Instructor:
Yunrong Zhu
(zhu_y@math.psu.edu,
McAllister 10)
Office Hours:
Tuesday 2:30pm -- 3:30pm and Thursday 9:00am--10:00am, or by appointment.
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)