Poisson’s Identity. Jacobi-Poisson Theorem and calculus of variation
Euler’s equation for one dependent function and its
generalization to (1) ‘n’ dependent functions, (ii) higher order
Brachistochrone problem, Isoperimetric problem and Geodesics
Brachistochrone problem, Isoperimetric problem and Geodesics_1
Brachistochrone problem, Isoperimetric problem and Geodesics_2
Mean Value Formulas for Laplace equation
Uniqueness and smoothness of Mean value formula and Liouville's theorem
Estimates on derivatives and Harnack's inequality
Analyticity, Derivation of Green's function
Symmetry of Green's function, Poisson formula for half space
Green,s function for half space
Green's funtion for the unit ball
Energy Methods and Dirichlet's principle
Heat Equation-Fundamental Solution, Mean Value Formula
Solution of initial value problem, Solution of non-homogeneous problem
Maximum principle for the heat equation and Maximum principle for Cauchy problem
Euler Poisson Durboux equation
Some quastion of attraction of a rod
Introduction to classical Mechanics
Hamilton's Principle from Lagrange's equation
Hamilton's canonical equation using Hamilton's Principle
Poincare Cartan integral invariant
Whittaker's equation and Jacobi's equation
The universal integral invariant of poincare and Lee Hwa Chung theorem
Properties of Generating Functions
Properties of Generating Functions_1
Properties of Generating Functions_2
Method of separation of variables
Invariance of Lagranges brackets and Poisson brackets under canonical transformations
Compatibility condition on boundary data
Hamilton Jacobi equations and Euler Lagrange equation
Convex duality on Hamiltonian and Lagrangian , Hopf-Lax Formula
A functional identity and Lipschitz continuity
Conservation Laws, Shock waves , LaxOleinik formula and Riemann’s Problem
Conservation Laws, Shock waves , LaxOleinik formula and Riemann’s Problem_1
Conservation Laws, Shock waves , LaxOleinik formula and Riemann’s Problem_2
Plane and Travelling Waves, Solitons
Applications of Fourier transform
Applications of Fourier transform_2
Laplace Transform, Hopf-Cole Transform
Geometric, Optics, Stationary Phase