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Essential Graduate Math


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Aims and Objectives

  • The aim of this course is to provide a basis for the mathematics required during the PhD studies in physics by revise several subfields of mathematics.
  • You should have a solid basis for further study if needed for your specific PhD project.
  • It is NOT the aim to replace or reiterate all mathematics taught on the undergraduate level.

  • To approach this general aim, the following subjects will be reviewed:
    • Basic calculus (differentiation & integration)
    • (nonlinear) Ordinary differential equations
    • Approximate solutions to ODEs
    • Special functions
    • Distributions in physics
    • Vector spaces and tensor algebra
    • Functions of complex variables
    • Contour integration
    • Partial differential equations

  • After the course you have have a good understanding of the subjects above.


  • The course is meant as a guide to self-study.
  • Weekly problem sheets will be given on Mondays (or earlier)
  • Answers should be returned by Thursday to Dirk Gericke
  • Problems with the problems given can be discussed Thursday 15:30-16:30

Problem Sheets

  • problem sheet 1
  • problem sheet 2
  • problem sheet 3
  • problem sheet 3a
  • problem sheet 4
  • problem sheet 5
  • problem sheet 6
  • problem sheet 7

  • book list