Mathematics: Mathematics for Scientists 2

In this course you study functions of several variables and learn how concepts such as continuity, partial derivatives, gradients, directional derivatives and extrema are used to describe and analyse multivariable models. You deepen your understanding of differential and integral calculus in two and three variables and use these methods to solve problems with clear scientific applications.

The course also develops your ability to work with ordinary differential equations and systems of differential equations, where you practise formulating models, analysing their behaviour and independently choosing suitable methods for solving them.

Linear algebra is another central component. You work with the vector space ℝⁿ, linear transformations and their matrix representations, matrices and determinants. You also explore the role of eigenvalues and eigenvectors in understanding dynamical systems, stability and other scientific models.

Throughout the course you integrate theory and application, formulate and solve problems, and strengthen your ability to present mathematical reasoning clearly and coherently.

The course is a compulsory mathematics course at the undergraduate level for the Master’s programme in Applied Computational Science with specialisations in biology, chemistry, geology, environmental science and physical geography. It is also offered as a standalone course.

Teaching consists of lectures and seminars in which you actively engage in problemsolving and present mathematical reasoning orally. The course also includes compulsory computerbased laboratory sessions, where you use digital tools to visualise and analyse concepts from multivariable calculus, linear algebra, and differential equations. These laboratory sessions give you practical experience with how mathematical methods are used to investigate scientific models.

Assessment is based on a written exam worth 12 credits, held at the end of the course, together with the computerbased laboratory assignments worth 3 credits, which are completed during the course. To pass the course, you must obtain a passing grade on both the written exam and the laboratory assignments. The grading scale comprises Fail, Pass, and Pass with Distinction, and the final course grade is determined by the result of the written exam.

After completing the course, you will master key methods in multivariable calculus and linear algebra and be able to use them to investigate and model complex natural processes. You will have developed the ability to formulate mathematical models, choose appropriate analytical methods, and present your solutions both orally and in writing using correct mathematical terminology. The course provides an essential foundation for further studies in applied computational science, biology, chemistry, environmental science, geology, and physical geography, and strengthens your analytical skills for more advanced courses and projects.

Prerequisites

To be admitted to the course, students must have 15 credits in mathematics, or knowledge equivalent to the course MATA03 Mathematics for scientists 1, 15 credits, as well as English 6/B.

Selection criteria

Seats are allocated according to the following: The general average (GPA) of your higher secondary school leaving certificate: 34 %, The Swedish national university aptitude test: 34 %, number of previous ECTS at the application deadline (up to 165): 32 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 46,250
First payment: SEK 46,250

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.