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SDS 401: Mathematical Modeling and Algorithms

Course Title

Mathematical Modeling and Algorithms 

Course Code

SDS 401

Course Type

Mandatory

Level

Master’s

Year / Semester

1st / 1st (subject to change)

Instructor’s Name

Yury Suleymanov

ECTS

10

Lectures / week

1 (2h)

Laboratories / week

1 (1h)

Course Purpose and Objectives

Introduce mathematical tools and algorithms used in computational sciences focusing on methods used in numerical simulation and data analysis. 

Learning Outcomes

The course will equip students with core techniques behind efficient methods to find numerical solutions to differential equations, iterative techniques to solve large, sparse linear systems, introduce modeling of real systems via partial differential equations and how to solve them numerically using examples from physical science and engineering domains.  

Prerequisites

None

 Requirements  -

Course Content

Linear algebra review, numerical differentiation and integration of functions, direct methods for linear system, nonlinear sets of equations, polynomial interpolation and extrapolation, sorting algorithms, fast Fourier transform. Introduction to the theory of partial differential equations (PDEs), and methods of solving linear and non-linear PDEs. Students will also learn how to solve equations that come from the world of physics and other sciences. 

Teaching Methodology

Lectures, exercises where numerical recipies will be examined.

Bibliography

Uri Ascher and Chen Greif, “A First Course in Numerical Methods”, SIAM, 2011. H. Gould, J. Tobochnik and W. Christian, “An introduction to Computer Simulation Methods: Applications to Physical Systems”, fairly basic level but covers a lot of ground.

Assessment

25% coursework, 75% exam

Language

English