Methods of applied mathematics
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Methods of Applied Mathematics — scope drawn from open applied methods notes and typical US applied mathematics methods syllabi.
Calculus of variations
- Euler–Lagrange equation — Euler–Lagrange equation
- Variational principles — Variational principles
- Brachistochrone and classical problems — Brachistochrone and classical problems
- Constraints — Constraints
- Lagrange multipliers in variational problems — Lagrange multipliers in variational problems
- Hamilton's principle — Hamilton's principle
- Mechanics (introduction) — Mechanics (introduction)
- Rayleigh–Ritz method (introduction) — Rayleigh–Ritz method (introduction)
Perturbation and asymptotic methods
- Regular perturbation expansions for algebraic equations — Regular perturbation expansions for algebraic equations
- Singular perturbations — Singular perturbations
- Boundary layers (introduction) — Boundary layers (introduction)
- Poincaré–Lindstedt method for weakly nonlinear oscillations — Poincaré–Lindstedt method for weakly nonlinear oscillations
- Multiple scales (overview at undergraduate level) — Multiple scales (overview at undergraduate level)
- Asymptotic matching (introduction) — Asymptotic matching (introduction)
Integral equations and transforms
- Volterra and Fredholm integral equations (introduction) — Volterra and Fredholm integral equations (introduction)
- Green's functions for ODE boundary-value problems — Green's functions for ODE boundary-value problems
- Transform methods for PDEs — Transform methods for PDEs
- Integral representations — Integral representations
- Convolution and superposition principles — Convolution and superposition principles
- Well-posedness — Well-posedness
- Conditioning in applied problems — Conditioning in applied problems
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Calculus of variations
Euler–Lagrange equation
Coming soon - Perturbation and asymptotic methods
Regular perturbation expansions for algebraic equations
Coming soon - Integral equations and transforms
Volterra and Fredholm integral equations (introduction)
Coming soon
Notes
Undergraduate Methods of Applied Mathematics — scope drawn from open applied methods notes and typical US applied mathematics methods syllabi. Topic outline: `content/topics/undergraduate/methods_applied_math.json`.