Mathematics: Ordinary Differential Equations 2

This course deepens your understanding of ordinary differential equations and how they are used to solve real-world problems in science and engineering. You will explore what happens when we step out in the complex plane and replace the usual derivative by a complex derivative. This allows you to solve equations involving singularities, which frequently appear in applications. You will see examples of special functions, which can be defined as solutions to such equations. You will also study boundary value problems and eigenfunction expansions. These generalisations of Fourier series are for example useful for solving partial differential equations. The theory from the first part of the course allows you to tackle more complicated equations, of relevance in other sciences such as quantum mechanics.

Course content includes

• Linear systems of ordinary differential equations in the complex plane. Power series solutions
• Singular points, Frobenius method
• Some classical differential equations and special functions
• Boundary value problems, Eigenfunction expansions, The spectral theorem
• Sturm-Liouville 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 compulsory assignment, a written exam and an oral exam. The oral exam is only given for students who pass the written exam. Re-examinations are offered shortly after the regular ones.

This course prepares you for advanced studies in mathematics, science, and engineering. The skills you gain, from solving complex problems to communicating mathematical ideas, are valuable in both academic research and industry. You will also build a strong foundation for roles that involve mathematical modelling and analysis.

Entry requirements

For admission to the course, English 6/B is required, as well as at least 90 credits in mathematics, or at least 60 credits mathematics and 90 credits physics, including knowledge equivalent to the courses MATC22 Ordinary Differential Equations 1, 7.5 credits and MATC21 Analytic Functions 1, 7.5 credits.

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.