| Math 2270-2 | Linear Algebra, Spring 2017 |
| Instructor | G.B. Gustafson, PDF Syllabus Here, HTML Syllabus Here |
| Office hours | JWB 113 after class, and by appointment. (801) 581-6879 Email preferred. Office Hours: Door Card Hours and Email Address. |
| Lecture |
Linear Algebra 2270-2 meets at 8:00am MWF in AEB 320.
Computer Lab in LCB 115 on select Tuesdays. Information about Problem sessions Here. |
| Midterm Exams | Exams held from 7:30am to 9:25am on Friday 24 Feb and Friday 7 Apr. |
| Final Exam | Exam 7:30am to 10:00am on Friday 28 April, regular classroom. |
| Textbook | David C. Lay, Linear Algebra and Its Applications, 5E (2015). Book Cover Here |
| Online Grades | Web site for Utah Canvas |
Last change: Tuesday May 30: 17:10PM, 2017 |
Course Calendar Weeks 1-6
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First Week |
First exercise package
Here is due on Friday of Week 1 [13 Jan]. If the bookstore has no 2270 textbooks, then get the first chapter here: Chapter 1 The Math Center is open, with study areas, computers and free tutoring: Read this memo for details. Course Web page access to all files: Directory Here |
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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. The article can be found on Utah CANVAS. |
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Jan 9-13 |
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 16 |
Martin Luther King Day, no university classes |
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Jan 16-20 |
Week 2:
Monday no class. |
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Jan 23-27 |
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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Jan 30, 31, Feb 1-3 |
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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Jan 31 |
Lab
1: Intro to Maple, Meet in computer lab LCB 115, 7:30am. Due by Feb 28.
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Feb 3 |
Project Deadline Feb 3: Create or join a project group by email. Text file of projects in progress, subject to change or join/split group. Please write to Dr G for changes. Project List and members from the Feb 3 deadline is Here (created Feb 5). |
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Feb 7 |
Lab 2: Traffic Flow. Meet in computer lab LCB 115, 7:30am. Due by Feb 28. |
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Feb 6-10 |
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 by Feb 3. Use email. YouTube video on LU-decomposition Friday HW: Here |
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Feb 13-17 |
Week 6:
§3.2 Properties of determinants, continued,
§3.3 Cramer’s rule, volume and linear transformations,
Summary of delayed section §2.8 Subspaces of R^n,
§4.1 Vector spaces and subspaces.
Exam 1 in one week. Maple from home, UofU Library Remote Maple 18 How To Use It |
Course Calendar Weeks 7-13
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Feb 20 |
President's Day, no university classes |
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Tuesday |
Exam Review, LCB 215 4:00-5:30pm Review session blackboard photos directory Here |
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Feb 20-24 |
Week 7:
No class on Monday. Exam 1 on 24 Feb. |
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Feb 28 |
Lab 3: Adjacency Matrices and Airline routes. Meet in
computer lab LCB 115, 7:30am. Due by Mar 31. Maple from home, UofU Library Remote Maple 18 How To Use It |
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Feb 27, 28, Mar 1-3 |
Week 8:
§4.4 Coordinate Systems,
§4.5 The dimension of a vector space,
§4.6 Rank.
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Mar 6-10 |
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 Project Deadline: Group leader submits project draft by Mar 10. Final copy due May 2. |
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Mar 11-19 |
Week 10: Spring Break, no classes |
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Mar 21 |
Lab 4: Equilibrium Temperature Distributions (Ref: §2.5 Exercise 31). Meet in computer lab LCB 115, 7:30am. Due by Mar 31. Lab session resources Here |
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Mar 20-24 |
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 28 |
Lab 5: Hill Substitution Ciphers (Ref: §4.1). Meet in computer lab LCB 115, 7:30am. Due by May 4. A transcript of the session appears in the Labs Directory (see file lab5-hillcipher-problems-1-2.mw) |
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Mar 27-31 |
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, Friday HW: Here. Chapter 6 Slides: Here. Project updated abstracts and table of contents can be found Here. |
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Apr 3-7 |
Week 13: §6.3 Orthogonal projections, §6.4 The Gram–Schmidt process. Friday HW: Here is due May 4 |
| Exam 2 Review, 4:30-6pm April 4 | Blackboard photo directory |
Apr 7 |
Exam 2. |
Course Calendar Weeks 14-16
| Apr 11 |
Lab
6, Fibonacci and Lucas Sequences is due by May 4. Meet in computer lab LCB 115, 7:30am |
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Apr 10-14 |
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,
Friday HW:
Here is due May 4. Project Presentation Details were sent in email on 13 April., Chapter 6 Slides: Here, see advancedTopicsLinearAlgebra.pdf. Project updated abstracts and table of contents can be found Here. Midterm 2 was returned 14 Apr. Link to Solutions to Midterm 2 |
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Apr 17-21 |
Week 15:
§7.2 Quadratic Forms,
§7.3 Constrained Optimization,
§7.4 The singular value decomposition,
§7.5 Optional Applications to Image Processing and Statistics. Friday Apr 21: Student Presentations of Selected Projects Project Presentation Confirmed for Friday 21 April (list of names), Project updated abstracts and table of contents can be found Here. Friday HW: Here [last homework] due May 4. Chapter 6 Slides: Here. |
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Apr 24 |
Week 16: Student Presentations of Selected Projects (continued) |
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Apr 25 |
Classes end. Office hours end. Projects due on May 5 by email. Submit no paper, only PDF or DOC or DOCX and a ZIP file for computer code. Send to Dr G at this Email Address Final Exam Review. Location and time: AEB 320 at 4:30pm until 6:30pm on Tuesday April 25 Photos and a transcript of the review session are in this DIRECTORY Published Projects for Spring 2017 will be found Here [available May 12, 2017]. |
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Friday Apr 28 |
Final Exam 7:30-10:00 am in AEB 320. Old S2012 final exam: Questions and Answers from S2012 Cachen's final exam F2010: Here Cachen's's F2010 final exam study guide and essay question info Here. |
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 file of the list above, with week due: Bookmark PDF Here.Week 1 [start Monday Jan 9, due Friday Jan 13]
Week 2 [start Jan 13, due Jan 20] Week 3 [start Jan 20, due Jan 27]
Week 4 [start Jan 27, due Feb 3] Week 5 [start Feb 3, due Feb 10]
Week 6 [start Feb 10, due Feb 17] Week 7 [start Feb 17, due Feb 24]
Week 8 [start Feb 24, due Mar 3] Week 9 [start Mar 3, due Mar 10]
Week 10 [Spring Break Mar 11 to 19, nothing due]
Week 11 [start Mar 10, due Mar 24] Week 12 [start Mar 24, due Mar 31]
Week 13 [start Mar 31, due Apr 7] Week 14 [start Apr 7, due Apr 14]
Week 15 [start Apr 14, due Apr 21]
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 Maple 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).
Click Here for Utah Maple Help 2017
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 Remote Maple
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 Math Center room, or a classroom, provided there are 3 or more persons. Problem sessions reduce to consultations or tutorials when there are one or two persons. We work from clipboards and computers, discussing problems, textbook topics 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.
Extra credit is organized by chapter: Download Extra Credit Problems Here.
Semester Project
The due date for the semester project is actually three dates.- Create or join a group by Friday, February 3. Group leaders report by email (1) the topic, (2) a summary of what will be done, and (3) a list of group members with email addresses.
- The group leader submits a draft summary of the project results on March 10.
- The best projects will be identified and scheduled for classroom presentation
on April 21 and 24.
- 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 21 or 24.
Some topics and sample projects can be found on the Projects Page.
Published Projects Spring 2017. Presented projects and all submitted projects will appear Here.
Text file of projects in progress s2017, subject to change or join/split group. Please write email (not CANVAS) to Dr G for changes. Project List Here.
Presented and submitted projects from the 2270 course in Spring 2016 appear Here.
Presented and submitted projects from the 2270 course in Spring 2012 appear Here.