Instructor:
Ming-Hsuan Kang
Office Hour: M 4:30~5:30 T 3:30~5:00 PM or by
appointment
Office : McAllist 012
Website:
http://www.math.psu.edu/kang_m/
Email: kang_m@math.psu.edu
Course
Coordinator:
Misha Guysinsky
(guysin_m@math.psu.edu)
Course
Description:
Systems of linear equations; matrix algebra; determinants;
eigenvalues and eigenvectors; orthogonality and least
squares.
Prerequisite:
Math 110 or 140.
Textbook:
Linear
Algebra and its Applications,
third edition update, by David Lay, published by Pearson/Addison
Wesley.
Midterm:
A 75-minute evening examination will be held on (TBA), 2007 at
6:30.
Final
Exam:
A comprehensive final examination, covering all the content of the
course, will be given. The final examination period will start
on Monday, December 17 and will end on Friday, December 21. Students
should not make plans to leave University Park before Saturday,
December 22.
Students must bring their student ID cards for all exams.
Conflict
and Makeup Exams:
Only students with official University conflicts, or a valid,
documented excuse, will be permitted to schedule the conflict or
makeup exams. Students must sign up for conflict or makeup exam at
least 48 hours in advance of the exam date.
Grading
Policy:
Grades will be assigned on the basis of 300 points distributed
as follows:
50 points
for homework and quizzes
100
points for the midterm exam
150 points for the final exam
Final grades will be assigned as
follows:
A
275-300
A- 265-274
B+ 255-264
B 245-254
B- 235-244
C+ 225-234
C
210-224
D
190-209
F
0-189
Academic
Integrity:
The following is the required academic integrity statement for
this course: During QUIZZES and EXAMS, the use of books,
calculators or notes of any sort is not permitted and
communicating with anyone or copying anything from anyone
is
not permitted. Cell phones must be turned OFF.
Also see
the Student
Guide to the University, Policy 49--20.
Course
outline:
(The number after each section is the
approximate number of class periods).
I. LINEAR EQUATIONS IN
LINEAR ALGEBRA
1.1 Systems of Linear Equations
(1.5)
1.2 Row Reduction and Echelon Forms
(1.5)
1.3 Vector Equations (1)
1.4 The Matrix Equation Ax=b (1)
1.5
Solution Sets of Linear Systems (1)
1.7 Linear
Independence (1)
1.8 Introduction to Linear
Transformations (1)
1.9 The Matrix of a Linear
Transformations (1)
II. MATRIX ALGEBRA
2.1
Matrix Operations (1)
2.2 The Inverse of a
Matrix (1)
2.3 Characterizations of Invertible
Matrices (1)
2.8 Linear Subspaces (1.5)
2.9 Dimension and Rank (1.5)
III. DETERMINANTS
3.1 Introduction to Determinants (1)
3.2
Properties of the Determinants +Cramer's rule from 3.3 (1)
V.
EIGENPROBLEMS
5.1
Eigenvalues and Eigenvectors (1)
5.2 The Characteristic Equation (1)
5.3 Diagonalization (1)
5.5
Complex Eigenvalues (1)
VI. ORTHOGONALITY AND LEAST SQUARES
6.1 Inner Product, Length, and Orthogonality
(1)
6.2 Orthogonal Sets
(1)
6.3 Orthogonal
Projections (1)
6.4 The
Gram-Schmidt Process (no Factorization) (1)
6.5 Least-Squares Problems (1)
VII. SYMMETRIC MATRICES
7.1 Diagonalization of Symmetric Matrices. (1)
HW1:
(Due 9/6)
1.1 #5,7,13,15,19,22,23,24,26
1.2
#1,3,5,7,9,11,15,17,21,22
HW2:
(Due 9/13)
1.3 #5,6,9,10,11,13,15,17,19,22,23,32
1.4
#1,3,5,7,9,11,13
HW3:
(Due 9/20)
1.4 #17,19,21,23,25
1.5
#3,7,11,13,17,19,23,29,30,31,32
HW4:
(Due 9/27)
1.7 #1,5,9,15,17,20,21,22
1.8 #3,5,7,9,11,13,15,21,31,32,33
HW5:
(Due 10/4)
1.9 #1,3,5,7,9,15,17,19,21,23,24
2.1 #1,3,5,9,22,27,39
HW6:
(Due 10/11)
2.2 #1,5,7,9,10,14,16,29,33,35
2.3 #1,3,4,11,12,13,29,24,30
HW7:
(Due 10/25)
2.8 #1,3,7,17,19,21,22,23,24
2.9 #1,3,5,8,9,15,17,18
HW8:
(Due 11/1)
3.1 #1,5,9,12,15,16
3.2 #5,6,11,15,17,20,27,28
3.3 #11,12,13
HW9:
(Due 11/8)
5.1 #1,2,3,4,9,10,15,16,21,22
5.2 #1,2,4,9,10,12,16,21,22
HW10
(Due 11/15)
5.3 #1,2,3,7,9,13,14,19,20,21,22,23,24
5.5 #1,3,4,7,8,13,14,15
HW11
(Due 11/29)
6.1 #1,2,3,4,11,12,19,20,25,26
6.2 #1,2,7,9,11,12,17,18,20,23,24
HW12
(Due 12/6)
6.3 #1,2,3,4,11,12,15,21,22
6.4 #1,2,711,12,15,16,17,18
HW13
(Due 12/11)
6.5 #1,3,9,11,17,18
7.1 #1,3,13,17,18,25,26
Quiz
Quiz1(9/13): 1.1~1.4 quiz, solution
Quiz2(9/27): 1.4~1.8 quiz, solution
Quiz3(10/9): 1.9~2.2 quiz, solution
Quiz4(10/25): 2.8~2.9 quiz, solution
Quiz5(11/8): 3.1~5.2 quiz, solution
Quiz6(11/29): 5.3~6.2 quiz, solution
Quiz7(12/11): 6.3~7.1 quiz, solution
Midterm:
Time: Oct, 15 ,
6:30~7:45 PM
Room: Sparks 121
Range: 1.1 to 2.3
Practice exam: FA06
Final Exam:
Time: Dec, 18 ,
2:30 PM
Room: Forum 102
Range: 1.1 to 7.1
Practice exam: FA03Room: Forum 102
Answer key: bccda|bccdb|bddca|dbbcd|dcdba
Practice exam: SP03