*label_important*1. MATRICES

10 Chapters | 59 Solved Problems

#### *label_important* 1.1 Matrix Introduction

#### *label_important*1.2 Real matrices: Symmetric, skew – symmetric, orthogonals

#### *label_important* 1.3 Complex matrices: Hermitian, Skew - Hermitian, Unitary Matrices

#### *label_important* 1.4 Rank of a matrix (Echelon form)

#### *label_important* 1.5 Rank of a matrix (Normal form or Canonical form)

#### *label_important* 1.6 Inverse of a matrix by Gauss – Jordan method

#### *label_important* 1.7 Consistency of Non-Homogenous Linear Equations

#### *label_important* 1.8 Gauss – Elimination method

#### *label_important* 1.9 Consistency of Homogenous Linear Equations

#### *label_important* 1.10 Gauss - Seidal Method

*label_important*2. EIGEN VALUES AND EIGEN VECTORS

6 Chapters | 47 Solved Problems

#### *label_important* 2.1 Characteristic Equation

#### *label_important*2.2 Eigen values and Eigen vectors

#### *label_important* 2.3 Properties of Eigen values and Eigen vectors

#### *label_important* 2.4 Cayley Hamilton Theorem

#### *label_important* 2.5 Diagonalisation of matrix (Similarity Transformation)

#### *label_important* 2.6 Diagonalisation of matrix (Orthogonal Transformation)

*label_important*3. SEQUENCES AND SERIES

11 Chapters | 54 Solved Problems

#### *label_important* 3.1 Sequences

#### *label_important*3.2 Infinite series

#### *label_important* 3.3 Comparison test

#### *label_important* 3.4 Integral test

#### *label_important* 3.5 D'Alembert's ratio test

#### *label_important* 3.6 Raabe's test

#### *label_important* 3.7 Cauchy's root test

#### *label_important* 3.8 Logarithmic test

#### *label_important* 3.9 Gauss's test

#### *label_important* 3.10 Alternating series

#### *label_important* 3.11 Absolute and and conditional convergence

*label_important*4. CALCULUS

7 Chapters | 62 Solved Problems

#### *label_important* 4.1 Rolle’s Mean value Theorem

#### *label_important*4.2 Lagrange’s Mean Value Theorem

#### *label_important* 4.3 Cauchy’s and Generalized mean value Theorem

#### *label_important* 4.4 Taylor & Maclaurin Series

#### *label_important* 4.5 Beta Function

#### *label_important* 4.6 Gamma Function

#### *label_important* 4.7 Relation Between Gamma and Beta Function

*label_important*5. MULTIVARIABLE CALCULUS (PARTIAL DIFFERENTIATION AND APPLICATIONS)

6 Chapters | 42 Solved Problems

#### *label_important* 5.1 Function of two or more variables (Limit & Continuity)

#### *label_important*5.2 Partial Differentiation

#### *label_important* 5.3 Euler's Theorems

#### *label_important* 5.4 Total Derivatives

#### *label_important* 5.5 Maxima & Minima

#### *label_important* 5.6 Lagrange's Method