Partial Differential Equations
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© 2011 ICTP
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
Giovanni Bellettini (Univ. of Roma Tor Vergata)
This course introduced the basic properties of separable Hilbert spaces, taking the space of sequences l^2 as the reference example. The properties of the Hilbert cube have been analyzed. The problem of the existence of a basis in an infinite dimensional vector (respectively Banach, and Hilbert) space, in particular the Hamel basis (respectively the Schauder basis and the Hilbert basis), was also discussed. The first basic theorems of linear functional analysis in Banach spaces, such as the HahnBanach theorem (analytical and geometric versions), the BanachSteinhaus theorem, the open mapping theorem, the closed graph theorem and their corollaries, were all studied. An other argument discussed in the course was distribution theory: the space of smooth functions with compact support was introduced, together with the notions of convergence required to introduce a distribution. Various properties and operations on distribution were studied, such as localization, support and convolution. Next, the Fourier transform and its main properties were carefully studied : the Fourier transform in L^1, in the space of rapidly decreasing functions, in L^2 and on tempered distributions. Some properties of Sobolev space (possibly with real exponent) have been analyzed, using mainly the Fourier transform. Applications of the Fourier transform to linear partial differential equations of elliptic, parabolic, and hyperbolic type, have been illustrated in the final part of the course. Several examples and exercises, as well as some counterexamples, have been illustrated during the lectures.  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
ICTP Science Dissemination Unit (SDU)
sdu@ictp.it
yes

1
01a Semiinner and inner product space. (recorded 2011.02.09 at 14:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.09_14.0014.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

2
01b Semiinner and inner product space. (recorded 2011.02.09 at 15:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.09_15.0015.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

3
02a Properties of l^2 space. (recorded 2011.02.10 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.10_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

4
02b Properties of l^2 space. (recorded 2011.02.10 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.10_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:30
mathematics, partial differential equations

5
03a Properties of l^2 space, Hilbert cube. (recorded 2011.02.11 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.11_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

6
03b Properties of l^2 space, Hilbert cube. (recorded 2011.02.11 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.11_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:36
mathematics, partial differential equations

7
04a Completion of a metric space. (recorded 2011.02.16 at 14:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.16_14.0014.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

8
04b Completion of a metric space.(recorded 2011.02.16 at 15:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.16_15.0015.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

9
05a Projection on a closed subspace of a Hilbert space. (recorded 2011.02.18 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.18_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

10
05b Projection on a closed subspace of a Hilbert space. (recorded 2011.02.18 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.18_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:43
mathematics, partial differential equations

11
06a Banach spaces. Linear operators on Banach spaces. (recorded 2011.02.23 at 14:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.23_14.0014.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

12
06b Banach spaces. Linear operators on Banach spaces. (recorded 2011.02.23 at 15:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.23_15.0015.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

13
07a The Riesz map. Hamel bases. Schauder bases. (recorded 2011.02.24 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.24_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

14
07b The Riesz map. Hamel bases. Schauder bases. (recorded 2011.02.24 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.24_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
24:03
mathematics, partial differential equations

15
08a Hilbert bases. Examples. (recorded 2011.02.25 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.25_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

16
08b Hilbert bases. Examples. (recorded 2011.02.25 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.02.25_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

17
09 On discontinuous linear operators. HahnBanach theorem, I. Norm preserving extension of a linear continuous operator. (recorded 2011.03.10 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.10_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

18
10a The HahnBanach theorems, II. (recorded 2011.03.11 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.11_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:43
mathematics, partial differential equations

19
10b The HahnBanach theorems, II. (recorded 2011.03.11 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.11_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:43
mathematics, partial differential equations

20
11a HahnBanach theorems, III. (recorded 2011.03.16 at 14:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.16_14.0014.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

21
11b HahnBanach theorems, III. (recorded 2011.03.16 at 15:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.16_15.0015.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

22
12a HahnBanach theorems, IV. BanachSteinhaus theorem. (recorded 2011.03.17 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.17_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

23
12b HahnBanach theorems, IV. BanachSteinhaus theorem. (recorded 2011.03.17 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.17_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:35
mathematics, partial differential equations

24
13a The open mapping theorem. The closed graph theorem. (recorded 2011.03.18 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.18_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

25
13b The open mapping theorem. The closed graph theorem. (recorded 2011.03.18 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.18_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

26
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)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.23_14.0014.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

27
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)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.23_15.0015.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:43
mathematics, partial differential equations

28
15a Dirac delta. Principal value. Operations on distributions. (recorded 2011.03.24 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.24_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

29
15b Dirac delta. Principal value. Operations on distributions. (recorded 2011.03.24 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.24_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:39
mathematics, partial differential equations

30
16a Distributional derivative. Examples. Distributional laplacian of 1/x in R^3. (recorded 2011.03.25 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.25_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

31
16b Distributional derivative. Examples. Distributional laplacian of 1/x in R^3. (recorded 2011.03.25 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.03.25_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:37
mathematics, partial differential equations

32
17a Fundamental solution of a linear differential operator with constant coefficients. Examples: heat kernel. (recorded 2011.04.06 at 14:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.06_14.0014.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

33
17b Fundamental solution of a linear differential operator with constant coefficients. Examples: heat kernel. (recorded 2011.04.06 at 15:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.06_15.0015.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:43
mathematics, partial differential equations

34
18a Localization and support of a distribution. (recorded 2011.04.07 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.07_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

35
18b Localization and support of a distribution. (recorded 2011.04.07 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.07_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:39
mathematics, partial differential equations

36
19a On the support of a distribution. Convolution of distributions. Pull back of a distribution. (recorded 2011.04.08 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.08_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

37
19b On the support of a distribution. Convolution of distributions. Pull back of a distribution. (recorded 2011.04.08 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.08_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

38
20a The Fourier transform in L^1. Properties and examples. Fourier transform of e^{x^2}. (recorded 2011.04.13 at 14:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.13_14.0014.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

39
20b The Fourier transform in L^1. Properties and examples. Fourier transform of e^{x^2}. (recorded 2011.04.13 at 15:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.13_15.0015.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

40
21a Fourier transform and differentiation. On the inversion of the Fourier transform. (recorded 2011.04.14 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.14_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

41
21b Fourier transform and differentiation. On the inversion of the Fourier transform. (recorded 2011.04.14 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.14_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:36
mathematics, partial differential equations

42
22a Uncertainty principle. Rapidly decreasing functions: the Schwarz space. (recorded 2011.04.15 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.15_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

43
22b Uncertainty principle. Rapidly decreasing functions: the Schwarz space. (recorded 2011.04.15 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.15_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:40
mathematics, partial differential equations

44
23a Some properties of the Schwarz space. Fourier transform on the Schwarz space. Tempered distributions. (recorded 2011.04.20 at 14:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.20_14.0014.59.m4v
Wed Aug 31 18:06:15 CEST 2011
32:55
mathematics, partial differential equations

45
23b Some properties of the Schwarz space. Fourier transform on the Schwarz space. Tempered distributions. (recorded 2011.04.20 at 15:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.20_15.0015.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:43
mathematics, partial differential equations

46
24a The Fourier transform on tempered distributions. (recorded 2011.04.21 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.21_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

47
24b The Fourier transform on tempered distributions. (recorded 2011.04.21 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.21_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

48
25a Sobolev spaces with natural exponent. Characterization using the Fourier transform. Embedding in spaces C^k. (recorded 2011.04.27 at 14:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.27_14.0014.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

49
25b Sobolev spaces with natural exponent. Characterization using the Fourier transform. Embedding in spaces C^k. (recorded 2011.04.27 at 15:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.27_15.0015.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

50
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)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.28_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:40
mathematics, partial differential equations

51
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)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.28_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

52
27a Linear elliptic operators and Fourier transform. Poisson equation in the halfspace. (recorded 2011.04.29 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.29_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:41
mathematics, partial differential equations

53
27b Linear elliptic operators and Fourier transform. Poisson equation in the halfspace. (recorded 2011.04.29 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.04.29_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:32
mathematics, partial differential equations

54
28a Weak solutions of the nonhomogeneous Poisson equation. Linear parabolic equations. The Cauchy problem and the Fourier transform. Qualitative properties of solutions. (recorded 2011.05.04 at 14:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.05.04_14.0014.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

55
28b Weak solutions of the nonhomogeneous Poisson equation. Linear parabolic equations. The Cauchy problem and the Fourier transform. Qualitative properties of solutions. (recorded 2011.05.04 at 15:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.05.04_15.0015.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:43
mathematics, partial differential equations

56
29a Weak solutions of the nonhomogeneous heat equation. The Cauchy problem for the wave equation. (recorded 2011.05.05 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.05.05_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

57
29b Weak solutions of the nonhomogeneous heat equation. The Cauchy problem for the wave equation. (recorded 2011.05.05 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.05.05_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:35
mathematics, partial differential equations

58
30a Convolution and Fourier transform. Fundamental solutions. (recorded 2011.05.06 at 09:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.05.06_09.0009.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:42
mathematics, partial differential equations

59
30b Convolution and Fourier transform. Fundamental solutions. (recorded 2011.05.06 at 10:00)
Giovanni Bellettini (Univ. of Roma Tor Vergata)
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations
ICTP Postgraduate Diploma Course in Mathematics  Lectures on Partial Differential Equations  NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.
http://podcast.ictp.tv/courses/2011/MTH_Partial_Differential_Equations/MTH_Partial_Differential_Equations_2011.05.06_10.0010.59.m4v
Wed Aug 31 18:06:15 CEST 2011
59:40
mathematics, partial differential equations