Numerical Methods
Root finding, linear systems, interpolation, numerical integration and ODE solvers.
MATH-300 Year 3 3 credits 5 lessons · 2 h 36 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
Course content
5 lessons · 2 h 36 min total · final exam
- 1 Errors and floating point 34 min · quiz
- 2 Root finding 31 min · quiz
- 3 Solving linear systems 32 min · quiz
- 4 Interpolation and curve fitting 29 min · quiz
- 5 Numerical integration and ODEs 30 min · quiz
- E Final exam 10 questions
Requirements
Recommended background. You can start any course at any time.
Description
Root finding, linear systems, interpolation, numerical integration and ODE solvers.
Part of the Engineering stream, typically taken in year 3.