Course Calendar Weeks 1-6
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First Week |
First exercise package
Here is due on Friday of Week 1 [15 Jan]. The bookstore has no 2270 textbooks. Get the first chapter here: Chapter 1 The Math Center is open, with study areas, computers and free tutoring: Read this memo for details. |
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Reading |
Background: Read Linear Equations no matrices. A major goal of the course is to be able to read and understand Gilbert Strang's article The Fundamental Theorem of Linear Algebra. |
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Jan 11-15 |
Week 1: §1.1 Systems of Linear Equations, §1.2 Row Reduction and Echelon Forms, §1.3 Vector Equations. Friday HW: Here, one problem. Chapter 1 slides Here |
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Jan 18 |
Martin Luther King Day, no university classes |
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Jan 19-22 |
Week 2: Monday no class, §1.4 The Matrix Equation A x = b , §1.5 Solution Sets of Linear Systems. Friday HW: Here. Chapter 1 slides Here |
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Jan 25-29 |
Week 3: §1.6 Applications of Linear System, §1.7 Linear Independence, §1.8 Introduction to Linear Transformations. Friday HW: Here |
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Feb 1-5 |
Week 4: §1.9 The Matrix of a Linear Transformation, Coordinates, Differential Geometry background §1.10 Optional Linear Models in Business, Science, and Engineering, §2.1 Matrix operations, §3.1 Determinants (Exercises 15-18, Sarrus' Rule), §2.2 The Inverse of a Matrix. §2.3 Characterizations of Invertible Matrices. Friday HW: Here. Chapter 2 slides Here |
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Feb 2 |
Lab
1: Intro to Maple, Meet in computer lab LCB 115, 7:30am. Due by Fri, Feb 26.
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Feb 9 |
Lab 2: Traffic Flow. Meet in computer lab LCB 115, 7:30am (was Feb 16). Due by Mon, Feb 29. |
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Feb 8-12 |
Week 5:
§2.4 Partitioned Matrices,
§2.5 Matrix Factorizations,
§3.1 Introduction to determinants. Continued from Week 4.
§2.6 Optional The Leontief Input–Output Model,
§2.7 Optional Applications to Computer Graphics,
§2.8 Subspaces of R^n, Delayed.
§2.9 Dimension and Rank, Delayed.
Project Deadline: Create or join a group. YouTube video on LU-decomposition Friday HW: Here |
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Feb 15 |
President's Day, no university classes |
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Feb 15-19 |
Week 6: Monday no class, §3.2 Properties of determinants, continued, §3.3 Cramer’s rule, volume and linear transformations. Exam 1. Friday HW: Here. Chapter 3 slides Here Maple from home, UofU Library Remote Maple 18 How To Use It |
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Feb 19 |
Exam 1. |
Course Calendar Weeks 7-13
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Feb 22-26 |
Week 7:
Summary of delayed section §2.8 Subspaces of R^n,
§4.1 Vector spaces and subspaces,
§4.2 Null spaces, column spaces, and linear transformations,
Summary of delayed section §2.9 Dimension and Rank, §4.3 Linearly independent sets and bases.
Friday HW:
Here. |
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Mar 1 |
Lab 3: Adjacency Matrices and Airline routes. Meet in
computer lab LCB 115, 7:30am Maple from home, UofU Library Remote Maple 18 How To Use It |
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Feb 29 to Mar 4 |
Week 8:
§4.4 Coordinate Systems,
§4.5 The dimension of a vector space,
§4.6 Rank.
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Mar 7-11 |
Week 9:
§4.7 Change of basis,
§4.8 optional, Applications to Difference Equations,
§4.9 optional, Applications to Markov chains,
§5.1 Eigenvectors and eigenvalues,
Appendix B: Review of complex numbers. Chapter 5 Slides: Here, Friday HW: Here |
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Mar 14 to 18 |
Week 10: Spring Break, no classes |
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Mar 22 |
Lab 4: Equilibrium Temperature Distributions (Ref: §2.5 Exercise 31). Meet in computer lab LCB 115, 7:30am. Lab session resources Here |
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Mar 21-25 |
Week 11:
Appendix B: Review of complex numbers,
§5.2 The characteristic equation,
§5.3 Diagonalization,
§5.4 Eigenvectors and linear transformations.
Chapter 5 Slides: Here, Friday HW: Here |
Mar 29 |
Lab 5: Hill Substitution Ciphers (Ref: §4.1). Meet in computer lab LCB 115, 7:30am. A transcript of the session appears in the Labs Directory (see file lab5-hillcipher-problems-1-2.mw) |
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Mar 28 to Apr 1 |
Week 12: §5.5 Complex eigenvalues, §5.6 optional, Discrete Dynamical Systems, §5.7 optional, Applications to differential equations, §5.8 optional, Iterative Estimates for Eigenvalues, §6.1 Inner product, length and orthogonality, §6.2 Orthogonal sets, Project Deadline: Group leader submits project draft. Final copy due May 2. Friday HW: Here. Chapter 6 Slides: Here. |
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Apr 4-8 |
Week 13: §6.3 Orthogonal projections, §6.4 The Gram–Schmidt process. Friday HW: Here is due May 4 |
Apr 8 |
Exam 2. |
Course Calendar Weeks 14-16
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Week 14: Apr 11-15 |
Apr 12: Lab2270final-solutions-student-S2016
6, Fibonacci and Lucas Sequences is due May 2. Meet in computer lab LCB 115, 7:30am |
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Apr 11-15 |
Week 14:
§6.4 The Gram–Schmidt process (continued); reference for A=QR in advancedTopicsLinearAlgebra.pdf,
§6.5 Least-squares problems,
§6.6 optional, Application to linear models,
§6.7 optional, Inner product spaces,
§6.8 optional, Applications of Inner Product Spaces,
§7.1 Diagonalization of symmetric matrices,2270final-solutions-student-S2016
§7.2 Quadratic Forms.
Friday HW:
Here is due May 4. Semester Project email 13 April Project Presentation Details, |
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Apr 18-22 |
Week 15:
§7.3 Constrained Optimization,
§7.4 The singular value decomposition,
§7.5 Optional Applications to Image Processing and Statistics. Apr 22: Student Presentations of Selected Projects Semester Project topics: Project Presentation Updated List, Friday HW: Here [last homework] due May 4. |
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Apr 25 |
Week 16: Student Presentations of Selected Projects (continued) and Final Exam Review. |
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Apr 26 |
Classes end. Office hours end. Projects due on Monday May 2 Published Projects for Spring 2016 can be found Here. |
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Thursday Apr 28 |
Final Exam 7:30-10:00 am in AEB 320. Gustafson's final exam S2012: Questions and Answers Cachen's final exam F2010: Here Cachen's's F2010 final exam study guide and essay question info Here. |
Syllabus
Math 2270-2 Linear Algebra
Instructor.
Professor Grant B. Gustafson
Email: See the online door card: Here.
Office: JWB 113
Syllabus: HTML
Here.
Course Web page, access to all files: Directory Here
Office Hours: MWF after class in JWB 113
Additional office hours Here.
Meetings.
Time: MWF 8:00am until 9:20am
Location: AEB 320
Prerequisites. MATH 2210 OR MATH 1260 OR MATH 1280
Textbook. Linear Algebra and Its Applications, Fifth Edition by David C. Lay et al, ISBN 978-0-321-98238-4 and
ISBN 0-321-98238-X.
Supplement:
Student Study Guide for Linear Algebra and Its Applications 5th Edition, David C. Lay el (2015).
ISBN-13: 978-0321982575 and
ISBN-10: 0321982576.
Homework, Labs, Problem Sessions, Extra Credit, Semester Project
Homework Packages
Homework is normally started in the 7-day period before the Friday due date.A complete list of exercises to be submitted for grading:
1.1: 7, 11, 19, 25, 34.
1.2: 1, 7, 11, 13, 15, 17, 19, 23, 25, 28, 33
1.3: 11, 13, 15, 21, 25, 34
1.4: 6, 8, 17, 23, 27, 31, 32
1.5: 7, 8, 10, 29, 31, 33, 35
1.6: 1, 7, 13
1.7: 7, 13, 17, 27, 37
1.8: 17, 20, 25, 31
1.9: 15, 25, 31, 39
2.1: 13, 18, 23, 28, 29
2.2: 11, 23, 24, 35;
2.3: 7, 13, 14, 17, 19, 20, 21, 33, 35
2.4: 3, 5, 15, 21, 23
2.5: 3, 7, 11, 25
3.1: 5, 9, 11, 15, 25, 27, 29, 31
3.2: 5, 9, 15, 19, 25
3.3: 3, 5, 13, 19, 31
4.1: 1, 5, 7, 11, 13, 21, 27
4.2: 3, 5, 11, 15, 23, 31
4.3: 5, 9, 11, 13, 15, 19, 34
4.4: 3, 7, 9, 13, 27
4.5: 5, 7, 11, 13, 21
4.6: 1, 3, 5, 7, 15, 21
5.1: 7, 13, 17, 23, 29, 37(M)
5.2: 3, 7, 13, 17, 25(M)
5.3: 5, 9, 19, 29, 35(M)
5.4: 5, 9, 11, 15
5.5: 5, 9, 13, 19
6.1: 11, 13, 17, 29, 31
6.2: 9, 11, 13, 15, 21, 27
6.3: 1, 3, 9, 11, 15
6.4: 5, 11, 13, 19
6.5: 3, 5, 7, 11, 15, 25
7.1: 9, 13, 17, 19, 35
7.2: 5, 7, 11, 17(M)
7.3: 1, 5, 9
7.4: 3, 7, 13, 15, 17, 23
Printable bookmark file of the list above, with week due, Here.Week 1 [start Monday Jan 11, due Friday Jan 15]
Week 2 [start Jan 15, due Jan 22] Week 3 [start Jan 2, due Jan 29]
Week 4 [start Jan 29, due Feb 5] Week 5 [start Feb 5, due Feb 12]
Week 6 [start Feb 12, due Feb 19] Week 7 [start Feb 19, due Feb 26]
Week 8 [start Feb 26, due Mar 4] Week 9 [start Mar 4, due Mar 11]
Week 10 [Spring Break Mar 12 to 20, nothing due]
Week 11 [start Mar 11, due Mar 25] Week 12 [start Mar 25, due Apr 1]
Week 13 [start Apr 1, due Apr 8] Week 14 [start Apr 8, due Apr 15]
Week 15 [start Apr 15, due Apr 22]
Maple Labs
Maple labs 1 to 6 are due as indicated, usually 7 days or more after the LCB 115 session. The labs are distributed in PDF format and also in MW and MPL formats suited for input into Maple. Download what you need from the Labs DirectoryUtah Maple Help gives examples of maple coding that can be mouse-copied into a maple session. Recorded here is how to setup maple as a worksheet, how to print and how to save files.
Also find here how to use the laylinag package described in the 2270 textbook (Lay, Lay, Calvis 2015). Questions arising from these documents can be answered in the Math Center, by email to me, or in person 113 JWB or phone (801-581-6879).
Utah Maple Help 2016
Lab 1 Due at the last February class
Lab
2: Traffic Flow Due at the last February class.
Resources and corrections are located in the Lab 2 source Directory
Lab 3: Adjacency Matrices and Airline Routes Due at the last March class
Lab 4: Equilibrium Temperature Distributions Due at the last March class
Lab 5: Hill Substitution Ciphers Due May 2
Lab 6: Fibonacci and Lucas Sequences Due May 2
Optional Lab 7: Polynomial Roots and the QR Method Due May 2, replaces any missing Lab
Remote Maple: Running Maple from Home
Maple can be run from home, a laptop, or even a phone or tablet, using a minimal internet connection. Instructions here for the UofU Library and the Math Department computers:Maple from home, UofU Library Remote Maple 18 How To Use It
Problem Sessions
The problem sessions are scheduled for fixed times during the week. You may add or remove your name from the problem session list of days and times, by sending email. The list is updated whenever this happens.View the Problem Session List for locations and times.
The default location is JWB 113. We would move from this office to a classroom or Math Center room, provided there are 3 or more persons. Problem sessions reduce to tutorials when there are one or two persons. We work from clipboards and computers, discussing problems and exam questions.
Extra Credit Problems
One collection of extra credit problems are matched to Otto Bretscher's textbook on
linear algebra. A second collection of extra credit problems is matched to Gilbert Strang's linear algebra textbook. Some problems are independent of any textbook. Credit is one-to-one for missed homework, whatever the reason, without any
effort to match subjects or chapters from the current textbook.
The extra credit PDF files, organized by chapter, are located Here.
Semester Project
The due date for the semester project is actually three dates.- Create or join a group by Friday, February 12. Group leaders report by email (1) the topic, (2) a summary of what will be done, and (3) a list of group members.
- The group leader submits a draft summary of the project results on April 1.
- The best projects will be identified and scheduled for classroom presentation
on April 22 and 25.
- The revised final semester project report in PDF form is due in email by May 2. A paper print of the PDF is not expected, although classroom copies and/or an internet link is recommended, if your group has a presentation on April 22 or 25.
Some topics and sample projects can be found on the Projects Page Here.
Published Projects Spring 2016. Presented projects and all submitted projects appear Here.
Presented and submitted projects from the 2270 course in Spring 2012 appear Here.