MTH 215, Fall 2004

Topics and Assignments

Week Topics Assignments

Sept 8 - 10

Vectors in Euclidean Spaces: 1.1
The Norm and the Dot Product: 1.2

Section 1.1:# 1,3,5,7,9,15,19,23,25,29,33,35,37

Sept 13 - 17

The Norm and the Dot Product: 1.2
Matrices and their Algebra: 1.3

Section 1.2: # 1,3,5,7,13,15,17,23,27,31,33,37,40
Additional problems for section 1.2:
1)Find the projection vector of (-1,2) to the line along (3,1) [Ans: projection vector = (-3/10, -1/10)]
2)Find the projection vector of (3,1) to the line along (1,2) [Ans: projection vector = (1,2)]
3)Find the distance from (3,1) to y=2x [Ans: distance = (5)^(1/2)]
Section 1.3: # 3,7,13,15,19,21,23,31,35,39,43,45

Sept 20 - 24

Solving Systems of Linear Equations: 1.4
Inverses of Square Matrices: 1.5

Section 1.4 # 3,9,13,15,23,25,27,29,41,43,45,47,49,57

Sept 27 - Oct 1

Inverses of Square Matrices: 1.5
Homogeneous Systems, Subspaces and Bases: 1.6

Section 1.5 # 3,5,13,15,17,21,23,29,31,35
Section 1.6 # 1,3,7,11,13,15,17,19,23,27,31,35

Oct 4 - 8

Homogeneous Systems, Subspaces and Bases: 1.6
Review
Exam I

Exam I, Friday October 8

Oct 11 - 15

Dimension, Rank and Linear Transformations: 2.1
The Rank of a Matrix: 2.2

Section 2.1 # 1,6,7,9,11,13,17,19,25,27,29,33
Section 2.2 # 1,3,5,7,9,11,13,15

Oct 18 - 22

Linear Transformations of Euclidean Spaces: 2.3
Linear Transformations of the Plane: 2.4

Section 2.3 # 1,3,5,7,13,15,19,21,29,31
Project I: Due November 1st.
Project I:PostScript, PDF

Oct 25 - 29

Linear Transformations of the Plane: 2.4
Areas, Volumes and Cross Products: 4.1
The Determinant of a Square Matrix: 4.2

Section 2.4 # 1,3,6,8,9,10,15
Section 4.1 # 1,5,7,11,13,15,19,21,25,33,35,37,45,49
Section 4.2 # 1,3,7,11,13,15,17,19,21,22,23,25,29

Nov 1 - 5

Computation of Determinants and Cramer's Rule: 4.3
Eigenvalues and Eigenvectors: 5.1

Section 4.3 # 1,3,5,15,17,21,25,29,35
Section 5.1 # 3,7,9,17,19,23,25,32,41

Nov 8 - 12

Diagonalization: 5.2
Review
Exam II

Section 5.2 # 1,3,5,9,11,13,14,15,19
ExamII.pdf

Nov 15 -19

Two Applications: 5.3
Projections: 6.1

Section 5.3 # 1,7,9

Nov 22 - 26

Projections: 6.1
Happy Thanksgiving !

Section 6.1 # 1,3,5,7,9,13,15,19,21,23,29
Project II: Due December 13.
Project II:PostScript, PDF

Nov 29 - Dec 3

The Gram-Schmidt Process: 6.2
Orthogonal Matrices: 6.3
The Method of Least Squares: 6.5

Section 6.2 # 1,3,5,7,9,11,13,17,19,25
Section 6.3 # 1,3,5,9,11,13,15,19,21,23

Dec 6 - 10

The Method of Least Squares: 6.5
Diagonalization of Quadratic Forms:8.1

Section 6.5 # 2,3,5,10,11,17,19,21
Section 8.1 # 1,3,5,7,8,11,15

Dec 13

Applications to Geometry: 8.2

Section 8.2 # 1,3,5,9,10a,b,d,j,13,15

Dec 18
Final!!

7:00-10:00 PM.
Washburn 220

Week	Topics	Assignments
Sept 8 - 10	Vectors in Euclidean Spaces: 1.1 The Norm and the Dot Product: 1.2	Section 1.1:# 1,3,5,7,9,15,19,23,25,29,33,35,37
Sept 13 - 17	The Norm and the Dot Product: 1.2 Matrices and their Algebra: 1.3	Section 1.2: # 1,3,5,7,13,15,17,23,27,31,33,37,40 Additional problems for section 1.2: 1)Find the projection vector of (-1,2) to the line along (3,1) [Ans: projection vector = (-3/10, -1/10)] 2)Find the projection vector of (3,1) to the line along (1,2) [Ans: projection vector = (1,2)] 3)Find the distance from (3,1) to y=2x [Ans: distance = (5)^(1/2)] Section 1.3: # 3,7,13,15,19,21,23,31,35,39,43,45
Sept 20 - 24	Solving Systems of Linear Equations: 1.4 Inverses of Square Matrices: 1.5	Section 1.4 # 3,9,13,15,23,25,27,29,41,43,45,47,49,57
Sept 27 - Oct 1	Inverses of Square Matrices: 1.5 Homogeneous Systems, Subspaces and Bases: 1.6	Section 1.5 # 3,5,13,15,17,21,23,29,31,35 Section 1.6 # 1,3,7,11,13,15,17,19,23,27,31,35
Oct 4 - 8	Homogeneous Systems, Subspaces and Bases: 1.6 Review Exam I	Exam I, Friday October 8
Oct 11 - 15	Dimension, Rank and Linear Transformations: 2.1 The Rank of a Matrix: 2.2	Section 2.1 # 1,6,7,9,11,13,17,19,25,27,29,33 Section 2.2 # 1,3,5,7,9,11,13,15
Oct 18 - 22	Linear Transformations of Euclidean Spaces: 2.3 Linear Transformations of the Plane: 2.4	Section 2.3 # 1,3,5,7,13,15,19,21,29,31 Project I: Due November 1st. Project I:PostScript, PDF
Oct 25 - 29	Linear Transformations of the Plane: 2.4 Areas, Volumes and Cross Products: 4.1 The Determinant of a Square Matrix: 4.2	Section 2.4 # 1,3,6,8,9,10,15 Section 4.1 # 1,5,7,11,13,15,19,21,25,33,35,37,45,49 Section 4.2 # 1,3,7,11,13,15,17,19,21,22,23,25,29
Nov 1 - 5	Computation of Determinants and Cramer's Rule: 4.3 Eigenvalues and Eigenvectors: 5.1	Section 4.3 # 1,3,5,15,17,21,25,29,35 Section 5.1 # 3,7,9,17,19,23,25,32,41
Nov 8 - 12	Diagonalization: 5.2 Review Exam II	Section 5.2 # 1,3,5,9,11,13,14,15,19 ExamII.pdf
Nov 15 -19	Two Applications: 5.3 Projections: 6.1	Section 5.3 # 1,7,9
Nov 22 - 26	Projections: 6.1 Happy Thanksgiving !	Section 6.1 # 1,3,5,7,9,13,15,19,21,23,29 Project II: Due December 13. Project II:PostScript, PDF
Nov 29 - Dec 3	The Gram-Schmidt Process: 6.2 Orthogonal Matrices: 6.3 The Method of Least Squares: 6.5	Section 6.2 # 1,3,5,7,9,11,13,17,19,25 Section 6.3 # 1,3,5,9,11,13,15,19,21,23
Dec 6 - 10	The Method of Least Squares: 6.5 Diagonalization of Quadratic Forms:8.1	Section 6.5 # 2,3,5,10,11,17,19,21 Section 8.1 # 1,3,5,7,8,11,15
Dec 13	Applications to Geometry: 8.2	Section 8.2 # 1,3,5,9,10a,b,d,j,13,15
Dec 18	Final!!	7:00-10:00 PM. Washburn 220