by David C. Lay
Addison-Wesley (January 2006) ISBN-10: 0321280628 ISBN-13: 978-0321280626
PREREQUISITE:
MATH 2411: Calculus II, or with instructor's approval
HOURS, PLACE: TR 10-11:15 pm, AR (Arts Bld) 298.
INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: TR 2-3 pm (or by appointment)
WWW: http://math.ucdenver.edu/~aknyazev/
TEXTBOOKS:
Required:
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Linear Algebra and Its Applications, Updated plus MyMathLab Student Access Kit, 3/E
by David C. Lay Addison-Wesley (January 2006) ISBN-10: 0321280628 ISBN-13: 978-0321280626 |
GRADING will be based on MyMathLab assignments (40% extra credit), homework assignments (40%), 3 take-home quizzes: one quiz for every two chapters, 10% each (30%), and the final in-class test (30%). MATLAB computer project gives 20% extra credit.
IMPORTANT: Every student must open a personal MyMathLab account in order to complete the MyMathLab assignments. To start, visit MyMathLab registration or just go directly to CourseCompass. To register at MyMathLab/CourseCompass, use your personal MyMathLab access code provided with a new textbook copy bundled with MyMathLab, or with the MyMathLab: Student Stand Alone Access Kit Addison-Wesley ISBN-10: 032119991X ISBN-13: 9780321199911. When asked during the registration process, enter the Course ID knyazev58137. For any questions with the registration and use of the MyMathLab/CourseCompass, please see CourseCompass/MyMathLab Contact page or call Product Support at 1-800-677-6337.
SUBJECT:
Topics include systems of equations, Gaussian elimination with partial pivoting, LU--decomposition of matrices, matrix algebra, determinants, vector spaces, linear transformations, eigenvalues and applications.
CONTENTS:
The class will follow the outline below, touching on each major topic
in a depth that will be determined by the pace of the class.
Chapter 1 Linear Equations in Linear Algebra
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax = b
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
1.10 Linear Models in Business, Science, and Engineering (Optional, independent reading)
Chapter 2 Matrix Algebra2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.4 Partitioned Matrices
2.5 Matrix Factorizations
2.6 The Leontief Input=Output Model (Optional, independent reading)
2.7 Applications to Computer Graphics (Optional, independent reading)
2.8 Subspaces of R^n
2.9 Dimension and Rank
Chapter 3 Determinants3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer’s Rule, Volume, and Linear Transformations
Chapter 4 Vector Spaces4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets; Bases
4.4 Coordinate Systems
4.5 The Dimension of a Vector Space
4.6 Rank
4.7 Change of Basis
4.8 Applications to Difference Equations (Optional, independent reading)
4.9 Applications to Markov Chains (Optional, independent reading)
Chapter 5 Eigenvalues and Eigenvectors5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
5.5 Complex Eigenvalues (Optional, independent reading)
5.6 Discrete Dynamical Systems (Optional, independent reading)
5.7 Applications to Differential Equations (Optional, independent reading)
5.8 Iterative Estimates for Eigenvalues (Optional, independent reading)
Chapter 6 Orthogonality and Least Squares6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram-Schmidt Process
6.5 Least-Squares Problems (Optional, independent reading)
6.6 Applications to Linear Models (Optional, independent reading)
6.7 Inner Product Spaces (Optional, independent reading)
6.8 Applications of Inner Product Spaces (Optional, independent reading)
Chapter 7 Symmetric Matrices and Quadratic Forms (Optional, independent reading)7.1 Diagonalization of Symmetric Matrices
7.2 Quadratic Forms
7.3 Constrained Optimization
7.4 The Singular Value Decomposition
7.5 Applications to Image Processing and Statistics
ONLINE ONLY Chapter 8 The Geometry of Vector Spaces (Optional, independent reading)8.1 Affine Combinations
8.2 Affine Independence
8.3 Convex Combinations
8.4 Hyperplanes
8.5 Polytopes
8.6 Curves and Surfaces
Chapter 9 Optimization (Optional, independent reading)9.1 Matrix Games
9.2 Linear Programming — Geometric Method
9.3 Linear Programming — Simplex Method
9.4 Duality
Spring 2007 CLAS Academic Policies
The following policies pertain to all students and are strictly adhered to by the College of Liberal Arts and Sciences (CLAS).
Every student MUST check and verify their schedule prior to the published drop/add deadlines. Failure to verify a schedule is not sufficient reason to justify a late add or drop later in the semester. It is the student’s responsibility to make sure that their schedule is correct prior to the appropriate deadlines.
CLAS students must always have an accurate mailing and email address. Email is the official method of communication for all University of Colorado Denver business. Go to http://www.ucdenver.edu/registrar to update and/or change your email address.
Students are NOT automatically added to a course off a wait list after wait lists are dropped. If a student is told by a faculty member that they will be added off the wait list, it is the responsibility of the student to complete the proper paperwork to add a course. Students are NOT automatically added to a course from the wait list after the 5th day of the semester when wait lists are dropped.
Students must complete and submit a drop/add form to make any schedule changes. Students are not automatically dropped from a class if they never attended, stopped attending or do not make tuition payments.
Late add’s will be approved only when circumstances surrounding the late add are beyond the student’s control and can be documented independently. This will require a petition and documentation from the student. Late add’s will only be approved if the student has not taken any exams, quizzes, or has not completed any other graded assignments. Independent verification of this from the professor of record will be required. Please note that the signature of a faculty member on an add form does not guarantee that a late add petition will be approved.
Late drops will be approved only when circumstances surrounding the late drop are beyond the student’s control and can be documented independently. This will require a petition and documentation from the student. Please note that the signature of a faculty member does not guarantee that a late drop petition will be approved.
Students wishing to graduate in spring of 2007 must meet with their academic advisor by the end of the drop/add period to obtain a graduation application. This application must be completed and submitted by 5 PM on January 31, 2007. You can obtain an application ONLY after meeting with your academic advisor. There are no exceptions to this policy or date.
Students are responsible for completing financial arrangements with financial aid, family, scholarships, etc. to pay their tuition. Students will be responsible for all tuition and fees for courses they do not officially drop using proper drop/add procedures and forms.
Students who drop after the published drop/add period will not be eligible for a refund of the COF hours or tuition.
Spring 2007 Important Dates
January 16, 2007; First day of Class
January 18, 2007; Last day to be added to a wait list
January 18 – January 31, 2007; Students are responsible for verifying an accurate spring 2007 course schedule via the SMART registration system. Students are NOT notified of their wait-list status by the university. All students must check their scheduled prior to January 31, 2007 for accuracy.
January 19, 2007 at 5PM; Wait lists are dropped. Any student who was not added to a course automatically from the wait list by this date and time MUST complete a drop/add form to be added to the class. Students are NOT automatically added to the class from the wait list after this date and time.
January 22, 2007; First day an instructor may approve a request to add a student to a course using the Schedule Adjustment Form (drop/add form).
January 25, 2007; Last day to add a course using the SMART Web Registration system. Students MUST check their registration to verify what classes they are enrolled in.
January 31, 2007 at 5 PM; Last day to add structured courses without a written petition for a late add. This is an absolute deadline and is treated as such. This deadline does not apply to independent study, internships, and late-starting modular courses.
January 31, 2007 at 5 PM; Last day to drop a spring 2007 course with a full tuition refund and no transcript notation. Drops after this date will appear on your transcript. This is an absolute deadline and is treated as such.
January 31, 2007 at 5 PM; Last day to completely withdraw from all spring 2007 courses with a full tuition refund and no transcript notation. Drops after this date will appear on your transcript. This is an absolute deadline and is treated as such.
January 31, 2007 at 5 PM; Last day for students to apply for Spring 2007 Graduation. Students MUST see their CLAS advisor to obtain a Graduation Application.
January 31, 2007 at 5 PM; Last day to request pass/fail option for a course.
January 31, 2007 at 5 PM: Last day to request a no credit option for a course.
January 31, 2007 at 5 PM: Last day to register for a Candidate for Degree.
January 31, 2007 at 5 PM: Last day to petition for a reduction in thesis or dissertation hours.
April 2, 2007 at 5 PM; Last day for Non-CLAS students to drop individual classes or withdraw from all classes without a petition and special approval from the student’s academic Dean. This is treated as an absolute deadline.
April 13, 2007 at 5 PM; Last day for CLAS students to drop individual classes or withdraw from all classes without a petition and special approval from the student’s academic Dean. This is treated as an absolute deadline.
No schedule changes will be granted once finals week has started. There are NO exceptions to this policy.