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Preface; Contents; Abbreviations; 1: Numbers and Mathematical Symbols; 1.1 What Are Numbers and Mathematical Symbols and Why Are They Used?; 1.2 Classes of Numbers; Exercise; 1.2.1 Arithmetic with Fractions; Exercise; Exercise; Exercise; 1.2.2 Arithmetic with Exponents and Logarithms; Exercise; Exercise; Exercise; 1.2.3 Numeral Systems; Exercise; Exercise; 1.2.4 Complex Numbers; Exercise; 1.2.4.1 Arithmetic with Complex Numbers; Exercise; 1.2.4.2 The Polar Form of Complex Numbers; 1.3 Mathematical Symbols and Formulas; 1.3.1 Conventions for Writing Mathematics
1.3.2 Latin and Greek Letters in Mathematics1.3.3 Reading Mathematical Formulas; Glossary; Symbols Used in This Chapter (in Order of Their Appearance); Overview of Equations, Rules and Theorems for Easy Reference; Answers to Exercises; References; Online Sources of Information: Methods; Online Sources of Information: Others; Books; Papers; 2: Equation Solving; 2.1 What Are Equations and How Are They Applied?; 2.1.1 Equation Solving in Daily Life; Example 2.1; Example 2.2; 2.2 General Definitions for Equations; 2.2.1 General Form of an Equation; 2.2.2 Types of Equations
2.3 Solving Linear Equations2.3.1 Combining Like Terms; Example 2.3; Exercise; 2.3.2 Simple Mathematical Operations with Equations; Box 2.1 Useful Arithmetic Rules for Solving Linear Equations; Exercise; 2.4 Solving Systems of Linear Equations; Example 2.4; Example 2.5; 2.4.1 Solving by Substitution; Example 2.6; Example 2.7; Exercises; 2.4.2 Solving by Elimination; Example 2.8; Example 2.9; Example 2.10; Exercise; 2.4.3 Solving Graphically; Example 2.11; 2.4.4 Solving Using Cramer's Rule; Box 2.2 Cramer's Rule for a System of 2 Linear Equations; 2.5 Solving Quadratic Equations; Example 2.12
Example 2.132.5.1 Solving Graphically; 2.5.2 Solving Using the Quadratic Equation Rule; Box 2.3 Quadratic Equation Rule; Example 2.14; Exercise; 2.5.3 Solving by Factoring; Example 2.15; Box 2.4 Factor Multiplication Rule; Example 2.16; Example 2.17; Example 2.18; Example 2.16 (continued); Exercise; 2.6 Rational Equations (Equations with Fractions); Example 2.19; 2.7 Transcendental Equations; 2.7.1 Exponential Equations; Example 2.20; Example 2.21; Exercise; 2.7.2 Logarithmic Equations; Example 2.22; Example 2.23; Exercise; 2.8 Inequations; 2.8.1 Introducing Inequations
2.8.2 Solving Linear InequationsExercise; 2.8.3 Solving Quadratic Inequations; Example 2.24; Example 2.25; Exercise; 2.9 Scientific Example; Example 2.26; Glossary; Symbols Used in This Chapter (in Order of Their Appearance); Overview of Equations for Easy Reference; Answers to Exercises; References; Online Sources of Information; Books; Papers; 3: Trigonometry; 3.1 What Is Trigonometry and How Is It Applied?; 3.2 Trigonometric Ratios and Angles; Exercise; 3.2.1 Degrees and Radians; Exercises; 3.3 Trigonometric Functions and Their Complex Definitions; Exercises; Exercise; Exercises
1.3.2 Latin and Greek Letters in Mathematics1.3.3 Reading Mathematical Formulas; Glossary; Symbols Used in This Chapter (in Order of Their Appearance); Overview of Equations, Rules and Theorems for Easy Reference; Answers to Exercises; References; Online Sources of Information: Methods; Online Sources of Information: Others; Books; Papers; 2: Equation Solving; 2.1 What Are Equations and How Are They Applied?; 2.1.1 Equation Solving in Daily Life; Example 2.1; Example 2.2; 2.2 General Definitions for Equations; 2.2.1 General Form of an Equation; 2.2.2 Types of Equations
2.3 Solving Linear Equations2.3.1 Combining Like Terms; Example 2.3; Exercise; 2.3.2 Simple Mathematical Operations with Equations; Box 2.1 Useful Arithmetic Rules for Solving Linear Equations; Exercise; 2.4 Solving Systems of Linear Equations; Example 2.4; Example 2.5; 2.4.1 Solving by Substitution; Example 2.6; Example 2.7; Exercises; 2.4.2 Solving by Elimination; Example 2.8; Example 2.9; Example 2.10; Exercise; 2.4.3 Solving Graphically; Example 2.11; 2.4.4 Solving Using Cramer's Rule; Box 2.2 Cramer's Rule for a System of 2 Linear Equations; 2.5 Solving Quadratic Equations; Example 2.12
Example 2.132.5.1 Solving Graphically; 2.5.2 Solving Using the Quadratic Equation Rule; Box 2.3 Quadratic Equation Rule; Example 2.14; Exercise; 2.5.3 Solving by Factoring; Example 2.15; Box 2.4 Factor Multiplication Rule; Example 2.16; Example 2.17; Example 2.18; Example 2.16 (continued); Exercise; 2.6 Rational Equations (Equations with Fractions); Example 2.19; 2.7 Transcendental Equations; 2.7.1 Exponential Equations; Example 2.20; Example 2.21; Exercise; 2.7.2 Logarithmic Equations; Example 2.22; Example 2.23; Exercise; 2.8 Inequations; 2.8.1 Introducing Inequations
2.8.2 Solving Linear InequationsExercise; 2.8.3 Solving Quadratic Inequations; Example 2.24; Example 2.25; Exercise; 2.9 Scientific Example; Example 2.26; Glossary; Symbols Used in This Chapter (in Order of Their Appearance); Overview of Equations for Easy Reference; Answers to Exercises; References; Online Sources of Information; Books; Papers; 3: Trigonometry; 3.1 What Is Trigonometry and How Is It Applied?; 3.2 Trigonometric Ratios and Angles; Exercise; 3.2.1 Degrees and Radians; Exercises; 3.3 Trigonometric Functions and Their Complex Definitions; Exercises; Exercise; Exercises