Elementary Functions and Analytic Geometry

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.

Contenu

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

2. Quadratic 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

3. Linear Systems and Intersections

4. Polynomials in Several Variables

5. Quadric Surfaces

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

Answers to Odd-Numbered Exercises

Tables

1. 4-Place Logarithm

2. 4-Place Antilogarithm

3. Powers and Roots

4. Trigonometric (Degrees)

5. Trigonometric (Radians)

6. Log-Trig (Degrees)

7. Trigonometric (p Radians)

Index