| Lectures | Tuesday 12:00-13:45, Levi 6 Thursday 14:00-14:45, Spr. 25 |
| Exams | |
| Lecturer | Office | Hours | Telephone | |
| Raz Kupferman | Math 303 | by appointment | raz(at)math.huji.ac.il | x 84159 |
This course will provide an introduction to scientific computing (a.k.a numerical
analysis). It will cover classical topics such as the solution of systems of
nonlinear equations, numerical linear algebra, interpolation and extrapolation,
approximation theory, and numerical differentiation and integration. The goal
of this course is to provide elementary tools for constructing and analyzing
numerical algorithms for various mathematical problems.
This course is intended for a wide audience of undergraduate and graduate student in mathematics, physics, computer science, and other disciplines in our faculty.
| Topic | Description |
| Basic concepts | Taylor series, order of convergence |
| Solution of nonlinear equations | Bisection method, Newton's method, secant method, multidimensional Newton's method, fixed point iterations |
| Computer arithmetics | Representation of real numbers, propagation or errors, stability, conditioning number |
| Systems of linear equations | LU decomposition, pivoting, vector and matrix norms, Neumann seires, iterative methods: Jacobi, Gauss-Seidel, general iterative methods, Chebyshev acceleration |
| Interpolation | Lagrange and Newton's representations, error minimization, convergence, divided differences, Hermite interpolation |
| Numerical differentiation | Differentiation at various orders, Richardson's extrapolation |
| Numerical integration | Newton-Cotes, trapezoidal rule, Simpson's rule, Gaussian quadrature |
| Title | Author | Shelf |
| Numerical Analysis | Kincaid and Cheney | 90 Ki |
| Applied Numerical Linear Algebra | James W. Demmel | |
| Introduction to Numerical Analysis | Bulirsch and Stoer | |
| Lecture notes (at your own risk) |
Mandatory (80%)
I will not publish solutions. Students who are uncertain about how to solve exercises should contact me. Students who are uncertain and do not contact me are in trouble....
| Ex # | Due date | Comments | |
| 1 | Nov 2 | ||
| 2 | Nov 9 | 2.6: the function is f(x) =arctan(x) | |
| 3 | Nov 16 | ||
| 4 | Nov 30 | ||
| 5 | Dec 7 | ||
| 6 | Dec 14 | ||
| 7 | Dec 21 | ||
| 8 | Jan 4 | ||
| 9 | Jan 11 | ||
| 10 |