Videos

Here are recorded videos on Youtube (the most recent ones first):

58. Discrete Fourier transform – Orthogonal functions

57. Residue theorem

56. Continuous Fourier transforms

55. Meromorphic functions

54. Essential singularities

53. Classification of isolated singularities

52. Oscillating integrals – Fourier transforms

51. Circular rings and Laurent series

50. Cauchy’ integral theorem – Dirac Delta function

49. Cycles, homology, and winding numbers

48. Entire function – Fundamental theorem of algebra

47. Cauchy’s inequalities – Root criteria

46. Holomorphy criteria

45. Cauchy’s integral formulas

44. Extended integral theorem by Goursat

43. Integral theorem by Goursat

42. Integration of positive and negative integer powers

41. Antiderivatives

40. Contour integrals of complex functions

39. Parameterized curves and integration contours

38. Wirtinger derivatives

37. Cauchy-Riemann differential equations

36. Complex differentiability

35. Branch cuts and Riemann sheets

34. Series representations and convergence radius

33. Elementary functions: integer powers and polynomials

32. Complex sequences, series, and functions

31. Complex analysis – Introduction

30. Numerical methods

29. Inhomogeneous systems of linear differential equations

28. The matrix exponential function, determinant, and trace

27. Linear systems of first-order differential equations

26. Cauchy-Euler differential equations

25. Linear differential equations with constant coefficients

24. Special techniques for second-order homogeneous linear ODEs

23. Variation of constants – Proof

22. Linear differential equations – Variation of constants

21. Linear differential equations – Wronski determinant

20. Solution techniques for higher-order ODEs

19. Systems of differential equations

18. Singular points – Chaotic systems

17. Theorem by Peano

16. Proof of the Picard-Linelöff theorem (strong form)

15. Proof of the Picard-Lindelöff theorem (weak form)

14. Banach fixed point theorem: Proof structure

13. Banach spaces: Topology, metric, norm, and completeness

12. Implicit differential equations – Cases 3 and 4

11. Implicit differential equations – Cases 1 and 2

10. Exact differential equations – Application and interpretation

9. Exact differential equations – Definition and examples

8. Short introduction to linear differential equations

7. Elementary solution techniques – examples of ODEs

6. Guiding vector fields

5. Reduction of higher-order ODEs to systems of first-order ODEs

4. Classification of differential equations, partial derivatives, PDEs

3. Separation ansatz, classification of differential equations

2. Mathematica, simple integration techniques, integration constants

1. Organization of the lecture, concept of continuum

0. Welcome Video