The course covers selected mathematical topics encountered in materials modelling and in related courses on quantum mechanics, statistical mechanics, thermodynamics and transport phenomena. The course will enable students to solve specific problems in integral and differential calculus and linear algebra that appear in physics and materials science and to understand common mathematical concepts in these fields.
The discussed topics include:
  • Complex analysis (functions of complex variable, Cauchy’s and residue theorem)
  • Analytic functions and their use in evaluation of definite integrals
  • Vectors and matrices
  • Linear transformations and tensors
  • Fourier series
  • Dirac’s delta function
  • Integral transforms (Fourier, Laplace, convolution theorem)
  • Sturm-Liouville theory of linear differential operators
  • Partial differential equations