BGU Physics Department
Mathematical Methods in Physics
(3.5 points, 4 hours)
Links
Syllabus
- Review of solution methods of ODE’s
- Separable equations, Integrating factors, Homogeneous equations
- Clairot, Ricatti & Bernoulli equations
- Qualitative difference between linear and nonlinear ODE’s
- The Wronskian
- Boundary value problems
- Green’s function
- Eigenvalue problems (Sturm-Liouville problem)
- Approximation methods
- Approximation of integrals - Steepest descent
- Approximation for solving boundary problems - WKB
- Solving linear equations with small nonlinearities
- (Poincare-Lindstedt, Multiple time scales)
- Review of solution methods for linear PDE’s
- Diffusion equation: Separation of variables, Green’s function
- Self-similar solutions and Green’s function
- Basic notions on continuous groups
- Pauli matrices, SU(2), SU(3)
- Rotation group
- Simple examples of discrete groups
- Fundamentals of integral equations
- Basic notions on fractals
Sources:
- Wilf, Mathematics for the Physical Sciences (Dover)
- Kahn, Mathematical Methods for Scientists and Engineers (Wiley)
- Byron & Fuller, Mathematical Methods of Classical &
Quantum Physics (Dover)
- Mathews & Walker, Mathematical Methods (Addison-Wesley)
- Bender & Orszag, Advanced Mathematical Methods for Scientists
& Engineers (McGraw-Hill)
- Arfken & Weber, Mathematical Methods for Physicists (Academic
Press)
- Collins- Mathematical Methods for Physicists and engineers (Dover)
- Ince - Ordinary Differential Equations (Dover)
- King & Billingham - Differential Equations (Cambridge)
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