MP11 · Asymptotics & advanced methods
A 36-module path through mp11 · asymptotics & advanced methods, in study order from foundations to the frontier.
Modules
- Asymptotic Series and Poincaré Expansions
- Order Symbols and Gauge Functions
- Watson's Lemma
- Laplace's Method for Integrals
- Method of Stationary Phase
- Method of Steepest Descent and Saddle Points
- Stokes Phenomenon and Anti-Stokes Lines
- Optimal Truncation and Superasymptotics
- Borel Summation and Resurgence
- WKB Approximation
- Connection Formulae and Turning Points
- Bohr–Sommerfeld Quantization
- Regular Perturbation Theory
- Singular Perturbation Theory
- Method of Matched Asymptotic Expansions
- Boundary Layer Theory
- Method of Multiple Scales
- Poincaré–Lindstedt Method
- WKB and Averaging for Slowly Varying Systems
- Fredholm Integral Equations
- Volterra Integral Equations
- Fredholm Theory and Fredholm Alternative
- Neumann Series and Resolvent Kernel
- Separable and Degenerate Kernels
- Symmetric Kernels and Mercer's Theorem
- Green's Functions for Ordinary Differential Equations
- Green's Functions for Partial Differential Equations
- Method of Images and Eigenfunction Expansions of Green's Functions
- Causal, Retarded, and Advanced Green's Functions
- Sturm–Liouville Green's Functions and Completeness
- Introduction to Numerical Methods
- Numerical Quadrature
- Root-Finding and Iterative Methods
- Numerical Solution of Ordinary Differential Equations
- Finite Difference Methods for PDEs
- Stability, Consistency, and Convergence of Numerical Schemes