Numerical Methods

Errors, root finding, linear systems, eigenvalues, fitting, optimization, ODE and PDE solvers and an introduction to finite elements.

MATH-300 Year 3 3 credits 12 lessons · 5 h 49 min

Offered by HSM University · Engineering Core

What you'll learn

Quantify absolute and relative error, explain floating-point representation, and avoid cancellation and step-size pitfalls
Find roots with bisection, fixed-point, Newton, secant and Brent's methods, and judge their convergence and failure modes
Solve linear systems with pivoted Gaussian elimination, LU factorization and iterative methods, and interpret condition numbers
Interpolate tabulated data with polynomials and splines, and fit linear and nonlinear models by least squares without overfitting
Integrate functions and data numerically, and solve ordinary differential equations with Runge–Kutta and implicit methods, recognising stiffness
Compute eigenvalues and eigenvectors with power, inverse and shifted iteration, and explain how library and sparse eigensolvers work
Minimize functions with golden-section, quasi-Newton and derivative-free methods, fit nonlinear models, and solve linear programs
Choose and control adaptive, implicit and symplectic ODE solvers, setting tolerances and detecting events
Solve boundary value problems by shooting and finite differences, including nonlinear and eigenvalue problems
Solve heat, wave and Poisson equations by finite differences, and analyze stability with von Neumann and CFL conditions
Formulate and solve one-dimensional finite element models, and use finite element software responsibly
Combine numerical methods with verification and uncertainty analysis to solve engineering problems

12 lessons · 5 h 49 min total · final exam

Recommended background. You can start any course at any time.

Errors, root finding, linear systems, eigenvalues, fitting, optimization, ODE and PDE solvers and an introduction to finite elements.

Part of the Engineering stream, typically taken in year 3.