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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