# Elementary Functions and Analytic Geometry

## 1st Edition

Authors:
eBook ISBN: 9781483271965
Published Date: 1st January 1973
Page Count: 402
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## Description

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.

﻿Preface

Chapter 1 Functions and Graphs

1. Introduction

2. Real Numbers

3. Coordinates on the Line and Plane

4. Functions

5. Construction of Functions

Tests

Chapter 2 Linear and Quadratic Functions

1. Linear Functions

3. Some Applications

4. Tips on Graphing

Tests

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

Tests

Chapter 4 Rational Functions

1. Basic Properties

2. Algebraic Operations

3. Graphs of Rational Functions

4. Division with Remainder

5. Partial Fractions

Tests

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

Tests

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

Tests

Chapter 7 Identities and Inverse Functions

1. Identities

2. Further Identities

3. Inverse Functions

4. Trigonometric Equations

Tests

Chapter 8 Trigonometry

1. Right Triangles

2. Laws of Cosines and Sines

3. Oblique Triangles [Optional]

Tests

Chapter 9 Vectors

1. Vector Algebra

2. Lines

3. Length and Inner Product

4. Normal Form

Tests

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]

Tests

Chapter 11 Solid Analytic Geometry

1. Coordinates and Vectors

2. Lines and Planes

5. Linear Systems and Intersections

4. Polynomials in Several Variables

6. Cylinders and Cones

Tests

Chapter 12 Complex Numbers

1. Complex Arithmetic

2. The Complex Plane

3. Zeros of Polynomials

4. De Moivre's Theorem and Roots of Unity

Tests

Chapter 13 Induction and the Binomial Theorem

1. Mathematical Induction

2. Binomial Coefficients

3. Binomial Theorem

Tests

Tables

1. 4-Place Logarithm

2. 4-Place Antilogarithm

3. Powers and Roots

4. Trigonometric (Degrees)

6. Log-Trig (Degrees)

Index

No. of pages:
402
Language:
English
Published:
Imprint: