1.1 Complex number introduction

1 & 1.1 Numerical Methods for Partial Differential equation

1.2 Algebra of complex numbers

1.2 & 1.2.1 Method of Separation of Variables with example

1.2.2 Example 2

1.2.3 Example 3

1.2.4 Example 4

1.3 square root of complex numbers

1.3 Vibration of String 1-D Wave equation

1.3.1 Example 1

1.3.2 Example 2

1.3.3 Example 3

1.4 Modulus & Argument of Complex number

1.4.1 D Heat Flow Equation

1.4.1 Example 1

1.4.2 Example 2

1.4.3 Example 3

1.4.4 Example 4

1.4.5 Example 5

1.5 General Equation Elliphic Hyperbolic Parabola

1.5.1 De Morire's theorem

1.5.2 Example on De Morireism Type 1

1.5.3 Examples on De Morire's Type 2

1.5.4 Example on De Morire's Type 3

1.6 Bender Schmidt Formula

1.6.1 Expression for power of sinƟ & CosƟNumerical Solutions of Transcendental & Linear

1.6.1 Example 1

1.6.2 Example 2

1.6.3 Example 3

1.7 Crank Nicolson Simplified Formula

1.7.1 Example 1

1.7.2 Example 2

1.7.3 Example 3

1.8.1 Example 1

1.8 2-D heat flow

2 Matrices

2.1 Hyperbolic function with examples

2.1.2 Triangular Matrix

2.1 & 2.1.2 Transpose of Matrix

2.1.3 Conjugate of Matrix

2.1.4 Transpose Conjugate of Matrix

2.1.5 Symmetric Matirx & Skew Symmetric Matrix

2.1.6 Hermitian & Skew Hermitian Matrix

2.1.7 Unitary & Orthogonal Matrix

2.2 Introduction of Eigen Values

2.2.1 Examples 1.4 on Hyperbolic Function

2.2 Hyperbolic identities & differentiation & integration

2.2.2 Examples 5.7 on Hyperbolic Function

2.3 Eigen Vectors Introduction

2.3.1 Separation of real & imaginary parts with examples

2.3.2 Examples 3 & 4

2.3.3 Example 5 & 6

2.3.4 Example 7 & 8

2.4 Inverse hyperbolic function

2.4.1 Example 1.mp4

2.4.2 Example 2.mp4

2.4.1 Examples Part 1

2.4.2 Examples Part 2

2.4.3 Examples Part 3

2.4.4 Examples Part 4

2.4.5 Examples Part 5

2.4.6 Examples Part 6

2.4 Properties of Eigen Values

2.5 Procedures to find Eigen Values & Eigen Vectors

2.5.1 Example 1

2.5.2 Example 2

2.5.3 Example 3

2.5.4 Example 4

2.5.5 Example 5

2.5.6 Example 6

2.6 Relation between Eigen Values & Eigen Vectors

2.7 Relation between Eigen Values & Matrix

2.7.1 Thoerems on Eigen Vectors

2.8 Cayley Hamilton Theorem Introduction

2.8.1 Example 1

2.8.2 Example 2

2.8.3 Example 3

2.9 similarity of Matrices

2.10 Algebraic & Geoetric Multiplicity

2.11 Modal Matrix & Diagonalising Matrix Introduction

2.11.1 Example 1

2.11.2 Example 2

2.11.3 Example 3

2.12 Function of Square Matrix

2.12.1 Example 1

3. Vectors Introduction & Application.mp4

3.1 Vectors Basic

3.1.1 Partial Differentiation

3.2 Curves Spaces & Point Function

3.2.1 Partial Derivative of the first order

3.2.1 Partial Derivative of the first order

3.2.2 Example 1

3.2.3 Example 2

3.3.1 Partial Derivative of Higher order

3.3.2 Partial Derivatives of some standard functions

3.3.3 Partial differentiation using standard rules with Examples

3.4.1 Differentiation of a function of function Some standard functions of the type Z=fu

3.5.1 Partial derivatives of first order of a function of a function

3.6.1 Partial Derivatives of second order of a function of a function

3.7.1 Examples satisfying Laplace equation

3.8.1 variable to be treated as constant

3.8.2 Example 1

3.8.3 Example 2

3.8.4 Example 3

3.9.1 Composite functions

3.9.2 Example 1 on composite functions

3.9.3 Example 2 on composite functions

3.10.1 Partial Differentiation of Composite functions

3.10.2 Example 1

3.10.3 Example 2 on Partial Differentiation

3.10.4 Example 3 on Partial Differntiation of composite functions

3.11.1 Homogenous functions

3.12.1 Euler's Theorem

3.12.2 Example 1 on Euler's Theorem

3.12.3 Example 2

3.12.4 Example 3 on Euler's Theorem

4.1.1 Applications of partial differentiation & Successive Differentiation

4.2.1 Method of finding maxima & minima

4.2.2 Example 1 on maxima & Minima

4.2.3 Example 2 on maxima & Minima

4.3.1 Lagrange's Method of undetermined multipliers

4.3.2 Procedure of Lagrange's Method Step 1 & 2

4.3.3 Example 1 on lagrange's method

4.3.4 Example 2 on lagrange's method

4.4.1 Successive Differentiation

4.5.1 Derivative of nth order

4.5.2 Example 1,2 & 3

4.6.1 Leibtniz's Theorem

4.6.2 Example 1

4.6.3 Example 2

4.6.4 Example 3

4.6.5 Example 4

5 Matrices

5.1.2 Singular Matrix

5.1.3 Symmetric Matrix

5.1.4 Skew Symmetric Matrix

5.1.5 Hermitian Matrix

5.1.6 Skew Hermitian Matrix

5.2.1 Operation of Matrices

5.3 Properties of Matrices

5.4 if A & B are Symmetric matrix then A is Symmetric

5.5 If A is any square matrix then A+AQ is Hermitian And A AQ is Skew Hermitian

5.5.1 Examples 1 & 2

5.6 Every Square matrix can be uniquely expressed as the sum of Hermitian matrix and Skew Hermitian

5.7 Orthogonal Matrix

5.8.1 Elementary Matrix

5.8.2 Rank of Matrix

5.8.3 Defination of Rank of Matrix

5.8.4 Example 1

5.8.5 Example 2

5.8.6 Example 3

5.8.7 Some important points on Rank of Matrix

5.9.1 Normal Form or Cononical Form

5.9.3 Example 3 on Normal form of Matrix

5.9.4 Rank of Matrix by Normal Form

5.9.5 Reduction of Matrix to PAQ form

5.9.5 Example 4 on Rank of Matrix by Normal Form

5.10.1 system of non Homogenous Linear equation

5.11.1 Solution to system of equation

5.11.2 Echelon form of Matrix

5.12.1 Consistency in Echelon form

5.12.2 Example 1

5.12.3 Example 2

5.12.4 Example 3

5.13.1 homogenous linear equation

5.13 2 Example 1 on Homogeneous linear equation

5.13.3 Example 2 on homogenous linear equation

5.13.4 Example 3 on homogenous linear equation

6. Numerical Solutions of Transcendental & Linear

6.1 Types of Equations

6.2.1 Methods of Solving Equation

6.2.2 Examples on Newton Raphson Method

6.2.3 Examples 2 on Newton Raphson Method

6.2.4 Example 3 on Newton Raphson Method

6.2.5 Example 4 on Newton Raphson Method

6.2.6 Regula Falsi Method

6.2.7 Example 1

6.2.8 Example 2

6.2.9 Example 3

6.2.10 Solution of Linear Algebraic Equation

6.2.11 Example 1 on Gauss Jacobi Iteration method

6.2.12 Example 2 & 3 by Gauss Jacobi Iteration method

6.2.13 Gauss Seidal Method

6.2.14 Example 1 on Gauss Seidal Method

6.2.15 Example 2 on Gauss Seidal method

6.3.1 Expansion of Function

6.3.2 Expansion of hyperbolic Function

6.3.3 Expansion of Some special function

6.3.4 Expansion of function of Power Series

6.3.5 Example 2

6.3.6 Example 3

6.3.7 Example 4, 5, 6, 7 & Example 8

6.3.8 Method of Invarsion with Example

6.3.9 Method of differentiation with Example

6.3.10 Taylor Series with Examples

Practice Session Complex numbers Part 1

Practice Session Complex Number Part 2

Practice Session Complex Numbers Part 3

Practice Session Hyperbolic Functions Part 1

Practice Session Hyperbolic Functions Part 1

Practice Session Hyperbolic Functions Part 2

Practice Session Hyperbolic Functions Part 3

Practice Session logorithmic functions Part 3

Practice Session Logorithmic Functions Part 1

Practice Session Logorithmic Functions Part 2

Practice Session Partial Differentiation & Applicatio

Practice Session Partial Differentiation & Application

Revision of Expansions of Function

Revision of Matrices with Examples

Revision of Numerical Method with Examples Part 1

Revision of Numerical Method with Examples Part 2

Revision of Numerical Method with Examples Part 3