Last modified by tssaksal@helsinki_fi on 2024/03/27 10:12
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1 {{panel}}
2 **Teacher:** [[doc:mathstatHenkilokunta.Gunther Uhlmann]]
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4 **Scope:** 1+1cr. 1 for attending lectures + 1 for solving exercise problems
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6 **Type:**
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8 **Teaching:**
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10 **Topics:**
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12 (% style="color: rgb(33,33,33);" %)Microlocal analysis, which is roughly speaking local analysis in (%%)
13 (% style="color: rgb(33,33,33);" %)phase space, has its roots in the classical methods of geometrical optics. (%%)
14 (% style="color: rgb(33,33,33);" %)In this minicourse we will introduce several basic concepts like wave (%%)
15 (% style="color: rgb(33,33,33);" %)front set, pseudodifferential operators and Fourier integral operators and (%%)
16 (% style="color: rgb(33,33,33);" %)apply them to study several inverse problems arising in different (%%)
17 (% style="color: rgb(33,33,33);" %)applications like X-ray tomography, seismic imaging, photoacoustic and (%%)
18 (% style="color: rgb(33,33,33);" %)thermoacoustic tomography, and electrical impedance tomography, also (%%)
19 (% style="color: rgb(33,33,33);" %)called Calderòn's problem.
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21 **Prerequisites:**
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23 Basics of Fourier and Functional analysis. Basics of Sobolev spaces.
24 {{/panel}}
25
26 == News ==
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28 * Solutions uploaded!
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30 == Teaching schedule ==
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32 Thursday 18.8., Friday 19.8., Monday 22.8. and Tuesday 23.8. from 13-15 in room D123.
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34 == Course material ==
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36 [[Lecture notes by Jere Lehtonen>>attach:lecture notes.pdf]]
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38 [[Lecture notes>>attach:MLA-Notes-1996-7 (1).pdf]]
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40 [[PDE notes>>attach:PDEnotes]]
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42 [[Melrose & Uhlmann: An Introduction to Microlocal Analysis >>attach:imaast.pdf]]
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44 [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=KOODI||style="font-size: 20.0px;line-height: 1.5;" shape="rect"]]
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46 Send E-mail to [[Teemu Saksala>>url:http://wiki.helsinki.fi/display/mathstatHenkilokunta/Teemu+Saksala||shape="rect"]] (teemu.saksala(a)helsinki.fi).
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48 == Exercises ==
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50 [[Problems>>attach:Homework problems.pdf]]
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52 [[partial solutions>>attach:Homework solutions.pdf]]
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54 === Course feedback ===
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56 Course feedback can be given at any point during the course. Click [[here>>url:https://elomake.helsinki.fi/lomakkeet/11954/lomake.html||style="line-height: 1.4285;" shape="rect"]].