complex analysis: polar forms and how branch cuts work

Lecture 3 of 36 in Complex Analysis by Maths 505. 14 min. Watch on YouTube

Course: Complex Analysis (Mathematics). Covers: complex numbers analytic functions contour integrals residues cauchy.

All lectures in Complex Analysis

  1. An unorthodox intro to complex numbers · 14 min
  2. A nice little proof for Euler's formula · 8 min
  3. complex analysis: polar forms and how branch cuts work · 14 min
  4. Complex Analysis: complex valued functions and some important concepts · 10 min
  5. limits and continuity in complex analysis · 8 min
  6. Complex Analysis: Powers and Nth roots · 19 min
  7. the complex exponential function · 10 min
  8. The fascinating case of the complex logarithm · 18 min
  9. Complex Analysis: Power Functions · 25 min
  10. Complex Analysis: trigonometric and inverse trigonometric functions · 15 min
  11. complex differentiation · 10 min
  12. Complex Analysis: what is an analytic function? · 25 min
  13. Complex Analysis: harmonic functions and differential operators · 8 min
  14. Complex Analysis: Conformal Mappings · 8 min
  15. Complex Analysis: what is a contour integral? · 10 min
  16. Complex Analysis: the fundamental theorem and independence of path for contour integrals · 17 min
  17. Complex Analysis: Gauss' Mean Value Theorem · 9 min
  18. What are the residues of the gamma function? · 7 min
  19. A surprisingly complex trigonometric integral: int (0,π/2) 1/(1+sin^4(x)) · 12 min
  20. 2 gorgeous results: derivatives of the eta and zeta functions at zero · 12 min
  21. int 0 to infinity (cos(x))/(π^2 - 4x^2): the best thing you'll see next week · 16 min
  22. This integral breaks math · 7 min
  23. Why this integral is MUCH harder than it looks · 21 min
  24. The fresnel integrals solved using contour integration · 14 min
  25. A surprisingly interesting integral · 10 min
  26. A (literally) complex integral · 12 min
  27. one of the best integrals you'll solve · 14 min
  28. This wacky integral has a beautiful result · 12 min
  29. Contour integration with a STUNNING result! · 16 min
  30. This is one of the coolest integrals ever solved · 9 min
  31. A simple looking integral with a complex solution · 12 min
  32. A wild complex integral! · 12 min
  33. A stellar integral solved using some wonderful complex analysis · 20 min
  34. My favorite contour integration problem! · 29 min
  35. This result is FANTASTIC · 15 min
  36. Complex Analysis: What is the residue theorem? · 14 min