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Linear Algebra

1. Introduction to Linear Algebra
2. Matrices
3. Matrix factorizations
- 3.3. Singular Value Decomposition
4. Linear Systems
5. Spectral decomposition
- 5.1. Spectral decomposition of symmetric matrices
- 5.2. Sensitivity of spectral decomposition

Multivariable Calculus

6. Introduction to multi-variable calculus

Differential Geometry

7. Introduction to Differential Geometry

Vector and Tensor Algebra and Calculus

8. Tensor Algebra
9. Tensor Calculus in Euclidean Spaces
10. Tensor Invariants
11. Unitary and rotation tensors
12. Isotropic Tensors
13. Time derivative of integrals over moving domains
14. Calculus identities

Functional Analysis

15. Introduction to Functional Analysis
16. Dirac’s delta

Complex Calculus

17. Complex Analysis
18. Laplace Transform
- 18.1. Definition and Properties
- 18.2. Applications of Laplace Transform
19. Fourier Transforms

Calculus of Variations

20. Introduction to Calculus of Variations

Ordinary Differential Equations

21. Introduction to Ordinary Differential Equations
22. Linear Time-Invariant Systems
23. LTI system response
24. LTI: stability and feedback

Partial Differential Equations

25. Introduction to Partial Differential Equations
26. Elliptic equations
27. Parabolic equations
28. Hyperbolic equations
29. Navier-Cauchy equations
30. Navier-Stokes equations
31. Arbitrary Lagrangian-Eulerian description

Numerical Methods for PDEs

32. Introduction to numerical methods for PDEs
33. Finite Element Method
- 33.1. 1-dimensional Poisson equation
34. Finite Volume Method
35. Boundary Element Method

Boundary Methods for PDEs

36. Green’s function method

Optimization

37. Optimization

Control

38. Introduction to control methods
- 38.1. Optimal control

Reinforcement Learning

39. Introduction to Reinforcement Learning
40. Markov Processes
41. Methods of solution of MPD: DP and LP
42. Methods of solution of MPD: RL
43. Large or Continuous MDPs

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Hyperbolic problems in multi-dimensional domains

28.7. Hyperbolic problems in multi-dimensional domains#

Examples

draft dummy page with the scheme used for all the systems
P-system
Euler equations
Shallow water

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28.7.1. General hyperbolic problem

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