Mathematics 4 - Further Mathematics for Physicists

SS 2020



The link to video of my lectures can be found on Moodle (use "Mathematics 4" for searching of the course)



LECTURE NOTES


Note 1 (Apr 06)

Note 2 (Apr 09)

Note 3 (Apr 16)

Note 4 (Apr 20)

Note 5 (Apr 23)

Note 6 (Apr 27)

Note 7 (Apr 30)

Note 8 (May 04)

Note 9 (May 07)

Note 10 (May 11)

Note 11 (May 14)

Note 12 (May 18)

Note 13 (May 25)

Note 14 (May 28)

Note 15 (June 4)

Note 16 (June 8)

Note 17 (June 11)

Note 18 (June 15)

Note 19 (June 18)

Note 20 (June 22)

Note 21 (June 25)

Note 22 (June 29)

Note 23 (July 2)

Note 24 (July 6)

Note 25 (July 9)

Note 26 (July 13)

Note 27 (July 16)



COURSE JOURNAL


  • Apr 06 - Main classes of sets
  • Apr 09 - Generated classes of sets. Borel sigma-algebra
  • Apr 16 - Measures: properties
  • Apr 20 - Measures: extension
  • Apr 23 - Measurable functions
  • Apr 27 - Properties of measurable functions
  • Apr 30 - Lebesgue integral
  • May 4 - Properties of Lebesgue integral
  • May 7 - Limit properties of Lebesgue integral
  • May 11 - Limit theorems II. Change of variables
  • May 14 - Metric spaces
  • May 18 - Convergence in metric spaces
  • May 25 - Completeness of metric spaces
  • May 28 - Normed and Banach spaces
  • June 4 - Linear operators
  • June 8 - Dual spaces
  • June 11 - Hilbert spaces
  • June 15 - Orthonormal sets
  • June 18 - Adjoint operators
  • June 22 - Spectral theory of bounded linear operators
  • June 25 - Spectral representation of bounded self-adjoint operators I
  • June 29 - Spectral representation of bounded self-adjoint operators II
  • July 2 - Compact linear operators
  • July 6 - Unbounded linear operators
  • July 9 - Spectral representation of unbounded self-adjoint operators. Curves in R3
  • July 13 - Curves in R3. Topological spaces
  • July 16 - Differentiable Manifolds