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Foundations of Mathematics : Algebra, Geometry, Trigonometry and Calculus.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Bloomfield :
Mercury Learning & Information,
2016.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover Page; Title; Copyright; Dedication; Contents; Preface; Acknowledgments; 1 The Laws of Algebra; 1.1 Introduction; 1.2 Numbers; 1.3 Fractions and Inequalities; 1.4 Notation for Sets; 1.5 Intervals of the Real Line and Set Intersections; 1.6 Absolute Value of a Real Number; 1.7 Algebraic Operations; 1.7.1 Addition and Subtraction; 1.7.2 Multiplication; 1.7.3 Division; 1.7.4 Recurring Decimals and Irrational Numbers; 1.8 An Algebraic System on the Set of Real Numbers; 1.8.1 Foil; 1.9 Natural Numbers as Exponents; 1.10 Order of Operations; 1.11 Laws of Division; 1.12 Decimal Notation.
- 1.12.1 Decimal Representation of Fractions1.12.2 Scientific Notation and Precision; 1.12.3 Decimal Representation of Irrational Numbers; 1.12.4 Conversion of Decimals into Fractions; 1.12.5 Rounding Off Decimals; 1.13 Divisibility of Natural Numbers; 1.13.1 Prime Decomposition of a Natural Number; 1.13.2 Finding the Prime Factors of a Natural Number; 1.13.3 Testing for Divisibility by Small Prime Numbers; 1.13.4 Adding Fractions Using Their Lowest Common Denominator; 1.14 Laws for Exponents; 1.15 Radicals; Exercises; 2 The Cartesian Plane; 2.1 Introduction; 2.2 Working in a Coordinate System.
- 2.3 Linear Equations and Straight Lines2.3.1 The Graph of a Linear Equation; 2.3.2 The Linear Equation of a Line; 2.3.3 Linear Relationships in Statistical Analysis; 2.3.4 Parallel and Perpendicular Lines; 2.3.5 The Distance between Points on a Line; 2.3.6 The Equation of a Perpendicular Bisector; 2.4 Circles in the Cartesian Plane; 2.5 Conic Sections in the Cartesian Plane; 2.6 Vector Algebra; 2.6.1 Addition and Scalar Multiplication of Vectors; 2.6.2 Subtraction of Vectors; 2.6.3 The Standard Basis Vectors; 2.6.4 The Dot Product of Vectors.
- 2.6.5 The Triangle Inequality and the Parallelogram LawExercises; 3 Solving Equations and Factorizing Polynomials; 3.1 Introduction; 3.2 Solving Linear Equations; 3.3 Solving Quadratic Equations by Completing the Square; 3.4 Polynomials; 3.4.1 Addition and Subtraction of Polynomials; 3.4.2 Multiplication of Polynomials; 3.4.3 Polynomials in More Than One Variable; 3.4.4 Long Division of Polynomials; 3.4.5 The Remainder Theorem and the Factor Theorem; 3.5 The Properties of Quadratic Polynomials; 3.5.1 The Graphs of Quadratic Polynomials; 3.5.2 The Nature of the Roots.
- 3.5.3 Factorizing Quadratic Polynomials3.5.4 Solving Quadratic Equations by Factorizing; 3.6 Complex Numbers as Matrices; 3.6.1 The Algebra of × 2 2 Matrices; 3.6.2 Complex Numbers as × 2 2 Matrices 743.7 Roots of Polynomials; 3.7 Roots of Polynomials; 3.7.1 Factorization Theorems; 3.7.2 A Method For Finding the Integer and Rational Roots of a Polynomial; 3.8 Graphs of Polynomials; 3.9 Solving Cubic, Quartic, and Quintic Equations; 3.9.1 Solving Cubic Equations; 3.9.2 Solving Quartic Equations; 3.9.3 Solving Quintic Equations; Exercises; 4 Trigonometry; 4.1 Introduction.