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.
Inhalt
Preface
Acknowledgments
To the Student
Chapter 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 Material
Chapter 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 Material
Chapter 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 Material
Chapter 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 Material
Chapter 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 Material
Chapter 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 Material
Chapter 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 Material
Chapter 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 Material
Chapter 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 Material
Chapter 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 Material
Chapter 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 Material
Chapter 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 Material
Appendix/Tables
Answers To Odd-Numbered Exercises, Review Exercises, And Progress Tests
Index