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1st Edition - January 1, 1981

Authors: Bernard Kolman, Arnold Shapiro

Language: EnglisheBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 6 3 9 1 - 5

Introduction to Algebra and Trigonometry provides a complete and self-contained presentation of the fundamentals of algebra and trigonometry. This book describes an axiomatic… Read more

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Introduction to Algebra and Trigonometry provides a complete and self-contained presentation of the fundamentals of algebra and trigonometry. This book describes an axiomatic development of the foundations of algebra, defining complex numbers that are used to find the roots of any quadratic equation. Advanced concepts involving complex numbers are also elaborated, including the roots of polynomials, functions and function notation, and computations with logarithms. This text also discusses trigonometry from a functional standpoint. The angles, triangles, and applications involving triangles are likewise treated. Other topics include analytic geometry, conic sections, and use of a coordinate system to prove theorems from plane, and matrix operations and inverses. This publication is valuable to students aiming to gain more knowledge of the fundamentals of mathematics.

PrefaceAcknowledgmentsTo the StudentChapter One The Foundations Of Algebra 1.1 The Real Number System 1.2 The Real Number Line 1.3 Algebraic Expressions; Polynomials 1.4 Factoring 1.5 Rational Expressions 1.6 Integer Exponents 1.7 Rational Exponents and Radicals 1.8 Complex Numbers Chapter Review MaterialChapter Two Equations And Inequalities 2.1 Linear Equations in One Unknown 2.2 Applications 2.3 Linear Inequalities 2.4 Absolute Value in Equations and Inequalities 2.5 The Quadratic Equation 2.6 Applications—Quadratic Equations 2.7 Second-Degree Inequalities Chapter Review MaterialChapter Three Functions 3.1 Rectangular Coordinate Systems 3.2 Functions and Function Notation 3.3 Graphs of Functions 3.4 Linear Functions 3.5 Direct and Inverse Variation 3.6 Combining Functions; Inverse Functions Chapter Review MaterialChapter Four Exponential And Logarithmic Functions 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Properties of Logarithms 4.4 Computing with Logarithms (Optional) 4.5 Exponential and Logarithmic Equations Chapter Review MaterialChapter Five Trigonometry: The Circular Functions 5.1 The Wrapping Function 5.2 The Sine, Cosine, and Tangent Functions 5.3 Graphs of Sine, Cosine, and Tangent 5.4 Variation of Sine, Cosine, and Tangent 5.5 Graphs: Amplitude, Variation, and Phase Shift 5.6 Secant, Cosecant, and Cotangent 5.7 The Inverse Trigonometric Functions Chapter Review MaterialChapter Six Angles And Triangles 6.1 Angles and Their Measurement 6.2 Trigonometric Functions of Angles 6.3 Right Angle Trigonometry 6.4 Law of Cosines 6.5 Law of Sines Chapter Review MaterialChapter Seven Analytic Trigonometry 7.1 Trigonometric Identities 7.2 The Addition Formulas 7.3 Double and Half-Angle Formulas 7.4 The Product-Sum Formulas 7.5 Trigonometric Equations 7.6 Trigonometry and Complex Numbers Chapter Review MaterialChapter Eight Analytic Geometry: The Conic Sections 8.1 Analytic Geometry 8.2 The Circle 8.3 The Parabola 8.4 The Ellipse and Hyperbola 8.5 Identifying the Conic Sections Chapter Review MaterialChapter Nine Systems Of Equations And Inequalities 9.1 Systems of Linear Equations 9.2 Solving by Elimination 9.3 Applications 9.4 Systems of Linear Equations in Three Unknowns 9.5 Systems Involving Nonlinear Equations 9.6 Systems of Linear Inequalities in Two Variables Chapter Review MaterialChapter Ten Matrices And Determinants 10.1 Matrices and Linear Systems 10.2 Matrix Operations and Applications (Optional) 10.3 Inverses of Matrices (Optional) 10.4 Determinants and Cramer's Rule Chapter Review MaterialChapter Eleven Roots Of Polynomials 11.1 Polynomial Division and Synthetic Division 11.2 The Remainder and Factor Theorems 11.3 Factors and Roots 11.4 Real and Rational Roots 11.5 Rational Functions and Their Graphs Chapter Review MaterialChapter Twelve Topics In Algebra 12.1 Arithmetic Progressions 12.2 Geometric Progressions 12.3 Mathematical Induction 12.4 The Binomial Theorem 12.5 Counting: Permutations and Combinations 12.6 Probability Chapter Review MaterialAppendix/TablesAnswers To Odd-Numbered Exercises, Review Exercises, And Progress TestsIndex

- No. of pages: 620
- Language: English
- Edition: 1
- Published: January 1, 1981
- Imprint: Academic Press
- eBook ISBN: 9781483263915

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