Math 2270-4 | Linear Algebra, Spring 2019 |
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 2270-4 meets at 12:55pm MTWF in JFB-102.
Computer Lab in LCB 115 on select Tuesdays, 12:55pm. Information about Problem sessions Here. |
Midterm Exams | Exams held from 12:50pm to 1:50pm on Friday 15 Feb, Friday 29 Mar, Friday 12 Apr. |
Final Exam | Exam 1:00pm to 3:00pm on Tuesday 30 April, regular classroom. |
Textbook |
David C. Lay, Linear Algebra and Its Applications, 5E (2015).
Book Cover Here
The default eBook includes Pearson MyLab. |
Online Grades | Web site for Utah Canvas |
Last change: Saturday December 08: 10:45AM, 2018 |
Course Calendar Weeks 1-6
First Week |
First exercise package
Here is due on Friday of Week 1 [11 Jan]. The default is an online textbook. If you require a printed book and 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 |
Reading |
Background: Read
Linear Equations no matrices |
Jan 7-11 |
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
|
Jan 15-18 |
Week 2: §1.4 The Matrix Equation A x = b , §1.5 Solution Sets of Linear Systems. Friday HW: Here. Chapter 1 slides Here |
Mon Jan 21 |
Martin Luther King Day, no university classes on Monday |
Jan 21-25 |
Week 3: §1.6 Applications of Linear System, §1.7 Linear Independence, §1.8 Introduction to Linear Transformations. Friday HW: Here |
Jan 28 to Feb 1 |
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 |
Tue Jan 29 |
Lab
1: Intro to Maple, Meet in computer lab LCB 115, 12:55pm. Due by Feb 28.
|
Feb 1 |
Semester Project Deadline Feb 1: Create or join a project group. Email to Dr G your Title, Group Members, Abstract, Contact email addresses. Please communicate edits/changes by email to Dr G until the last day of classes. Presentations of projects on April 22 and 23. The project is submitted by email, deadline midnight May 7. |
Tue Feb 5 |
Lab 2: Traffic Flow. Meet in computer lab LCB 115, 12:55pm. Due by Feb 27. |
Feb 4-8 |
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.
Missed the Project Deadline? Create or join a group by Feb 2. Use email. YouTube video on LU-decomposition Chemical Balance example from 1.6 PDF: maple shortcuts LU-Decomposition MAPLE DEMO from Friday 8 Feb TEXT: maple text and PDF: Output from the computation Chapter 2 slides Here (Determinants, PIVOT Theorem, Fund Thm Toolkit Sequences) Friday HW: Here ONE WEEK WARNING: Exam 1 is Friday February 15, 12:50pm to 1:50pm. Exam 1 Review, 4:30-6pm LCB 215 Thursday February 7, Blackboard photo directory |
Feb 11-15 |
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.
Friday HW:
Here.
Chapter 3 slides Here, Chapter 4 slides Here
|
Course Calendar Weeks 7-13
Mon Feb 18 |
President's Day, no university classes |
Feb 18-22 |
Week 7:
No class Monday: President's Day holiday |
Tue Feb 26 |
Lab 3: Adjacency Matrices and Airline routes. Meet in
computer lab LCB 115, 12:55pm. Due by Mar 29. |
Feb 25-28, Mar 1 |
Week 8:
§4.4 Coordinate Systems,
§4.5 The dimension of a vector space,
§4.6 Rank.
|
Mar 4-8 |
Week 9:
§4.7 Change of basis,
§4.8 optional, Applications to Difference Equations,
§4.9 optional, Applications to Markov chains,
Google search algorithm and Markov Chains: Perron-Frobenius Theorem,
Chapter 10 online at PearsonHigherEd.com,
§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 8. Final copy due by Midnight May 7. Project ABSTRACTS Click Here |
Tue Mar 5 |
Lab 4: Equilibrium Temperature Distributions (Ref: §2.5 Exercise 31). Meet in computer lab LCB 115, 12:55pm. Due by Mar 29. Lab session resources Here |
Mar 9-17 |
Week 10: Spring Break, no classes |
Mar 18-22 |
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 Project ABSTRACTS Orig abstracts Click Here
|
Tue Mar 19 |
Lab
5: Hill Substitution Ciphers (Ref: §4.1). Meet in computer lab
LCB 115, 12:55pm. Due by May 7. A transcript of the session appears in the
Labs Directory (see file lab5-hillcipher-problems-1-2.mw)
|
Thu Mar 21 |
ONE WEEK WARNING: Exam 2 is Friday March 29, 12:50pm to 1:50pm. |
Mar 25-29 |
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. Exam 2 references are in the Ch6 directory. EXAM 2: 12:50-1:50pm Friday March 29
|
Apr 1-5 |
Week 13: §6.3 Orthogonal projections, §6.4 The Gram–Schmidt process. Friday HW: Here is due May 7 |
Course Calendar Weeks 14-16
Tue Apr 9 |
Lab
6, Fibonacci and Lucas Sequences is due by May 7. Meet in computer lab LCB 115, 12:55pm Lab 5 has caused lost time for many due to off-by-one errors. Load the rewritten upstart file lab5-hillcipher-problems-1-2-5 located HERE |
Apr 8-12 |
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 7. Project Presentation Details will be sent to you in email on 12 April. Chapter 6 Slides: Here, especially files advancedTopicsLinearAlgebra.pdf and InvertibleMatrixTheorem.pdf (all parts a to x). |
Apr 5 |
EXAM 3: 12:50-1:50pm Friday April 12 Link to Student Solutions to 2019 Midterm 3 (uploaded after the exam) |
Apr 15-19 |
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 HW: Here [last homework] due May 7. Chapter 6 Slides: Here. Solutions to Exam 1, Exam 2 and Exam 3 can be found below in Week 16. |
Apr 22,23 |
Week 16: Student Presentations of Selected Projects (continued) |
Apr 24 |
Classes end. Office hours end. Projects due by Midnight May 7 by email. Submit no paper. Project must be PDF. Submit in addition DOC, DOCX and a ZIP file for computer code. Send to Dr G at this Email Address Solutions to S2019 Exams 1, 2 and 3 Exam 1 S2019 Typeset Solutions Exam 2 S2019 Student Solutions Exam 3 S2019 Student Solutions Final Exam Review. Location and time: LCB 215 at 4:30pm until 6:30pm on Wednesday April 24 Link to Final Exam Review Photos Here (uploaded after the session) Published Projects for Spring 2019 are found Here |
Tuesday Apr 30 |
Final Exam 1:00 to 3:00pm in JFB-102. 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, 23Printable file of the list above, with week due: Bookmark TEXT File Here.
Week 1 [start Monday Jan 7, due Friday Jan 11]
Week 2 [start Jan 11, due Jan 18] Week 3 [start Jan 18, due Jan 25]
Week 4 [start Jan 25, due Feb 1] Week 5 [start Feb 1, due Feb 8]
Week 6 [start Feb 8, due Feb 15] Week 7 [start Feb 15, due Feb 22]
Week 8 [start Feb 22, due Mar 1] Week 9 [start Mar 1, due Mar 8]
Week 10 [Spring Break Mar 9 to 17, nothing due]
Week 11 [start Mar 8, due Mar 22]
Week 12 [start Mar 22, due Mar 29] Week 13 [start Mar 29, due by May 7]
Week 14 [start Apr 5, due by May 7] Week 15 [start Apr 12, due by May 7]
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, in person 113 JWB or phone (801-581-6879).
Click Here for Utah Maple Help 2019
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 by May 7
Lab 6: Fibonacci and Lucas Sequences Due by May 7
Optional Lab 7: Polynomial Roots and the QR Method Due by May 7, 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 2017 How To Use Remote Maple
Problem Sessions
The problem sessions can be 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 a consultation or a tutorial 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 1. 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 8.
- Presentation selection is the week of April 14. Submit final drafts by Midnight April 17.
- The best projects will be identified and scheduled for classroom presentation
on April 22 and 23.
- The revised final semester project report in PDF form is due in email by Midnight May 7. 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 23.
Some topics and sample projects can be found on the Projects Page.
Published Projects for Spring 2019 are found Here
Text file of projects in progress s2019, 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 2018 appear Here.
Presented and submitted projects from the 2270 course in Spring 2017 appear 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.