The exhaustive list of topics in Numerical Methods in which we provide Help with Homework Assignment and Help with Project is as follows:
- Ordinary differential equation - initial value problems (ODE-IVP) and numerical integration
- Multiple minima
- Singular value decomposition (SVD)
- Implicit ordinary differential equation (ODE) solvers
- Function space vs. real space methods for partial differential equations (PDEs)
- Modeling intrinsically stochastic processes
- Uncertainties in model predictions
- Function space
- Eigenvalues and eigenvectors
- Strang splitting
- Matrix factorization
- Solving systems of linear equations
- MATLAB® ordinary differential equation (ODE) solvers
- Shooting
- Differential algebraic equations (DAEs)
- Constructing and using the eigenvector basis
- Modern methods for solving nonlinear equations
- Operator splitting
- Using MATLAB® to evaluate and plot expressions
- Modularization
- Optimization
- Kinetic Monte Carlo and turbulence modeling
- Multiscale modeling
- Stiffness
- Global optimization
- Models vs. Data recapitulation
- Numerical calculation of eigenvalues and eigenvectors
- Boundary value problems (BVPs)
- Optimization
- Fourier transforms
- Sensitivity analysis
- Systems of nonlinear equations
- Fast fourier transform (FFT)
- Constrained optimization
- Fluctuation-dissipation theorem
- Unconstrained optimization
- Numerical error, ill-conditioning, and tolerances
- Monte Carlo and molecular dynamics