arminstraub.com

Fall 2014: Applied Linear Algebra (Math 415)

Overview

Instructor Armin Straub
247A Illini Hall
astraub@illinois.edu
(217) 300-0426 (please use e-mail whenever possible)
Office hours MW, 12:30-1:30pm, or by appointment
Lecture Section AL1 meets MWF, 9:00-9:50am, in 151 Everitt.
Section AL2 meets MWF, 11:00-11:50am, in 151 Everitt.
Help session Mondays, 4:00-6:00pm, in 441 Altgeld Hall
Tuesdays, 5:00-7:00pm, in 441 Altgeld Hall
Wednesdays, 4:00-6:00pm, in 441 Altgeld Hall
Thursdays, 5:00-7:00pm, in 441 Altgeld Hall
Online questions https://piazza.com/illinois/fall2014/math415
Midterm exams Thursday, September 25 — 7:00-8:20pm
Thursday, October 23 — 7:00-8:20pm
Thursday, November 20 — 7:00-8:20pm
Final exam Friday, December 12 — 7:00-10:00pm
(Conflict Final Exam: Monday, December 15 — 7:00-10:00pm)
Text Linear Algebra and Its Applications,
4th Edition, by Gilbert Strang (Cengage Publishing, 2011)
Syllabus syllabus.pdf
Emergency information
Online Grades Compass 2g

Getting help

There is a number of options for you to get help with any questions.

  • Once a week, you meet in small groups for discussion sections with a TA and you will have a chance to ask questions, especially those which concern the discussion problems posted each week.
  • Instead of TA office hours, we will offer help sessions. Four evenings a week, a classroom is staffed by two of our TAs and you are free to go and ask any questions you may have. See above for times and location.
  • Moreover, we are (experimentally) using Piazza for online discussions and questions. Rather than emailing questions to me or a TA, you are strongly encouraged to post them on Piazza so that the whole class can join and benefit from the discussion (you have the option to post your question anonymously). You can find our class at https://piazza.com/illinois/fall2014/math415/home.
  • If you still have any questions, please visit me during office hours; send me an email; or ask before, during or after class.

Lecture notes

For lectures, I will use a mix of interactive slides and the blackboard. Both pre-lecture notes (with blanks) and post-lecture notes are posted here.

My personal suggestion on how to use them:

  • before lecture: have a quick look (just a couple of minutes) at the pre-lecture notes to see where things are going
  • during lecture: take a minimal amount of notes (everything on the screens will be in the post-lecture notes) and focus on the ideas
  • after lecture (as soon as possible): go through the pre-lecture notes and try to fill in all the blanks
  • then compare with the post-lecture notes

Since I am writing the pre-lecture notes a week ahead of time, there is usually some minor differences to the post-lecture notes; examples may be added or transformed to practice problems, and the content might be a bit rearranged to make each lecture stand by itself. In particular, the numbering is not consistent between the pre-lecture and post-lecture slides; the only reason examples are numbered at all, is to make it easier to refer to them in questions ("I have a question about Example 27 in Lecture 3").

Pre-lecture notes

The lecture slides are grouped by topics and so the files below usually do not correspond to individual lectures (see the post-lecture notes below for that).

# Slides Topic Textbook
1 slides01.pdf Introduction to systems of linear equations Chapters 1.3 / 2.2
2 slides02.pdf The geometry of linear equations Chapter 1.2
3 slides03.pdf Matrix operations Chapter 1.4
4 slides04.pdf LU decomposition Chapter 1.5
5 slides05.pdf The inverse of a matrix Chapter 1.6
6 slides06.pdf Application: finite differences Chapter 1.7
7 slides07.pdf Vector spaces and subspaces Chapter 2.1
8 slides08.pdf Solving Ax=0 and Ax=b (null and column spaces) Chapter 2.2
9 slides09.pdf Linear independence, basis and dimension Chapter 2.3
10 slides10.pdf The four fundamental subspaces Chapter 2.4
11 slides11.pdf Linear transformations Chapter 2.6
12 slides12.pdf Orthogonal vectors and subspaces Chapter 3.1
13 slides13.pdf Application: directed graphs Chapter 2.5
14 slides14.pdf Orthogonal bases and projections Chapter 3.2-4 (in parts)
15 slides15.pdf Least squares Chapter 3.3
16 slides16.pdf Gram-Schmidt Chapter 3.4
17 slides17.pdf Application: Fourier series Chapter 3.4
18 slides18.pdf Determinants Chapter 4.2
19 slides19.pdf Eigenvectors and eigenvalues Chapter 5.1
20 slides20.pdf Diagonalization Chapter 5.2/5.6
21 slides21.pdf Difference equations, transition matrices Chapter 5.3
22 slides22.pdf Differential equations, matrix exponentials Chapter 5.4

Post-lecture notes

Below are the notes from class containing what we actually covered.

Date Slides Suggested practice problems
all lectures-combined.pdf (all lecture slides in one large file)
08/25 lecture01.pdf Section 1.3: 1, 4, 5, 10, 11
08/27 lecture02.pdf Section 1.3: 13, 20; Section 2.2: 2 (only reduce A,B to echelon form)
08/29 lecture03.pdf read Section 1.2; Section 1.3: 9 (drawing optional)
09/03 lecture04.pdf redo examples from class by hand; Section 2.1: 22
09/05 lecture05.pdf problems at end of notes; Section 1.4: 1, 2, 12
09/08 lecture06.pdf problems at end of notes; Section 1.4: 11, 14, 22, 30
09/10 lecture07.pdf problems at end of notes; Section 1.5: 4, 11, 23, 29
09/12 lecture08.pdf Section 1.6: 6, 10, 11, 35, 38, 40, 49
09/15 lecture09.pdf do the LU decomposition in the notes yourself; Section 1.7: 4, 6
09/17 lecture10.pdf do the practice exam (solutions posted by Monday); Section 2.1: 5 (very optional)
09/19 no class
09/22 lecture11.pdf problems at end of notes
09/24 lecture12.pdf get ready for the midterm!
09/26 lecture13.pdf problems at end of notes
09/29 lecture14.pdf Section 2.3: 1, 2, 3, 5, 9, 11, 16
10/01 lecture15.pdf problems at end of slides09.pdf; Section 2.3: 19, 21, 22, 27
10/03 lecture16.pdf Section 2.3: 20, 24, 30, 31, 32, 35
10/06 lecture17.pdf look at Example 11 and practice problems at end of notes
10/08 lecture18.pdf practice problem at end of notes; Section 2.6: 5, 6, 36, 37
10/10 lecture19.pdf Section 2.6: 7, 15, 17; Section 3.1: 1, 5
10/13 lecture20.pdf Section 3.1: 7, 15, 38
10/15 lecture21.pdf Section 3.1: 16, 21, 42, 43; Section 2.5: 6 (only matrix), 10 (only draw)
10/17 lecture22.pdf practice problems at end of notes
10/22 lecture23.pdf get ready for the midterm! (test yourself with more practice problems in the notes)
10/24 lecture24.pdf Section 3.2: 17, 22, 24
10/27 lecture25.pdf Section 3.3: 7, 8, 12
10/29 lecture26.pdf Section 3.3: 2, 3, 6, 13
10/31 lecture27.pdf Section 3.3: 18; Section 3.4: 9, 12, 13 (no factorization)
11/03 lecture28.pdf practice problem at end of notes; Section 3.4: 16, 27
11/05 lecture29.pdf go through the calculus of the last example (Example 9)
11/07 lecture30.pdf practice problem at end of notes; Section 4.2: 5, 7
11/10 lecture31.pdf practice problem at end of notes; Section 4.2: 25; Section 4.3: 31
11/12 lecture32.pdf practice problems at end of notes; Section 5.1: 20, 22
11/14 lecture33.pdf practice problem at end of notes; Section 5.1: 23, 34
11/17 lecture34.pdf practice problem at end of notes; fill in details of Fibonacci example
11/19 lecture35.pdf get ready for the midterm!
12/01 lecture36.pdf Section 5.3: 9, 12
12/03 lecture37.pdf review example on diagonalization at end of notes
12/05 lecture38.pdf do Example 6 in notes (then compare with the included solution)
12/10 lecture39.pdf get ready for the final!
all lectures-combined.pdf (all lecture slides in one large file)

Discussion problems

The first set of discussion problems will be discussed in the discussion sections meeting in the second week of the semester.

Here is a list of all discussion sections:

# Time Place TA
AD1 R 3:00-3:50 2 ILL HALL Hakobyan, Tigran
AD2 R 9:00-9:50 149 HENRY BLD Karimi, Pouyan
AD3 R 10:00-10:50 137 HENRY BLD Etedadi Aliabadi, Mahmood
AD4 R 11:00-11:50 2 ILL HALL Oyengo, Michael Obiero
ADA T 8:00-8:50 241 ALTGELD Karimi, Pouyan
ADD T 11:00-11:50 341 ALTGELD Nell, Travis
ADF T 12:00-12:50 2 ILL HALL Bernshteyn, Anton
ADB T 9:00-9:50 137 HENRY BLD Karimi, Pouyan
ADC T 10:00-10:50 137 HENRY BLD Etedadi Aliabadi, Mahmood
ADE R 1:00-1:50 2 ILL HALL Oyengo, Michael Obiero
ADG T 2:00-2:50 441 ALTGELD Gehret, Allen
ADH T 3:00-3:50 147 ALTGELD Hakobyan, Tigran
ADI T 4:00-4:50 143 HENRY BLD Nell, Travis
ADJ R 8:00-8:50 241 ALTGELD Karimi, Pouyan
ADK R 9:00-9:50 137 HENRY BLD Rehfuss, Nathan
ADL R 10:00-10:50 149 HENRY BLD Gehret, Allen
ADM R 11:00-11:50 341 ALTGELD Gehret, Allen
ADN R 12:00-12:50 2 ILL HALL Bernshteyn, Anton
ADO T 1:00-1:50 2 ILL HALL Oyengo, Michael Obiero
ADP R 2:00-2:50 441 ALTGELD Gehret, Allen
ADQ R 3:00-3:50 147 ALTGELD Nell, Travis
ADR R 4:00-4:50 143 HENRY BLD Nell, Travis
ADS T 8:00-8:50 341 ALTGELD Rehfuss, Nathan
ADT T 9:00-9:50 149 HENRY BLD Rehfuss, Nathan
ADU T 10:00-10:50 149 HENRY BLD Gehret, Allen
ADV T 11:00-11:50 2 ILL HALL Oyengo, Michael Obiero
ADW R 8:00-8:50 341 ALTGELD Rehfuss, Nathan
ADX T 2:00-2:50 2 ILL HALL Hakobyan, Tigran
ADY R 2:00-2:50 2 ILL HALL Hakobyan, Tigran
ADZ T 3:00-3:50 2 ILL HALL Nell, Travis

Exams and practice material

There will be three midterm exams and a comprehensive final exam. Notes, books, calculators or computers are not allowed during any of the exams.

Our exam schedule is:

The following material will help you prepare for the exams.

Last change: 2014/12/11
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