A good grasp of calculus, differential equations and linear algebra is required to fully enjoy it.
The topics covered are:
- Series expansions: from calculus to computation
- Integrals as sums and derivatives as differences
- Interpolation, splines, and a second look at numerical calculus
- Numerical methods for ODE, initial-value problems
- Root finding, Newton's method, boundary-value problems
- Fourier transform, Fourier series, Shannon sampling theory
- Bandlimited interpolation, spectral methods
- Least-squares approximation
- Principal component analysis
Numerical Analysis is the underpinning of modelisation and simulation , at the heart of modern physics and engineering fields.