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Algebra and Trigonometry

1st Edition - January 1, 1975

Authors: Harley Flanders, Justin J. Price

eBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 7 1 0 4 - 0

Algebra and Trigonometry presents the essentials of algebra and trigonometry with some applications. The emphasis is on practical skills, problem solving, and computational… Read more

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Algebra and Trigonometry presents the essentials of algebra and trigonometry with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered. Comprised of 11 chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of algebraic notation and practical manipulative skills such as factoring, using exponents and radicals, and simplifying rational expressions is highlighted, along with the most common mistakes in algebra. The reader is then introduced to the solution of linear, quadratic, and other types of equations and systems of equations, as well as the solution of inequalities. Subsequent chapters deal with the most basic functions: polynomial, rational, exponential, logarithm, and trigonometric. Trigonometry and the inverse trigonometric functions and identities are also presented. The book concludes with a review of progressions, permutations, combinations, and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

Preface

1 Basic Algebra

1. The Nature of Algebra

2. Algebraic Notation

3. The Rules of Algebra

4. Integers and Rationals

5. Integral Exponents

6. Roots and Radicals

7. Rational Exponents

8. Polynomials

9. Polynomials in Several Variables

10. Factoring

11. Rational Expressions

12. Common Errors in Algebra

Tests

2 Equations and Inequalities

1. Equations and Identities

2. Linear Equations

3. Quadratic Equations

4. Other Types of Equations

5. Applications

6. Order

7. Absolute Values

8. Inequalities

Tests

3 Functions and Graphs

1. Introduction

2. Coordinates in the Plane

3. Functions

4. Construction of Functions

5. Linear Functions

6. Quadratic Functions

7. Tips on Graphing

Tests

4 Polynomial and Rational Functions

1. Introduction

2. Graphs of Polynomials

3. Graphs of Factored Polynomials

4. Rational Functions

5. Graphs of Rational Functions

6. Factored Rational Functions

Tests

5 Exponentials and Logarithms

1. Exponential Functions

2. Logarithm Functions

3. Power Functions

4. Accuracy and Round-Off

5. Tables and Interpolation

6. Computations with Logarithms (Optional)

7. Computations with a Small Calculator (Optional)

8. Applications

9. Business Applications (Optional)

Tests

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

7 Identities and Inverse Functions

1. Basic Identities

2. The Addition Laws

3. Further Identities

4. Inverse Functions

5. Applications

Tests

8 Trigonometry

1. Right Triangles

2. Oblique Triangles

3. Numerical Solution

4. Applications to Geometry

5. Vectors (Optional)

6. Length and Inner Product (Optional)

Tests

9 Topics in Algebra

1. Division of Polynomials

2. Zeros of Polynomials

3. Partial Fractions

4. Systems of Linear Equations

5. Determinants

Tests

10 Complex Numbers

1. Complex Arithmetic

2. The Complex Plane

3. Zeros of Polynomials

4. De Moivre's Theorem and Roots of Unity

Tests

11 Discrete Algebra

1. Sequences

2. Permutations and Combinations

3. Binomial Theorem

4. Summation

5. Mathematical Induction

Tests

Answers to Odd-Numbered Exercises

Tables

1. 4-Place Logarithms

2. 4-Place Antilogarithms

3. Powers and Roots

4. Trigonometric (Degrees)

5. Trigonometric (Radians)

6. Log-Trig (Degrees)

7. Trigonometric (π Radians)

Index