Numerical Methods II (88-377)
This is a continuation of the course
Numerical Methods I. The subject matter of the course is as
follows:
-
Integration of ordinary differential equations. Finite difference methods for
initial value problems: basic methods (explicit and implicit, one step and
multistep), order, stability, stiff systems,
convergence, stepsize control, matlab functions. Boundary value and
eigenvalue problems: shooting, finite difference, collocation and finite
element (Galerkin) methods, singular problems.
- Optimization. Unconstrained minimization of functions in one
dimension and in multiple dimensions: steepest descent, Newton's method,
conjugate gradient method. Nonlinear least squares.
Minimization of linear functions with linear constraints (simplex
method).
- Discrete Spectral Methods.
Discrete Fourier transform, inversion, convolution and Parseval theorems.
Fast Fourier transform. Interpolation and decimation of data by spectral
methods. Digital filtering: FIR and IIR approximations for low, high and
band pass filters. Optimal (Wiener) filtering.
- Random numbers and simulation. Random number generators, generation of
random numbers with given distributions, Monte Carlo method for computing
integrals.
Students are expected to be familiar with Matlab
Course technicalities: lecture Thursday 5-6:30pm, targil Wednesday.
The metargelet is Shira Zur.
The exam (open book, 2.5 hours) will comprise 80% of the course
grade, the other 20% will be based on exercises which must be submitted
on time and done individually.
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Useful Stuff
Exercise Sets
Exams
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