Mathematics: Calculus of Variations

This course introduces you to the calculus of variations — a branch of mathematics that helps solve problems where you want to find the best possible outcome, such as the shortest path or the most efficient shape. You will explore how small changes can affect a system and how to model these changes mathematically. The course combines theory with practical problem-solving and helps you develop skills in mathematical reasoning, both written and oral.

Course content includes

• Variational problems with and without constraints
• Euler’s equations
• Legendre’s, Jacobi’s and Weierstrass’s conditions for local minima
• Hilbert’s invariant integral
• Hamilton’s principle and equations.

This is an elective course in applied mathematics within the Bachelor’s Programme in Mathematics at Lund University. The course is taught together with students from the engineering programme at LTH and is not offered as a standalone course.

Teaching consists of lectures and compulsory written assignments. You will work with mathematical problems and present your solutions both in writing and orally. The course encourages logical thinking and clear communication using correct mathematical terminology.

Assessment includes written assignments and an oral exam. Re-examinations are offered shortly after the regular ones.

This course gives you tools that are useful in many areas of mathematics, physics, and engineering. It’s especially relevant if you’re interested in optimization, mechanics, or mathematical modelling.

After completing the course, you will be well prepared for further studies in applied mathematics or theoretical physics. The skills you gain are also valuable in research, data analysis, and technical roles where mathematical modelling is key.

Prerequisites

General and at least 60 credits in mathematics, including courses corresponding to MATB22 Mathematics: Linear Algebra 2, 7.5 credits, MATB21 Mathematics: Analysis in Several Variables 1, 7.5 credits, and MATB23 Mathematics: Analysis in Several Variables 2, 7.5 credits.

Selection criteria

Seats are allocated according to: The general average (GPA) of your higher secondary school leaving certificate: 20 %, The Swedish national university aptitude test: 10 %, number of previous ECTS at application deadline (up to 165): 70 %.

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 21,250
First payment: SEK 21,250

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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.