*label_important*1. MATRICES

11 Chapters | 80 Solved Problems

#### *label_important* 1.1 Matrix Introduction

#### *label_important*1.2 Rank of a matrix (Echelon form)

#### *label_important* 1.3 Rank of a matrix (Normal form or Canonical form)

#### *label_important* 1.4 Consistency of Non-Homogenous Linear Equations

#### *label_important* 1.5 Consistency of Homogenous Linear Equations

#### *label_important* 1.6 Real matrices: Symmetric, Skew – Symmetric, Orthogonals

#### *label_important* 1.7 Characteristic Equation

#### *label_important* 1.8 Eigen Values and Eigen Vectors

#### *label_important* 1.9 Properties of Eigen Values and Eigen Vectors

#### *label_important* 1.10 Cayley Hamilton Theorem

#### *label_important* 1.11 Diagonalisation of matrix (Orthogonal Transformation)

*label_important*2. FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

7 Chapters | 50 Solved Problems

#### *label_important* 2.1 Linear Differential Equation

#### *label_important*2.2 Bernoulli's Equation

#### *label_important* 2.3 Exact Differential Equation

#### *label_important* 2.4 Non-Linear Differential Equation (Equation Solvable for p)

#### *label_important*2.5 Equation Solvable for Y

#### *label_important* 2.6 Equation Solvable for X

#### *label_important* 2.7 Clairaut's Equation

*label_important* 3. ORDINARY DIFFERENTIAL EQUATIONS OF HIGHER ORDERS

9 Chapters | 85 Solved Problems

#### *label_important* 3.1 Linear Differential Equations of Higher Order

#### *label_important*3.2 General solution of f(D)y = e^ax

#### *label_important*3.3 General solution of f(D)y = cos ax or sin ax

#### *label_important* 3.4 General solution of f(D)y = x^m

#### *label_important* 3.5 General solution of f(D)y = e^ax . f(x)

#### *label_important* 3.6 General solution of f(D)y = x^m . f(x)

#### *label_important* 3.7 Method of variation of parameters

#### *label_important* 3.8 Cauchy's Differential Equations

#### *label_important* 3.9 Legendre Differential Equations

*label_important* 4. PARTIAL DIFFERENTIAL EQUATIONS - FIRST ORDERS

6 Chapters | 60 Solved Problems

#### *label_important* 4.1 Formation of PDE's by elimination of arbitrary constants

#### *label_important*4.2 Formation of PDE's by elimination of arbitrary functions

#### *label_important* 4.3 Solutions of standard first order partial differential equations

#### *label_important* 4.4 First Order Linear(Lagrange's) Equation

#### *label_important* 4.5 Higher Order Partial Differential Equation

#### *label_important* 4.6 Complementary Function for a Non-homogenous Linear Equation

*label_important* 5. PARTIAL DIFFERENTIAL EQUATIONS - HIGHER ORDER

4 Chapters | 35 Solved Problems

#### *label_important* 5.1 Classification of second order PDE

#### *label_important*5.2 Method of Separation of Variables

#### *label_important*5.3 Solutions of One Dimensional Wave Equation

#### *label_important* 5.4 Solutions of One Dimensional Heat Equation