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Kies de Nederlandse taal
Course module: 191506001
191506001
Mathematical Methods
Course infoSchedule
Course module191506001
Credits (ECTS)5
Course typeCourse
Language of instructionEnglish
Contact persondr. H.G.E. Meijer
E-mailh.g.e.meijer@utwente.nl
Lecturer(s)
Examiner
dr. H.G.E. Meijer
Contactperson for the course
dr. H.G.E. Meijer
Lecturer
dr. M. Schlottbom
Academic year2021
Starting block
1B
Application procedureYou apply via OSIRIS Student
Registration using OSIRISYes
Aims
After this course, the student is able to
1. find roots of nonlinear functions;
2. linearize near equilibria of an ODE and classify equilibria using eigenvalues;
3. simulate deterministic and stochastic ODEs as well as perform quadrature;
4. to construct solutions of second order PDE’s equation using Fourier series or finite differences;
5. assess accuracy of results from algorithms using numerical error analysis;
6. choose or modify algorithms for new numerical problems.
The understanding of scientific models and solving complicated engineering problems requires the correct use of programming and mathematical algorithms. Typical problems involve numerical solutions of nonlinear equations, simulations of dynamical systems, stability via eigenvalues, finite-dimensional approximations of spatial systems by discretisation or Fourier analysis. The art is not just to be able to solve such problems but also to have an intuition for the accuracy of the solution. We will develop some analytical insight, derive several algorithms and discuss error analysis.
 
During the bachelor study, an engineering student learns several mathematical methods through a number of calculus and linear algebra courses. Starting from this bachelor level, this course has three aims:
1. Refresh and enrich the students' knowledge on calculus, linear algebra, and Fourier analysis,
2. Expose the student to other areas such as numerical analysis and mathematical algorithms, and stochastic and partial differential equations,
3. Practising programming using Matlab with emphasis on efficiency and correctness. After this course the student has the ability to efficiently simulate and analyse models given by differential equations. In a more complicated setting, the student will be able to choose and adopt a method for an application.

The course consists of lectures providing an intuition to the mathematical methods. A few tutorials focus on Matlab programming. The homework problems deal with applications in neuroscience and biomedical engineering.
 
Participating study
Master Technical Medicine
Participating study
Master Biomedical Engineering
Required materials
-
Recommended materials
Course material
Lecture notes via Canvas
Course material
Advanced Engineering Mathematics. Erwin Kreyszig. Wiley. 2011 (10th edition).
Instructional modes
Lecture

Practical

Tests
Written exam, Take-home assignment

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Kies de Nederlandse taal