## Details

The book has a two-fold advantage: (a) Conceptual strength provided by accurate, precise but sufficient coverage of topics; (b) solved and unsolved problems as per JEE (Main & Advanced) pattern for strengthening concepts. The main idea is to make students understand the theory behind to enable them to strategize a given problem and tactically solve it. The topics covered in this volume are: Sets, Relations and Functions; Exponentials and Logarithms; Complex Numbers; Quadratic Numbers; Progressions, Sequences and Series; Permutations and Combinations; Binomial Theorem; Matrices, Determinants and System of Equations; Partial Fractions.

**Chapter 1: Sets, Relations and Functions**

1.1 Sets: Definition and Examples

1.2 Set Operations

1.3 Venn Diagrams

1.4 Relations

1.5 Equivalence Relations and Partitions

1.6 Functions

1.7 Graph of a Function

1.8 Even Functions and Odd Functions**Chapter 2: Exponentials and Logarithms**

2.1 Exponential Function

2.2 Logarithmic Function

2.3 Exponential Equations

2.4 Logarithmic Equations

2.5 Systems of Exponential and Logarithmic Equations

2.6 Exponential and Logarithmic Inequalities**Chapter 3: Complex Numbers**

3.1 Ordered Pairs of Real Numbers

3.2 Algebraic Form a + ib

3.3 Geometric Interpretation

3.4 The Trigonometric Form

3.5 De Moivre’s Theorem

3.6 Algebraic Equations**Chapter 4: Quadratic Equations **

4.1 Quadratic Expressions and Equations**Chapter 5: Progressions, Sequences and Series **

5.1 Sequences and Series

5.2 Arithmetic Progressions

5.3 Geometric Progressions

5.4 Harmonic Progressions and Series

5.5 Some Useful Formulae**Chapter 6: Permutations and Combinations **

6.1 Factorial Notation

6.2 Permutations

6.3 Combinations**Chapter 7: Binomial Theorem **

7.1 Binomial Theorem for Positive Integral Index

7.2 Binomial Theorem for Rational Index**Chapter 8: Matrices, Determinants and System of Equations **

8.1 Matrices

8.2 Determinants

8.3 Solutions of Linear Equations**Chapter 9: Partial Fractions**

9.1 Rational Fractions

9.2 Partial Fractions

Index

For Engineering students.

Dr. G.S.N. Murti: An eminent mathematician, accomplished author and a dedicated teacher, Dr. G.S.N. Murti brings vast knowledge and experience to teaching the fundamental concepts of pure Mathematics. Dr. Murti has taught Mathematics at degree level for 27 years before moving onto coach prospective JEE (Main & Advanced) candidates. Over the last 25 years, his name has become synonymous with the best quality JEE (Main & Advanced) coaching in Mathematics. In addition to being a great teacher, Dr. Murti is also considered a master trainer and mentor by a huge community of Mathematics teachers who prepare students for engineering entrance examinations.

Dr. U.M. Swamy: He is an illustrious Mathematician with 40 years of teaching and research experience who served at various levels in the Department of Mathematics at Andhra University and superannuated as Chairman of the Faculty of Science in 200 from the University. He is acclaimed as a distinguished teacher in the teaching community. Government of Andhra Pradesh felicitated him with the “Best Teacher Award” in 2006.