Introduction scientific computing

Course goals

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Content

This course provides an introduction to Scientific Computing through case studies from various application areas. The entire Scientific Computing process is covered, from mathematical modeling to visualizing the numerical solution (simulation) via discretization, algebraic solution techniques, and implementation. The focus is on commonly used techniques in Numerical Mathematics, both for simulating differential equations and processing data from a CT scanner. Both theoretical and practical, software-related aspects are addressed.

The course consists of two modules (differential equations and CT scans), which are assessed separately and together determine the final grade.

This course serves as a solid orientation for a potential Master's specialization in Scientific Computing and offers a broad perspective on the field. "Introduction to Scientific Computing" is one of the modeling courses, of which mathematics students must choose at least one. For more information about the study paths, consult the student website.

Skills:
The student will learn:

• The theory behind various widely used numerical methods for (fractional) differential equations, systems of equations, and discrete Fourier transforms.
• That Scientific Computing employs techniques from Numerical Mathematics (analysis and algebra), Computer Science, and the application domain, and that optimizing performance in solution methods requires knowledge of these fields. Specifically, students will realize that Scientific Computing in professional practice is teamwork, but effective communication within the team requires knowledge of all disciplines.
• That designing a well-performing solution method often requires complementing theoretical analysis with targeted numerical experiments.
• To understand modeling arguments and apply them to problems related to the course material.
• To adopt a critical attitude toward their own numerical experimental results.
• To code the numerical solution method in a structured program.
• To write a clear and concise report based on given assignments, focusing on justified choices for the numerical solution method and conducting numerical experiments within the context of the application domain (including modeling and coding).

Format of the course:
There are two two-hour lectures and two two-hour tutorials each week.

Final grade:
Two reports (one per module), each contributing equally to the final grade, determine the course grade. Each report must achieve a minimum grade of 5, and the rounded final grade must be at least a 6. Reports may be written in collaboration with (at most) one fellow student, but each student is individually responsible for the entire report. Reports may be discussed individually, which could influence the grade.

Retake and participation obligation:
Students with a final grade of 4 or 5, or those who do not meet the stated criteria, may retake the course. The retake consists of improving one of the two reports within three weeks after determining the course’s final grade.

Students with a final grade lower than 4 can only participate in the retake if they meet the course participation requirement, which entails: attending at least half of the course sessions (per module) and submitting at least one report graded at a minimum of 5.

Language:
Dutch, though the course can also be taught in English if international participants are present. All information and course materials are available in English, as specified on the course website.