TABLE OF CONTENTS
GENERAL MATHEMATICS-1 (INTRODUCTION TO ALGEBRA)
Unit # | CONTENTS | Page # |
1 | 1. INTRODUCTION TO MATHEMATICS | 1 |
2 | 2. REAL NUMBER SYSTEMS | |
2.1 Real Numbers | 7 | |
2.2 Properties of Real Numbers | 11 | |
2.3 Rational and Irrational Numbers | 16 | |
2.4 Decimal Presentation of Rational and Irrational Numbers | 18 | |
PRACTICE EXERCISE – 2.1 | 21 | |
2.5 HCF & LCM | 29 | |
PRACTICE EXERCISE – 2.2 | 32 | |
3 | 3. COMPLEX NUMBERS | |
3.1 Definition of Complex Numbers | 35 | |
3.2 Operations on Complex Numbers | 37 | |
3.3 Properties of the Complex Numbers | 39 | |
3.4 Geometrical Representation of Complex Numbers | 42 | |
3.5 Graphical Addition and Subtraction of Complex Numbers | 44 | |
PRACTICE EXERCISE – 3 | 45 | |
4 | 4. INTRODUCTION TO SETS | |
4.1 Basic Definitions of Sets | 54 | |
4.2 Representation of Sets in Set Theory | 56 | |
4.3 Types of Sets | 57 | |
4.4 Subsets and its Types with Examples | 58 | |
4.5 Operations on Sets | 60 | |
4.6 Properties of Sets | 62 | |
PRACTICE EXERCISE – 4 | 63 | |
5 | 5. FUNCTIONS | |
5.1 Definition of Function | 75 | |
5.2 How to Evaluate the Function | 76 | |
5.3 Function, Domain and Range | 78 | |
5.4 SET- Builder Notation for a Function | 79 | |
5.5 Types of Function | 80 | |
5.6 Linear and Quadratic Function | 86 | |
5.7 Inverse of Function | 88 | |
PRACTICE EXERCISE – 5 | 89 | |
6 | 6. INTRODUCTION TO MATRIX | |
6.1 Basic Introduction | 99 | |
6.2 Important Formulas for Matrices | 100 | |
6.3 Types of Matrices | 101 | |
6.4 Operations on Matrices | 103 | |
6.5 Properties of Matrix | 105 | |
6.6 Transpose of Matrix with Examples | 106 | |
6.7 Special Types of Matrices | 108 | |
6.8 Echelon and Reduced Echelon Forms of Matrices | 110 | |
6.9 Invertible Matrix | 112 | |
PRACTICE EXERCISE – 6 | 114 | |
7 | 7. DETERMINANTS | |
7.1 Determinants of Square Matrix | 126 | |
7.2 Types of Determinants | 127 | |
7.3 Properties of Determinants | 130 | |
7.4 Adjoint of a Matrix | 136 | |
7.5 Application of Determinants and Matrices | 138 | |
PRACTICE EXERCISE – 7 | 140 | |
8 | 8. SYSTEMS OF LINEAR EQUATIONS | |
8.1 Basic Introduction | 149 | |
8.2 Methods to Solve Systems of Linear Equation | 150 | |
8.3 Systems of Linear Equations in Two Variables | 153 | |
8.4 Cramer’s Rule | 161 | |
8.5 Application of Systems of Linear Equations | 163 | |
PRACTICE EXERCISE – 8 | 164 | |
9 | 9. SOLUTION OF QUADRATIC EQUATIONS | |
9.1 Basic Introduction | 174 | |
9.2 Solution of Quadratic Equations with Examples | 174 | |
9.3 Derivation of the Quadratic Formula | 180 | |
PRACTICE EXERCISE – 9.1 | 184 | |
9.4 Qualitative Analysis of Roots of Quadratic Equations | 189 | |
PRACTICE EXERCISE – 9.2 | 192 | |
9.6 Solution of Equations Reducible to the Quadratic Equation with Examples | 194 | |
PRACTICE EXERCISE – 9.3 | 203 | |
9.7 Cube Root of Unity | 204 | |
9.8 Properties of Cube Root of Unity | 209 | |
9.9 Four Fourth Roots of Unity | 212 | |
PRACTICE EXERCISE – 9.4 | 213 | |
9.10 Relations Between the Roots and the Coefficients of a Quadratic Equation | 216 | |
PRACTICE EXERCISE – 9.5 | 219 | |
10 | 10. SEQUENCES & SERIES | |
10.1 Introduction to Sequence and Series | 226 | |
10.2 Types of Sequence & Series | 228 | |
10.3 Sequence and Series Formulas | 228 | |
PRACTICE EXERCISE – 10.1 | 232 | |
10.4 Arithmetic Progression / Sequence | 236 | |
PRACTICE EXERCISE – 10.2 | 240 | |
10.5 Arithmetic Mean (A.M) | 242 | |
PRACTICE EXERCISE – 10.3 | 243 | |
10.6 Arithmetic Series | 244 | |
PRACTICE EXERCISE – 10.4 | 247 | |
10.8 Geometric Progression / Sequence | 251 | |
PRACTICE EXERCISE – 10.5 | 254 | |
10.9 Geometric Means (G.M) | 256 | |
PRACTICE EXERCISE – 10.6 | 258 | |
10.10 Geometric Series | 260 | |
PRACTICE EXERCISE – 10.7 | 264 | |
10.11 Application of Geometric Sequence & Series | 266 | |
10.12 Harmonic Progression / Sequence | 268 | |
10.13 Harmonic Mean | 270 | |
10.14 Application of Harmonic Sequence | 272 | |
PRACTICE EXERCISE – 10.8 | 273 | |
11 | 11. MATHEMATICAL INDUCTION | |
11.1 Principles of Mathematical Induction | 282 | |
11.2 Principles of Extended Mathematical Induction | 284 | |
PRACTICE EXERCISE – 11 | 286 | |
12 | 12. BINOMIAL THEOREM | |
12.1 Introduction to Binomial Theorem | 291 | |
PRACTICE EXERCISE – 12.1 | 296 | |
12.2 Application of Binomial Theorem | 303 | |
PRACTICE EXERCISE – 12.2 | 308 | |
13 | 13. TRIGONOMETRY | |
13.1 Fundamentals of Trigonometry | 313 | |
Practice Exercise 13.1 | 320 | |
13.2 Trigonometric Functions | 323 | |
Practice Exercise 13.2 | 327 | |
13.3 The Values of Trigonometric Functions | 331 | |
Practice Exercise 13.3 | 334 | |
13.4 Fundamental Law of Trigonometry | 344 | |
13.5 Trigonometric Ratios of Allied Angles | 344 | |
13.6 Applications of Basic Identities | 346 | |
Practice Exercise 13.4 | 349 | |
13.7 Half, Double and Triple Angle Identities |
352 | |
Practice Exercise 13.5 | 354 | |
14 | Important Definitions | 361 |
15 | Paper Pattern and Guideline for Mid and Final Exam | 373 |
16 | Question Papers | 374 |
17 | References | 382 |
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