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MA 5340: Selected chapters from mathematical continuum mechanics

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This lecture is aimed at students with a physical interest. The focus is on mathematical relevant methods. Topics from the following list are chosen:

Lecture and Exercise Schedule

Lecture   Date      Topic       Script
1. 30.04.19      
      IV.11 Reaction-diffusion systems
   
 Cont
 Cont
    General Diffusion system (IV11.2)
    IV.11.1 Chemical potential, IV.11.2 Entropy Theorem
2. 30.04.19      
      IV.13 (or IV.12)
    Chemical reactions
   
 Cont
 Cont
 Cont
 Cont
    IV.13.1 (or IV.12.1) Specific free Energy
    Stoichiometric equations ((IV13.8) or (IV12.8))
    IV.13.3 (or IV.12.3) Reaction rates, IV.12.4 Assumptions
    IV.12.5 Chemical reaction rates, IV.12.6 Lemma
3. 14.05.19      
      IV.13 (or IV.12)
    Chemical reactions
    Exercise
 Cont
 Cont
 Cont
    IV.13.7 (or IV.12.7) Equilibria, Mass action law
    IV.13.8 (or IV.12.8) Water, IV.13.10 (or IV.12.10) Saha equation
    IV.13.9 (or IV.12.9) Haber-Bosch process
4. 15.05.19      
      Temperature-dependent reactions
   
    IV.11 (or IV.13) Gradient dependence
 Cont
 Cont
 Cont
 Cont
    IV.13.11 (or IV.12.11) Example (by B. Larrouturou)
    IV.11.3 Alternative version of the entropy principle
    IV.11.11 (or IV.13.2) Chemical potential
    IV.11.13 (or IV.13.4) Special cases: (1) Reaction-diffusion models
5. 28.05.19      
     
   
   
    Exercise
 Cont
 Cont
 Cont
 Cont
    IV.13.4 Special cases: (2) Allen-Cahn equation,
    (3) Cahn-Hilliard equation, Proof of IV.13.4
    IV.13.5 Symmetry of Π
    II.2 Lorentz transformation
6. 29.05.19      
      VI. Speed ​​of Light
    VI.2. Maxwell equations
 Cont
 Cont
 Cont
    VI.1 Observers transformations, VI.1.1 Lorentz case
    Ampère’s circuital law (VI2.1), VI.2.1 Conservation of charge
    VI.2.2 Special case: (VI2.5), (VI2.6)
7. 18.06.19      
     
   
   
    Exercise
 Cont
 Cont
 Cont
 
    VI.2.3 Example: Stationary point charge, VI.2.5 Example: Static conductor
    VI.2.6 E is a covariant tensor, VI.2.7 Special: Lorentz case
    Faraday’s law of induction (VI2.16), VI.2.8 and VI.2.9
    Lorentz transformation and its relation to geometry G_c
8. 19.06.19      
      VI.2. Maxwell equations
   
   
   
 Cont
 Cont
 Cont
 Cont
    Maxwell equations in Lorentz case (VI2.18)
    VI.2.10 Lemma of Poincare with proof, VI.2.11 4-vector potential
    VI.2.12 Gauge invariance, VI.2.14 Maxwell equations without polarization
    VI.2.15 Lorentz frame, VI.2.16 Lorenz convention
9. 25.06.19      
     
    VI.4. Magnetohydrodynamics
    Exercise
 Cont
 Cont
 Exe
    VI.2.17 Electromagnetic waves, VI.2.18 Wave solution
    VI.4.1 Ampère’s circuital law, VI.4.2 Faraday’s induction law
    13. Lemma von Poincaré
10. 26.06.19      
     
   
   
 Cont
 Cont
 Cont
    VI.4.3 Transformation rules, VI.4.4 Newton force and Lorentz force
    VI.4.5 Dimension analysis, Magnetohydrodynamics (VI4.7)
    Applications of MHD
11. 9.07.19      
     
    Exercise
 Cont
    VI.3 Light in media
   
12. 10.07.19      
     
 Cont
 
    VI.3 Light in media
13. 13.07.19      
     
    Exercise
 Cont
 
    VI.6 Ohm's law
   
14. 24.07.19      
     
 Cont
    VI.7 Entropy for MHD

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