Algebra - 1st Edition - ISBN: 9780122596667, 9781483265087

Algebra

1st Edition

Authors: Harley Flanders Justin J. Price
eBook ISBN: 9781483265087
Imprint: Academic Press
Published Date: 1st January 1975
Page Count: 324
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Description

Algebra presents the essentials of algebra 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, together with exponentials and logarithms.

Comprised of eight 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 of algebra: polynomial, rational, exponential, and logarithm. The book concludes with a review of sequences, permutations and combinations, and the binomial theorem, as well as summation and mathematical induction.

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

Table of Contents


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 Topics in Algebra

1. Division of Polynomials

2. Zeros of Polynomials

3. Partial Fractions

4. Systems of Linear Equations

5. Determinants

Tests

7 Complex Numbers

1. The Complex Number System

2. Complex Arithmetic

3. Quadratic Equations

4. Zeros of Polynomials

Tests

8 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

Index

Details

No. of pages:
324
Language:
English
Copyright:
© Academic Press 1975
Published:
Imprint:
Academic Press
eBook ISBN:
9781483265087

About the Author

Harley Flanders

Affiliations and Expertise

Purdue University Lafayette, Indiana

Justin J. Price