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Mathematics for Physics II - Coggle Diagram
Mathematics for Physics II
Master and Fokker Plank Equations
Stochastic Differential Equations
Lagrange Multipliers
Optimisation Problems
Maximum Entropy Distributions
Fisher Information
Cramer - Rao Lower Bound
Eigen treatment of ODE's
Eigenvalues, Eigenvectors and Diagonalisation of a Matrix
Solving Systems of 1st order ODEs as an eigenvalue problem
Solving systems of 2nd order ODEs as an Eigenvalue problem
Complex Analysis
Open and Closed Sets
Transformations of Objects from z plane to w plane
Limits and Continuity
Complex Exponential and Trigonometric Functions
Evaluating Logarithms and Complex Powers
Differentiability (Holomorphic, Entire functions) and CR equations
Integration (Cauchy, alternate functions, residue thm)
Partial Differential Equations
Classification of 2nd Order Linear PDE's
Changing Variables
D'Alembert's Solution
Linearisation of Nonlinear PDEs about a constant state
Dispersion Relation, dispersive and non dispersive equations
Phase and Group Velocities
Travelling Wave Solutions
Fourier Transforms and Green Functions
Finding Fourier Transforms
Solving ODE's and PDE's via Fourier Transforms
Green's Function