## 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.

- math415-ds-01.pdf (for Sep 2 and 4)

Solutions: math415-ds-01-sol.pdf - math415-ds-02.pdf (for Sep 9 and 11)

Solutions: math415-ds-02-sol.pdf - math415-ds-03.pdf (for Sep 16 and 18)

Solutions: math415-ds-03-sol.pdf - math415-ds-04.pdf (for Sep 23 and 25)

Solutions: math415-ds-04-sol.pdf - math415-ds-05.pdf (for Sep 30 and Oct 2)

Solutions: math415-ds-05-sol.pdf - math415-ds-06.pdf (for Oct 7 and Oct 9)

Solutions: math415-ds-06-sol.pdf - math415-ds-07.pdf (for Oct 14 and Oct 16)

Solutions: math415-ds-07-sol.pdf - math415-ds-08.pdf (for Oct 21 and Oct 23)

Solutions: math415-ds-08-sol-scanned.pdf - math415-ds-09.pdf (for Oct 28 and Oct 30)

Solutions: math415-ds-09-sol.pdf - math415-ds-10.pdf (for Nov 4 and Nov 6)

Solutions: math415-ds-10-sol.pdf - math415-ds-11.pdf (for Nov 11 and Nov 13)

Solutions: math415-ds-11-sol.pdf - math415-ds-12.pdf (for Nov 18 and Nov 20)

Solutions: math415-ds-12-sol.pdf - math415-ds-13.pdf (for Dec 4 and Dec 9)

Solutions: math415-ds-13-sol.pdf

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:

- Midterm Exam 1: Thursday, September 25 — 7:00-8:20pm

midterm1.pdf, midterm1-sol.pdf - Midterm Exam 2: Thursday, October 23 — 7:00-8:20pm

midterm2.pdf, midterm2-sol.pdf - Midterm Exam 3: Thursday, November 20 — 7:00-8:20pm

midterm3.pdf, midterm3-sol.pdf - Final Exam: Friday, December 12 — 7:00-10:00pm

(Conflict Final Exam: Monday, December 15 — 7:00-10:00pm)

The following material will help you prepare for the exams.

- Midterm Exam 1: midterm1-practice.pdf

Solutions: midterm1-practice-sol.pdf - Midterm Exam 2: midterm2-practice.pdf

Solutions: midterm2-practice-sol.pdf - Midterm Exam 3: midterm3-practice.pdf

Solutions: midterm3-practice-sol.pdf - Final Exam: final-practice.pdf

Solutions: final-practice-sol.pdf