Applied Mathematics

Wat kun je straks?

Basic linear algebra, basis calculus, basic statistics and basic fourier analysis.

Inhoud

On completion of this module, you should be able to:

Basic Linear algebra:

1. Understand algebraic and geometric representations of vectors and typical operations.
2. Formulate, solve, apply, and interpret properties of linear systems.
3. Apply and use matrix algebra and properties and reflect on its interpretation.
4. Understand the relationship between a linear transformation and its matrix representation.
5. Find the eigenvalues and eigenvectors of a matrix.

Basic Calculus:

1. Demonstrate a mastery of the fundamental concepts of calculus, including functions, limits, derivatives, and integrals.
2. Apply differentiation techniques to solve a wide range of problems, including optimization, analysis of the behaviour of functions and curve sketching.
3. Use differentiation to solve real world problems in fields such as physics, and engineering.
4. Understand how differential equations are used to model real-world and quantum problems and to apply them in solving these problems.

Basic Statistics:

1. Apply the principles of statistical analysis and probability theory as they apply to quantum phenomena.

Basic Fourier analysis:

1. Understanding and applying the properties and operations of complex numbers, solve complex equations, and utilize complex numbers in various mathematical and scientific contexts.
2. Understanding and applying the concepts of Fourier series, Fourier transforms, and frequency analysis to analyse and manipulate signals in both time and frequency domains.

Programma

This course consists of a lecture part, followed by two seminar (exercise classes) where we jointly work on typical problems. The weekly lecture consists of 2 hours being flipped classroom. In a flipped classroom, you watch pre-recorded lectures and read the background material on the subject matter before class, and then engage in collaborative and interactive activities during class time. The weekly seminars (exercise classes) consist of 2 hours each where selected problems will be discussed among all, students and lecturer.

We recommend you to make pro-actively use of the solutions manual as it can provide several benefits studying in various subjects, particularly in fields like mathematics, physics, and engineering.

It's important to note that while solutions manuals can be highly beneficial, they should be used as a supplementary resource rather than a replacement for active learning and engagement with course materials.

A mock exam just before the final assessment in week 10 will be offered in order to prepare you for your exam. The module duration is 6 weeks and holds a typical workload between 5 and 10 hours per week, depending on preknowledge of your previous study. Note that there might be a significant variation across students and the above numbers are a very rough indication. You should nevertheless count on investing time in keeping up with the lectures since the tempo of instruction is relatively high.

Afronding

The assessment of this course consists of one final assessment, the written exam with a grade on scale 1-10. To pass the course, a grade of at least 5.5 is required. A retake opportunity is offered.

Praktische informatie

Do you have any questions? If so, please get in touch at [email protected].

Start 31 August 2026

This course will take 10 weeks.

Toelating en aanmelden

There will be an intake in advance. You need to know the basics of mathematics.

• 2 hours per week lecture
• 4 hours per week seminar
• 100 hours self-study