Mathematical Methods in Physics

| Subject classification: this is a physics resource.

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| Subject classification: this is a mathematics resource.

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## Content

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### Second order differential equations

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1. Introduction to 2nd order differential equations
2. Solution of homogeneous equations with constant coefficients
3. Solution of inhomogeneous equations with constant coefficients
4. Singularities and series solutions
5. Frobenius method

### Special functions

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1. Cylindrical and spherical coordinates
2. Boundary value problems
3. Sturm-Liouville problem
4. Legendre polynomials
5. Bessel functions
6. Associated Legendre functions
7. Spherical harmonics
8. Neumann functions
9. Modified Bessel functions
10. Fourier-Legendre series
11. Asymptotic behaviors of certain special functions

### Complex functions

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1. Complex numbers
2. Basic operations with complex functions, analytic functions
3. Cauchy theorem
4. Singularities
5. Taylor and Laurent series
6. Residue theorem and applications
7. Complex functions

### Partial differential equations

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1. General definition
2. Separation of variables method
3. Wave equation
4. Laplace and Poisson equations
5. Diffusion equation
6. Helmholtz equation
7. Continuum eigenvalue spectrum

### Green functions

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1. For Sturm-Liouville operators
2. For 2 dimensions
3. For initial value problems
4. For boundary value problems
5. Solution of higher-order differential equations
6. Reduction to canonical form

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