1. (7.4-7.6) Vector spaces, subspaces, linear combination, linear independence, basis dimension, dot product, Cauchy-Schwarz inequality.
2. (8.1, 8.3-8.5) Matrices, addition, multiplication and trasposition, elementary row operations, rank of a matrix.
3. (8.6-8.8) Systems of linear equations, inversion of a matrix.
4. (8.9-8.10) Substitutions, determinants and their applications, Cramer's rule.
5. (9.1-9.2) Eigenvalues, eigenvectors and eigenspaces, diagonalization.
6. (10.1-10.2) Linear systems, real eigenvalues.
7. (10.3-10.4) Complex eigenvalues, Non-homogeneous systems.
8. (10.5-10.6) Matrix exponential and variation of parameters.
9. Review
10. 1-st exam
11. (11.1-11.2) Phase plane, autonomous sustems, linear approximation.
12. (11.3) Almost linear systems.
13. (3.1-3.3) Laplace transform, transformations.
14. (3.4-3.5) Convolution, delta functions.
15. (3.6) Solution of systems via Laplace transf.
16. (14.1-14.3) Fourier series, convergence, even and odd functions, sine and cosine series.
17. (14.4-14.5) Amplitude spectrum, Fourier Integral
18. (14.6) Complex notations
19. (15.1-15.2) Fourier transforms
20. (15.5) Sine and Cosine Transforms (?)
21. (6.1) Sturm--Liouville Theory.
22. Review
23. Review
24. Second exam
25. (16.1) PDE, separation of variables, heat equation
26. (16.2-3) Laplace equation, wave equation
27. (16.4-5) Unbouhnded domains
28. (16.6-7) Use of Laplace and Fourier transfporms.
29. (16.8) Heat equation in infinite cylinder.
30. Review
31. Review