Algebra and Trigonometry

Algebra and Trigonometry

1st Edition - January 1, 1975

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  • Authors: Harley Flanders, Justin J. Price
  • eBook ISBN: 9781483271040

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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.

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


    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


    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


    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


    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)


    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


    7 Identities and Inverse Functions

    1. Basic Identities

    2. The Addition Laws

    3. Further Identities

    4. Inverse Functions

    5. Applications


    8 Trigonometry

    1. Right Triangles

    2. Oblique Triangles

    3. Numerical Solution

    4. Applications to Geometry

    5. Vectors (Optional)

    6. Length and Inner Product (Optional)


    9 Topics in Algebra

    1. Division of Polynomials

    2. Zeros of Polynomials

    3. Partial Fractions

    4. Systems of Linear Equations

    5. Determinants


    10 Complex Numbers

    1. Complex Arithmetic

    2. The Complex Plane

    3. Zeros of Polynomials

    4. De Moivre's Theorem and Roots of Unity


    11 Discrete Algebra

    1. Sequences

    2. Permutations and Combinations

    3. Binomial Theorem

    4. Summation

    5. Mathematical Induction


    Answers to Odd-Numbered Exercises


    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)


Product details

  • No. of pages: 442
  • Language: English
  • Copyright: © Academic Press 1975
  • Published: January 1, 1975
  • Imprint: Academic Press
  • eBook ISBN: 9781483271040

About the Authors

Harley Flanders

Affiliations and Expertise

Purdue University Lafayette, Indiana

Justin J. Price

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