Mathematics: Partial Differential Equations

This course gives you a solid foundation in partial differential equations, which are essential in many areas of mathematics, physics, and engineering. You will encounter three classical examples: Laplace’s equation, the heat equation and the wave equation, but also see how their properties can be generalised to wider classes of equations: elliptic, parabolic and hyperbolic. You will also learn tools of wide use, such as energy estimates, Sobolev spaces and maximum principles.

Course content includes

• The method of characteristics and nonlinear equations of the first order.
• Laplace’s equation, the heat equation, and the wave equation.
• The Cauchy-Kowalevski theorem.
• Sobolev spaces and weak solutions.Existence, uniqueness and regularity for weak solutions to linear second order elliptic, parabolic and hyperbolic equations.
• Maximum principles and regularity theory.

The course is alternative-compulsory within the Master’s Programme in Mathematics and Numerical Analysis at Lund University. It is also available as a stand-alone course, and can be taken as an elective course by Bachelor’s students in mathematics.

Teaching consists of lectures and seminars. You will work with both theory and problem-solving, and develop your ability to communicate mathematical reasoning. Assessment includes a written exam and an oral exam at the end of the course. The oral exam is only available to students who pass the written exam. Re-examinations are offered shortly after the regular ones.

Partial differential equations are used in everything from climate models to quantum mechanics. This course prepares you for advanced studies in analysis, applied mathematics, and mathematical physics, and gives you tools that are highly valued in both academia and industry.

Entry requirements

For admission to the course, English 6/B is required as well as at least 90 higher education credits in mathematics, including knowledge equivalent to the courses MATB34 Linear Analysis, 7.5 credits, MATC22 Ordinary Differential Equations 1, 7.5 credits and MATC21 Complex Analysis 1, 7.5 credits. The courses MATM39 Integration Theory, 7.5 credits and MATP35 Linear Functional Analysis, 7.5 credits are recommended but not compulsory.

Selection criteria

Seats are allocated according to: ECTS (HPAV): 100 %.

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 23,125
First payment: SEK 23,125

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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.