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Linear Algebra

1. Matrices
2. Matrix factorizations
- 2.1. Singular Value Decomposition
3. Linear Systems

Multivariable Calculus

4. Introduction to multi-variable calculus

Differential Geometry

5. Introduction to Differential Geometry

Vector and Tensor Algebra and Calculus

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

Functional Analysis

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

Complex Calculus

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

Calculus of Variations

15. Introduction to Calculus of Variations

Ordinary Differential Equations

16. Introduction to Ordinary Differential Equations
17. Linear Time-Invariant Systems

Partial Differential Equations

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

Numerical Methods for PDEs

25. Introduction to numerical methods for PDEs

Boundary Methods for PDEs

26. Green’s function method

Index

By basics

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