http://interval.louisiana.edu/courses/362/362-02-fa-15-syllabus.txt Math. 362 tentative syllabus (Fall, 2015, R. B. Kearfott) Wiley Plus problems on each topic will be given as the topics are presented. The topics and sections are from "Elementary Linear Algebra, Applications Version", 11th edition, by Howard Anton and Chris Rorres. This schedule will be modified as we proceed. Section Material 1. 1.1 Intro. to linear systems (geometry, row operations) 2. 1.2 Gaussian elimination (Row echelon and reduced row echelon form; free variables, homogeneous systems) 3. 1.3, 1.4 Matrix operations, inverses 4. 1.5, 1.6 More on inverses 5. 1.7, 1.8 Types of matrices, matrices as linear transformations. 6. 1.9 Applications 7. First exam 8. 2.1, 2.2 Determinants by cofactor expansion and by row reduction. 9. 2.3 Cramer's rule and review. 10. 3.1, 3.2 vectors, norm, dot-product, distance (Note: the material in 3.3 and 3.4 are covered in our Math. 302 course; that is the only reason they are omitted here.) 11. 4.1, 4.2 Vector spaces in general; subspaces 12. 4.3, 4.4 linear independence; coordinates and bases 13. 4.5, 4.6 Dimension; change of basis 14. 4.7, 4.8 row space, column space, rank, null space, orthogonal complement. 15. 4.9, 4.10 reflectors and rotators, properties of transformations. 16. 4.11, review geometrical significance of transformations. 17. Second exam 18. 5.1 eigenvalues and eigenvectors; bases 19. 5.2, 5.3 diagonalization, matrix factorizations, complex vector spaces. 20. 5.4 eigenvalues and eigenvectors in differential equations. 21. Review 22. Third exam The following topics are dependent on how quickly and well we have covered the previous ones. 23. 6.3 Gram Schmidt process and QR factorization 24. 6.4 Least squares approximation 25. 9.4 The singular value decomposition 26. Review 27. Fourth exam 28. Review