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Linear Algebra

1. Introduction to Linear Algebra
2. Matrices
3. Matrix factorizations
4. Linear Systems
5. Spectral decomposition
- 5.1. Spectral decomposition of symmetric matrices
- 5.2. Sensitivity of spectral decomposition
6. Cayley-Hamilton theorem

Multivariable Calculus

Differential Geometry

Vector and Tensor Algebra and Calculus

Functional Analysis

Complex Calculus

18. Complex Algebra
19. Complex Analysis
20. Laplace Transform
- 20.1. Definition and Properties
- 20.2. Applications of Laplace Transform
21. Fourier Transforms
22. Z-transform

Approximation of Functions

Calculus of Variations

Ordinary Differential Equations

System Theory

Control Theory

43. Introduction to control methods
44. Closed-loop control: requirements and performance
- 44.1. Stability (SISO)
- 44.2. Reference tracking (SISO)
45. Frequency domain control
46. Optimal control
47. Pole placement
48. Examples

Partial Differential Equations

Numerical Methods for PDEs

Boundary Methods for PDEs

Optimization

Reinforcement Learning

Introduction to function approximation

23. Introduction to function approximation#

Useful, because derivatives and integrals of polynomial functions are easy to evaluate exactly. Used in:

numerical methods for ODEs, e.g. multi-step methods
numerical methods for PDEs, e.g. base functions of FEM.
- Gaussian quadrature provides exact integration of integrals.
- FEM uses piece-wise Lagrangian interpolation of the fields
…

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