Mathematical Methods

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Cursusdoel

After completing this course students are able to:
  1. Solve partial differential equations using Fourier analysis.
  2. Apply mathematical techniques to the study of physical problems such as wave and heat propagation.
  3. Use polar and cylindrical coordinates to treat such problems.
  4. Define and apply basic concepts of real analysis such as continuity, differentiability, and uniform and nonuniform convergence.
  5. Prove and apply basic theoretical results of Fourier analysis using concepts of linear algebra as well as real analysis.
Relationship between assessment and learning goals:
  1. Assignments: 1, 2, 3, 4, 5
  2. Mid term exam: 1, 2, 3, 4, 5
  3. Final exam: 1, 2, 3, 4, 5

Vakinhoudelijk

Mathematics is at the same time a conceptual framework, a collection of proven theorems, and a toolbox. In this course, the student encounters all three of these aspects by studying one of the central mathematical issues for applications in science and engineering. The general topic of the course is the solution of linear partial differential equations using separation of variables, Fourier series and Fourier transforms. The study will involve both computational and rigorous mathematical aspects. While the actual computation of solutions is the main objective, the student will also learn the mathematical theorems establishing the validity and limitation of the different methods. Interested students will also be offered the possibility to experiment numerical approaches.
Format
In addition to the contact hours, each student is expected to work nine hours a week on the course. This time should be devoted to:
  • reviewing the material of the preceding lecture;
  • finishing the exercises started in the preceding problem session;
  • preparing exercises to hand in;
  • studying the corrections of the previously returned hand-in problems, making sure everything is clear.

Werkvormen

UCU SCI 2 course

Toetsing

Hand-in assignments

Verplicht | Weging 30% | ECTS 2,25

*midterm FEEDBACK*

Niet verplicht

mid term exam

Verplicht | Weging 30% | ECTS 2,25

Final exam

Verplicht | Weging 40% | ECTS 3

Ingangseisen en voorkennis

Ingangseisen

Er moet voldaan zijn aan de cursus:

Voorkennis

Er is geen informatie over benodigde voorkennis bekend.

Voertalen

  • Engels

Cursusmomenten

Gerelateerde studies

Tentamens

Er is geen tentamenrooster beschikbaar voor deze cursus

Verplicht materiaal

Materiaal Omschrijving
BOEK Partial Differential Equations with Fourier Series and Boundary Value Problems, Nakhle H. Asmar, Third Edition, Dover Books on Mathematics, 2016, ISBN 978-0486807379

Aanbevolen materiaal

Er is geen informatie over de aanbevolen literatuur bekend

Coördinator

dr. V.N.E. Blasjö v.n.e.blasjo@uu.nl

Docenten

prof. dr. ir. J.E. Frank j.e.frank@uu.nl

Inschrijving

Let op: deze cursus is niet toegankelijk voor studenten van andere faculteiten, bijvakkers mogen zich dus niet inschrijven.

Naar OSIRIS-inschrijvingen
Permanente link naar de cursuspagina
Laat in de Cursus-Catalogus zien