Mathematical Methods for Physics pdf hand written notes for BS, MSc and Mphil METHODS OF MATHEMATICAL PHYSICS COMPLETE HNAD WRITTEN NOTES | MMP COMPLETE NOTES TOPICS,EXAMPLES,PROBLEMS SOLUTIONS PDF MMP notes

Mathematical Methods for Physics pdf hand written  notes for BS, MSc and Mphil  

 METHODS OF MATHEMATICAL PHYSICS COMPLETE HNAD WRITTEN NOTES | MMP COMPLETE NOTES TOPICS,EXAMPLES,PROBLEMS SOLUTIONS PDF

MMP notes

TOPICS COVERED IN GIVEN PDF

 

Linear and non-linear differential equation

·        . Non-linear ODE’s

·         .Solutions of ODE’s

·         .Explicit solution

·         .Implicit solution

·         .Non-linear ODE’s

·         .Riccati’s equation

 

Physical application of non-linear differential equation          

Ø  .Simple  Harmonic

Ø  .Pendulum

Ø  .Free- fall

  

                                       

Factoring left members

C-discrimenant

P-discrimenant

Envelops

Eliminating the dependant variable

Clairaut’s Equation

 

Some  non-linear ODE’s

·      .   Dependent  variable missing

·       .  Independent  variable absent

.   Bernouli’s   Equation

·       .  Riccati’s  Equation

 

                   

Transformations

 

Solution of homogeneous Riccati  equation

Solution of general Riccati equation

Relationship between Riccati and 2nd order ODE’s and its reverse

 Riccati equation

Applications

 

Solution of Riccati’s  equation

Special forms of Riccati’s equation

Power series solution of special form of Riccati equation

Relation with Bessel ‘s function

Bessel’s Equation

    

 

Elliptical  Integrals  and  Elliptical  Functions

Special case Jacobi canonical form

§    Elliptic Integrals of 1st kind (or Legendre elliptic integral )

§    2nd type

§    3rd type

Expansion of   K and  E

 

Applications of Elliptic integral

Arc length

Hypergeometric Equations and Functions

 Expansion of elliptic integral of 1st and 2nd type

 

Reduction formula

Elliptic Functions

Relationship between weierstrass function and Jacobi elliptic  (S_n) function

The Lane-Emden Equation

Simple Pendulum

Duffing’s Equation

Pinney’s Equation

 

Approximation Methods

Perturbation solution of non-linear ODE

Duffing’s equation

Non-linear  Oscillator

 

Bogoliubov-Krylou  Method  (How to remove secular terms in a given problems)

 

Linear partial differential equations

Boundary conditions

1.       Dirichlet boundary condition

2.       Neumann boundary condition

3.       Robbin condition

 

Types of PDE’s

·         Hyperbolic equation

·         Parabolic equation

·         Elliptic equation

 

Solution of PDE’s

 

Classical Partial Differential Equations

·         Heat equation

·         Wave equation

·         Laplace equation

                                                     

Initial  conditions (IC’s)

Boundary condition (BC’s)

Non-homogeneous boundary value problems

Orthogonal Series Expansion

Boundary value problems in other coordinate systems

 

and topics related examples and problems solutions

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