Standard syllabus
Methods of applied mathematics · Undergraduate · Math
Topics
Calculus of variations
- Euler–Lagrange equation and variational principles
- Brachistochrone and classical problems
- Constraints and Lagrange multipliers in variational problems
- Hamilton's principle and mechanics (introduction)
- Rayleigh–Ritz method (introduction)
Perturbation and asymptotic methods
- Regular perturbation expansions for algebraic equations
- Singular perturbations and boundary layers (introduction)
- Poincaré–Lindstedt method for weakly nonlinear oscillations
- Multiple scales (overview at undergraduate level)
- Asymptotic matching (introduction)
Integral equations and transforms
- Volterra and Fredholm integral equations (introduction)
- Green's functions for ODE boundary-value problems
- Transform methods for PDEs and integral representations
- Convolution and superposition principles
- Well-posedness and conditioning in applied problems
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$1,162 · Methods of applied mathematics · 18 tutoring hrs
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