]


Chapter 9 Vectors

1. Vector Algebra

2. Lines

3. Length and Inner Product

4. Normal Form


Chapter 10 Analytic Geometry

1. Translation of Axes

2. The Circle

3. Tangents and Loci

4. Polar Coordinates

5. Conics: The Parabola

6. The Ellipse

7. The Hyperbola

8. Rotation of Axes [Optional]

9. Additional Exercises on Conics [Optional]


Chapter 11 Solid Analytic Geometry

1. Coordinates and Vectors

2. Lines and Planes

5. Linear Systems and Intersections

4. Polynomials in Several Variables

5. Quadric Surfaces

6. Cylinders and Cones


Chapter 12 Complex Numbers

1. Complex Arithmetic

2. The Complex Plane

3. Zeros of Polynomials

4. De Moivre's Theorem and Roots of Unity


Chapter 13 Induction and the Binomial Theorem

1. Mathematical Induction

2. Binomial Coefficients

3. Binomial Theorem


Answers to Odd-Numbered Exercises


1. 4-Place Logarithm

2. 4-Place Antilogarithm

3. Powers and Roots

4. Trigonometric (Degrees)

5. Trigonometric (Radians)

6. Log-Trig (Degrees)

7. Trigonometric (π Radians)



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© Academic Press 1973
Academic Press
eBook ISBN:

About the Author

Harley Flanders

Affiliations and Expertise

Purdue University Lafayette, Indiana

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