SDS 401: Mathematical Modeling and Algorithms
Course Title |
Mathematical Modeling and Algorithms |
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Course Code |
SDS 401 |
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Course Type |
Mandatory |
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Level |
Master’s |
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Year / Semester |
1^{st} / 1^{st} (subject to change) |
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Instructor’s Name |
Nikos Savva |
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ECTS |
10 |
Lectures / week |
1 (2.5h) |
Laboratories / week |
1 (1.5h) |
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Course Purpose and Objectives |
Introduce mathematical tools and algorithms used in computational sciences focusing on methods used in numerical simulation and data analysis. |
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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. |
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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. |
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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. |
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Assessment |
25% coursework, 75% exam |
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Language |
English |