Partial Differential Equations

01a Semi-inner and inner product space. (recorded 2011.02.09 at 14:00)

59 perc 59. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

01b Semi-inner and inner product space. (recorded 2011.02.09 at 15:00)

59 perc 58. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

02a Properties of l^2 space. (recorded 2011.02.10 at 09:00)

59 perc 57. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

02b Properties of l^2 space. (recorded 2011.02.10 at 10:00)

59 perc 56. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

03a Properties of l^2 space, Hilbert cube. (recorded 2011.02.11 at 09:00)

59 perc 55. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

03b Properties of l^2 space, Hilbert cube. (recorded 2011.02.11 at 10:00)

59 perc 54. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

04a Completion of a metric space. (recorded 2011.02.16 at 14:00)

59 perc 53. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

04b Completion of a metric space.(recorded 2011.02.16 at 15:00)

59 perc 52. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

05a Projection on a closed subspace of a Hilbert space. (recorded 2011.02.18 at 09:00)

59 perc 51. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

05b Projection on a closed subspace of a Hilbert space. (recorded 2011.02.18 at 10:00)

59 perc 50. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

06a Banach spaces. Linear operators on Banach spaces. (recorded 2011.02.23 at 14:00)

59 perc 49. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

06b Banach spaces. Linear operators on Banach spaces. (recorded 2011.02.23 at 15:00)

59 perc 48. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

07a The Riesz map. Hamel bases. Schauder bases. (recorded 2011.02.24 at 09:00)

59 perc 47. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

07b The Riesz map. Hamel bases. Schauder bases. (recorded 2011.02.24 at 10:00)

24 perc 46. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

08a Hilbert bases. Examples. (recorded 2011.02.25 at 09:00)

59 perc 45. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

08b Hilbert bases. Examples. (recorded 2011.02.25 at 10:00)

59 perc 44. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

09 On discontinuous linear operators. Hahn-Banach theorem, I. Norm preserving extension of a linear continuous operator. (recorded 2011.03.10 at 09:00)

59 perc 43. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

10a The Hahn-Banach theorems, II. (recorded 2011.03.11 at 09:00)

59 perc 42. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

10b The Hahn-Banach theorems, II. (recorded 2011.03.11 at 10:00)

59 perc 41. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

11a Hahn-Banach theorems, III. (recorded 2011.03.16 at 14:00)

59 perc 40. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

11b Hahn-Banach theorems, III. (recorded 2011.03.16 at 15:00)

59 perc 39. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

12a Hahn-Banach theorems, IV. Banach-Steinhaus theorem. (recorded 2011.03.17 at 09:00)

59 perc 38. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

12b Hahn-Banach theorems, IV. Banach-Steinhaus theorem. (recorded 2011.03.17 at 10:00)

59 perc 37. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

13a The open mapping theorem. The closed graph theorem. (recorded 2011.03.18 at 09:00)

59 perc 36. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

13b The open mapping theorem. The closed graph theorem. (recorded 2011.03.18 at 10:00)

59 perc 35. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

14a The space of smooth functions with compact support: notion of convergence. Distributions. Criterion to be a distribution. Distributions representable by integration. (recorded 2011.03.23 at 14:00)

59 perc 34. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

14b The space of smooth functions with compact support: notion of convergence. Distributions. Criterion to be a distribution. Distributions representable by integration. (recorded 2011.03.23 at 15:00)

59 perc 33. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

15a Dirac delta. Principal value. Operations on distributions. (recorded 2011.03.24 at 09:00)

59 perc 32. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

15b Dirac delta. Principal value. Operations on distributions. (recorded 2011.03.24 at 10:00)

59 perc 31. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

16a Distributional derivative. Examples. Distributional laplacian of 1/|x| in R^3. (recorded 2011.03.25 at 09:00)

59 perc 30. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

16b Distributional derivative. Examples. Distributional laplacian of 1/|x| in R^3. (recorded 2011.03.25 at 10:00)

59 perc 29. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

17a Fundamental solution of a linear differential operator with constant coefficients. Examples: heat kernel. (recorded 2011.04.06 at 14:00)

59 perc 28. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

17b Fundamental solution of a linear differential operator with constant coefficients. Examples: heat kernel. (recorded 2011.04.06 at 15:00)

59 perc 27. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

18a Localization and support of a distribution. (recorded 2011.04.07 at 09:00)

59 perc 26. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

18b Localization and support of a distribution. (recorded 2011.04.07 at 10:00)

59 perc 25. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

19a On the support of a distribution. Convolution of distributions. Pull back of a distribution. (recorded 2011.04.08 at 09:00)

59 perc 24. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

19b On the support of a distribution. Convolution of distributions. Pull back of a distribution. (recorded 2011.04.08 at 10:00)

59 perc 23. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

20a The Fourier transform in L^1. Properties and examples. Fourier transform of e^{-|x|^2}. (recorded 2011.04.13 at 14:00)

59 perc 22. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

20b The Fourier transform in L^1. Properties and examples. Fourier transform of e^{-|x|^2}. (recorded 2011.04.13 at 15:00)

59 perc 21. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

21a Fourier transform and differentiation. On the inversion of the Fourier transform. (recorded 2011.04.14 at 09:00)

59 perc 20. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

21b Fourier transform and differentiation. On the inversion of the Fourier transform. (recorded 2011.04.14 at 10:00)

59 perc 19. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

22a Uncertainty principle. Rapidly decreasing functions: the Schwarz space. (recorded 2011.04.15 at 09:00)

59 perc 18. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

22b Uncertainty principle. Rapidly decreasing functions: the Schwarz space. (recorded 2011.04.15 at 10:00)

59 perc 17. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

23a Some properties of the Schwarz space. Fourier transform on the Schwarz space. Tempered distributions. (recorded 2011.04.20 at 14:00)

32 perc 16. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

23b Some properties of the Schwarz space. Fourier transform on the Schwarz space. Tempered distributions. (recorded 2011.04.20 at 15:00)

59 perc 15. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

24a The Fourier transform on tempered distributions. (recorded 2011.04.21 at 09:00)

59 perc 14. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

24b The Fourier transform on tempered distributions. (recorded 2011.04.21 at 10:00)

59 perc 13. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

25a Sobolev spaces with natural exponent. Characterization using the Fourier transform. Embedding in spaces C^k. (recorded 2011.04.27 at 14:00)

59 perc 12. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

25b Sobolev spaces with natural exponent. Characterization using the Fourier transform. Embedding in spaces C^k. (recorded 2011.04.27 at 15:00)

59 perc 11. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

26a Sobolev spaces with real exponent using the Fourier transform. Applications of the Fourier transform to linear elliptic PDEs. (recorded 2011.04.28 at 09:00)

59 perc 10. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

26b Sobolev spaces with real exponent using the Fourier transform. Applications of the Fourier transform to linear elliptic PDEs. (recorded 2011.04.28 at 10:00)

59 perc 9. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

27a Linear elliptic operators and Fourier transform. Poisson equation in the half-space. (recorded 2011.04.29 at 09:00)

59 perc 8. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

27b Linear elliptic operators and Fourier transform. Poisson equation in the half-space. (recorded 2011.04.29 at 10:00)

59 perc 7. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

28a Weak solutions of the non-homogeneous Poisson equation. Linear parabolic equations. The Cauchy problem and the Fourier transform. Qualitative properties of solutions. (recorded 2011.05.04 at 14:00

59 perc 6. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

28b Weak solutions of the non-homogeneous Poisson equation. Linear parabolic equations. The Cauchy problem and the Fourier transform. Qualitative properties of solutions. (recorded 2011.05.04 at 15:00

59 perc 5. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

29a Weak solutions of the non-homogeneous heat equation. The Cauchy problem for the wave equation. (recorded 2011.05.05 at 09:00)

59 perc 4. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

29b Weak solutions of the non-homogeneous heat equation. The Cauchy problem for the wave equation. (recorded 2011.05.05 at 10:00)

59 perc 3. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

30a Convolution and Fourier transform. Fundamental solutions. (recorded 2011.05.06 at 09:00)

59 perc 2. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)

30b Convolution and Fourier transform. Fundamental solutions. (recorded 2011.05.06 at 10:00)

59 perc 1. rész Giovanni Bellettini (Univ. of Roma Tor Vergata)