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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. 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. Time derivative of integrals over moving domains
11. Calculus identities

Functional Analysis

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

Complex Calculus

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

Calculus of Variations

17. Introduction to Calculus of Variations

Ordinary Differential Equations

18. Introduction to Ordinary Differential Equations
19. Linear Time-Invariant Systems
20. LTI system response
21. LTI: stability and feedback

Partial Differential Equations

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

Numerical Methods for PDEs

29. Introduction to numerical methods for PDEs

Boundary Methods for PDEs

30. Green’s function method

Optimization

31. Optimization

Control

32. Introduction to control methods
- 32.1. Optimal control

Reinforcement Learning

33. Introduction to Reinforcement Learning
34. Markov Processes
35. Methods of solution of MPD: DP and LP
36. Methods of solution of MPD: RL
37. Large or Continuous MDPs

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Boundary Element Method

29.3. Boundary Element Method#

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29.2. Finite Volume Method

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30. Green’s function method

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