1. REVIEW: Separation of Variables

2. Fourier’s Theorem

3. Friday Sept 17th: Linear Algebra Vector/matrix operations Index notation Determinants Cartesian position vectors Eigenvalues/eigenvectors

4. Scalars and vectors A scalar a is just a single number. A vector is, in the simplest definition, just a list of numbers:

6. Matrices

9. Determinant of a matrix

13. Matrix-vector multiplication, linear systems

14. Cross product

15. ocean beach 60% speldfar, 40% schwartz A linear system ?

16. Crimea R. Rollinonthe R. ocean beach 90% speldfar, 10% schwartz 40% speldfar, 60% schwartz 60% speldfar, 40% schwartz C R A linear system

17. Beach sand is 40% from Crimea R., 60% from Rollinonthe R.

18. Cartesian position vectors unit vectors

19. Cartesian position vectors unit vectors Right-handed Left-handed

20. Matrices as transformations

22. reversible

23. Matrices as transformations reversible

24. Matrices as transformations

28. Eigenvalues and eigenvectors Typo on p. 50

29. Eigenvalues and eigenvectors (special matrix)

30. Eigenvalues and eigenvectors

31. Finding eigvals and eigvecs

32. Example: eigvals 3 rd order polynomial equation

33. Example: eigvecs =

34. =

36. Homework Section 4.1, Section 4.2, Section 4.3, omit #1, Section 4.4, plus: