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Linear Algebra

1. Introduction to Linear Algebra
2. Matrices
3. Matrix factorizations
- 3.3. Singular Value Decomposition
4. Linear Systems

Multivariable Calculus

5. Introduction to multi-variable calculus

Differential Geometry

6. Introduction to Differential Geometry

Vector and Tensor Algebra and Calculus

7. Tensor Algebra
8. Tensor Calculus in Euclidean Spaces
9. Time derivative of integrals over moving domains
10. Calculus identities

Functional Analysis

11. Introduction to Functional Analysis
12. Dirac’s delta

Complex Calculus

13. Complex Analysis
14. Laplace Transform
15. Fourier Transforms

Calculus of Variations

16. Introduction to Calculus of Variations

Ordinary Differential Equations

17. Introduction to Ordinary Differential Equations
18. Linear Time-Invariant Systems
19. LTI system response

Partial Differential Equations

20. Introduction to Partial Differential Equations
21. Elliptic equations
22. Parabolic equations
23. Hyperbolic problems
24. Navier-Cauchy equations
25. Navier-Stokes equations
26. Arbitrary Lagrangian-Eulerian description

Numerical Methods for PDEs

27. Introduction to numerical methods for PDEs

Boundary Methods for PDEs

28. Green’s function method

Optimization

29. Optimization

Reinforcement Learning

30. Introduction to Reinforcement Learning
31. Markov Processes
32. Methods of solution of MPD: DP and LP
33. Methods of solution of MPD: RL
34. Large or Continuous MDPs

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Finite Element Method

27.1. Finite Element Method#

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27. Introduction to numerical methods for PDEs

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27.2. Finite Volume Method

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