MATH 251- FALL 2001- COURSE OUTLINE  AND HOMEWORK

Remark: outline for the last 5 weeks of the course

10/26 to 11/2: Vector spaces and subspaces (chapter 5)

Exam 2: Monday, 11/5  Sections: chapter 5, 5.1 to 5.6

11/7 to 11/16: Inner products and applications

6.1: optional reading (p.282 needed for 9.4)
6.2: orthogonal complements  12,13,15,16
6.3:orthonormal basis, projections, Gram-Schmidt 9,10,11,12,13,17,18,19,21,23

Quiz 1: Monday, 11/12 sections: 6.2,6.3

6.4-Least squares 1,2,3,4,5,9,10
9.3-Least squares fitting to data 2,3,4,8
6.5-Orthogonal matrices, change of basis 6,16,18,25,26

Exam 3: Monday, 11/19 Sections: 6.2,6.3,6.4,9.3,6.5

11/21 to 12/5: Eigenvalues and diagonalization

9.2 Geometry of linear transformations 3,5,11,12,13,14,15,16

Quiz 2: Monday, 11/26 section:9.2

7.1:Eigenvalues/eigenvectors 4,5,6,10,11,12,13
7.2: Diagonalization 1,2, 8-11, 12-14, 19,21,22
7.3: Orthogonal diagonalization 2,5,10,15

Quiz 3:Monday, 12/3 sections: 7.1,7.2,7.3
Quiz 3-SOLUTIONS

9.5:Quadratic forms and symmetric matrices 3(a)(b)(c),8,11,12
9.6: Level sets of non-degenerate quadratic foms (two variables) 8,9,10
Remark:set the linear terms equal to zero when doing the problems for 9.6,9.7
9.7 4(a)(b)(c),7,8,9,10

FINAL EXAM:Tuesday 12/11, 8-10 a.m., Ayres 318
Sections: all sections covered in class from chapters 5,6,7,9