STEM / applied
Methods of applied mathematics · Undergraduate · Math
Learning objectives from the Methods of applied mathematics syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
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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
Learning objectives
Click an objective for study materials.
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
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
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- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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$1,162 · Methods of applied mathematics · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.