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## Numerical Methods

2019-2020

### Course Objective

At the end of this course students will be able to ...
... implement the main algorithms of numerical analysis correctly and
efficiently in Matlab.
... perform numerical calculations to solve nonlinear algebraic
problems, eigenvalue problems, interpolation problems, signal processing
and ODEs.
... apply methods from numerical analysis in a scientific setting.
... evaluate the reliability of numerical methods.
... report comprehensively on the structure of her/his algorithms as
well as the computations performed using her/his code.

### Course Content

Numerical methods are used frequently in all areas of science, such as
fluid dynamics, meteorology and financial risk management. Moreover,
techniques from numerical analysis play an important role in
mathematical research on differential equations, stochastics,
optimization, etcetera. We focus on the main numerical methods from
modern-day analysis and scientific computing.

The list of subjects includes:
* error analysis
* systems of nonlinear equations
* eigenvalue problems
* least square methods
* fast Fourier transform
* ordinary (and partial) differential equations (no prerequisites
needed)

Applications include
* phone number recognition
* data analysis
* curve following
* planet motions
* and more.

### Teaching Methods

Lectures (once a week, 1x2=2 hours) and computer labs (once a week,
1x2=2 hours). A number of Matlab assignments form an integral part of
the course.

### Method of Assessment

The final grade is based on a set of reports and computer codes that
have to be handed in. In 2017/18 the weights were as listed below, but
these may be revised for 2018/19. Precise details will be available on
Canvas at the start of the course.

First assignment; two exercises [2 x 4.5 = 9%]
Second assignment; two exercises [2 x 5.5 = 11%]
Third assignment; three exercises [3 x 6.5 = 19.5%]
Fourth assignment; two exercises [2 x 8 = 16%]
Fifth assignment; two exercises [2 x 8 = 16%]
Sixth assignment; three exercises [3 x 9.5 = 28.5%]

Resit opportunities: if the weighted average of the submitted exercises
fails to surpass the necessary 55% needed to pass the course, then there
will be an option of re-submitting inadequate submissions. A
re-submission cannot attain a score greater than 60%.

### Entry Requirements

A basic course in Linear algebra (e.g. X_400041, X_400042, X_400638 or
X_400639) and Multivariable calculus (e.g. XB_41008).

### Literature

There is no mandatory literature.

The following book is recommended for the first half of the course:
Scientific Computing with MATLAB and Octave by Alfio Quarteroni and
Fausto Saleri, ISBN: 978-3642453663

### Target Audience

Bachelor Mathematics year 2

### General Information

Course Code X_401039 6 EC P1+2 300 English Faculty of Science dr. M.B. Botnan dr. M.B. Botnan dr. M.B. Botnan

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

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