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UCSCIMAT217.5 ECTSEnglishBachelor

Mathematical Methods

Faculteit—
NiveauBachelor
Studiejaar2026-2027

Beschrijving

Course goals

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

Content

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.

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