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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