1. | Mathematical model 2: Inverse Problem (1) | Shear modulus reconstruction by low-frequency harmonic vibration | ||
2. | Mathematical model 2: Inverse Problem (2) | Generalized Hookes law | ||
3. | Mathematical model 2: Inverse Problem (1) | Maxwell equation - Eddy current model | ||
4. | Mathematical model 2: Inverse Problem (2) | Basics in MRI | ||
5. | Mathematical model 2: Inverse Problem (3) | |||
6. | Mathematical model 2: Inverse Problem (4) | |||
7. | Mathematical model 2: Inverse Problem (1) | |||
8. | Mathematical model 2: Inverse Problem (2) | |||
9. | Mathematical model 2: Inverse Problem (3) | |||
10. | Mathematical model 2: Inverse Problem | Principle of MRI : reconstruction | ||
11. | Mathematical model 2: Inverse Problem (2) | Basics in MREIT(2) | ||
12. | Mathematical model 2: Inverse Problem (1) | Basics in MREIT | ||
13. | Mathematical model 2: Inverse Problem (3) | Basics in MREPT (3) | ||
14. | Mathematical model 2: Inverse Problem | MR-based Impedance Imaging : MREIT vs MREPT | ||
15. | Mathematical model 2: Inverse Problem | MR-based Impedance Imaging : MREPT | ||
16. | Mathematical model 2: Inverse Problem | Conductivity Reconstruction using D-bar method for EIT | ||
17. | Mathematical model 1: Optimization Problem (1) | Preliminary to Sobolev space | ||
18. | Mathematical model 1: Optimization Problem (2) | Sobolev space : definitions | ||
19. | Mathematical model 1: Optimization Problem (3) | Sobolev space : theory and examples | ||
20. | Mathematical model 1: Optimization Problem (4) | Sobolev space : Sobolevs inequality for gradient | ||
21. | Mathematical model 1: Optimization Problem | Sobolev space : three important theorems Sobolev space : Sobolev Imbedding theorem Sobolev space : Proof of Sobolev Imbedding theorem, Study H^s Sobolev space : Study H^s |
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22. | Mathematical model 1: Optimization Problem (1) | Review / Motivation of Sobolev space Sobolev space : Example1 Sobolev space : Example2 |
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23. | Mathematical model 1: Optimization Problem (2) | Sobolev space : dual space and theorem Sobolev space : Exercise1 Sobolev space : Exercise2 Sobolev space : Proof of exercise2 |
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24. | Mathematical model 1: Optimization Problem (3) | Sobolev space : Lemma | ||
25. | Mathematical model 2: Inverse Problem (1) | hybrid MREIT _ Applied mathematics in biomedical science : The goal of EIT&MREIT Applied mathematics in biomedical science : Motivation, Introduction |
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26. | Mathematical model 2: Inverse Problem (2) | Applied mathematics in biomedical science : EIT method(N-channel EIT system) Applied mathematics in biomedical science : EIT method |
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27. | Mathematical model 2: Inverse Problem (3) | Applied mathematics in biomedical science : Method of MREIT | ||
28. | Special Lecture | Basics of MRI | ||
29. | Special Lecture | MR Quantitative susceptibility mapping(QSM) for quantifying biomarkers, removing artifacts and revealing hypointensity soure in MRI | ||
30. | Mathematical model 2: Inverse Problem (1) | Uniqueness theory in EIT | ||
31. | Mathematical model 2: Inverse Problem (2) | Reconstruction method in EIT : Dbar method |