Single-Course English 5 ECTS

Applied mathematics for physicists

Overall Course Objectives

To introduce concepts, tools and methods from applied mathematics to technical physics students.

Learning Objectives

  • Determine whether an operator and an equation is linear or nonlinear and understand the difference between the two types.
  • Solve linear partial differential equations with Fourier transformation and understand the relation between a function and its Fourier spectrum.
  • Solve linear ordinary differential equations with Green’s function.
  • Derive the properties of Sturm-Liouville operators and Sturm-Liouville eigenvalue problems.
  • Solve linear partial differential equations using separation of variables.
  • Solve singular linear ordinary differential equations using Frobenius’ method.
  • Know Bessel’s equations and be able to use Bessel functions.
  • Derive the Euler-Lagrange equations and understand the concept of calculus of variations and Hamilton’s Principle for multi-dimensional systems with several variables.
  • Apply the Rayleigh-Ritz variational technique to find ground state eigenfunctions and eigenvalues.
  • Apply the collective coordinate variational approach to find and analyse solutions to nonlinear partial differential equations.

Course Content

Fourier transformation and general integral transformations. Sturm-Liouville problems and special functions. Bessel functions. Green’s function. Calculus of variations.

In the 4 larger projects you will use the techniques you have learned to analyse Bose-Einstein Condensates, optical fibers, electromagnetic wave propagation, nonlinear crystals, laser beams, and free electrons.

Recommended prerequisites


Teaching Method

13 morning sessions (8-12) beginning with 3 lectures (of 35 minutes each) and group work (2 hours) about 4 projects.


Arfken & Weber: Mathematical Methods for Physicists, 6th Ed., Elsevier.

See course in the course database.





13 weeks




DTU Lyngby Campus

Course code 34031
Course type Bachelor
Semester start Week 5
Semester end Week 19
Days Tues 8-12

7.500,00 DKK