On this page will be posted the different announcements for the class. Please make sure to come and check back often to find the latest updates.


Tuesday, September 1st - Runge--Kutta schemes
As a complement to yesterday's lecture on ODE

Tuesday, September 1st - Homework 4
As I received several emails yesterday regarding the code that I gave you for HW4 Problem 2 (int_trap.m), I think it is better that everyone gets the following clarifications:

1/ the code given to you in the text of the HW is absolutely correct and works: I tested it yesterday with one of you during the lecture break and tested it again this morning. It is possible that some of you have made mistakes in recopying this code from the text so to make it easier, I have added the file to the website where you can download it from (see the Homework page)

2/ Possible mistakes in the use of the code can be the following:
 - the function int_trap.m requires a function handle as first input. I refer you to the introduction to Matlab of the first week of class. You need to understand that the following two statements are not equivalent:
            (i) f=sin(x);
            (ii) f=@(x) sin(x);
The first one creates a vector f of the value of sin(x) evaluated at an already existing vector x. The second one creates a function handle that will allow to execute such commands as f(pi), f(0), etc....

- in the definition of your function, you need to pay attention in using the element-by-element operations and not the matrix multiplications. THe following two statements are not equivalent:
            (i) (2*x+3/x)^2
            (ii) (2*x+3./x).^2

3/ this code is not necessary to solve Problem 2 and was only given to you as one option to compute an estimate of the integral using the composite trapezoidal rule: you have several other possibilities, including using the one of the textbook, writing your own, or even just using a calculator. The important point of this problem is for you to understand how to use Romberg integration. If you do not manage to use this routine, you are therefore responsible for finding another way to compute the integral with the composite trapezoidal rule and the required number of segments.


Monday, August 31 - Final's week information
The final week of the term is already here and you will find below some important information regarding its organization. The TAs and myself have in particular increased the time of their office hours for you to have more opportunity to come to ask us the questions you have as you prepare for Friday's final exam.

1/ Final Exam

The final exam will be this Friday, September 4 from 3p to 6p in Center Hall Room 212. It will be a 3-hour closed book/closed notes exam, no computer or calculator allowed. Just plain paper and pencils/pen (remember to bring your own paper and writing material as well as a way to attach all the pages of your exam together).

Note: the sample final indicates a one-page sheet that you are allowed to bring. This was the policy of the professor who designed that final. Such policy is not implemented this quarter: no notes or books are allowed.

2/ Discussion sessions

As you now prepare for the final that will only include minor programming I have asked the TAs to focus the discussion sessions on problem solving. This week's sessions will therefore not be held in the computer labs but in the classroom:
- Krishna: Tuesday, 2p-3p in Room 305 (EBU2)
- Robert: Thursday, 11a-12p in Room 105 (EBU2)

There will not be any session this Friday due to the exam, so I encourage the students who usually come to that discussion session to come to any of the two others that fit their schedule.

3/ Office hours

Krishna will have office hours tomorrow (Tuesday) from 3p to 5p in Room 305.
Robert will have office hours on Thursday morning from 10a to 11a in his usual room (EBU2 Room 105) and will be available in his office (EBU1 1803) before 10a that morning if you have more questions.

I will have special office hours on Thursday afternoon from 2p to 4.30p for you to be able to come and ask me questions about any of the material covered in the class (my office is EBU2 - Room 378)

4/ Material

The material of the final exam includes the material of all lectures (including today's and Wednesday's), all required reading assignments (see website), all homework assignements and quizzes, the midterm, the midterm and final samples and the different handouts I have placed on the webpage (Matlab, Linear Algebra, Taylor Series, Finite differences....).

5/ Course evaluations

By now, you should have received an email regarding the online course evaluations. Paper evaluations are not implemented anymore so I refer you to the email you have received from the Course Evaluation office for specific instructions. These evaluations are very important for the university, the department, myself and future students to have some feedback from you on the organization of this class this Summer, in order to improve it in the future. Your constructive (positive or negative) comments on what was good in this class and what can be improved are particularly appreciated. I thank you in advance for taking the time to fill them out. The deadline to fill in these evaluations is Thursday.


Friday, August 28 - Finite differences
To complement Wednesday's lecture on numerical differentiation, I have posted an example on how to obtain finite difference schemes from Taylor Series expansion, as well as some exercises with answers. I strongly encourage you to look at this document and try to understand it and come and see me if something remains unclear concerning this technique. You can find that document on the Lectures webpage. It has also been added to the list of required reading for the class.

Friday, August 28 - Quizz #3
Quizz #3 has been graded. Please pick it up outside of my office. I remind you that graded homeworks and quizzes are available for pick-up outside my office (EBU2 378). Many of you still haven't picked up their graded Homework 1 or/and 2 as well as quizzes 1 and 2. I highly recommend you to study carefully what you did not understand in an assignement to be able to do better the next time


Wednesday, August 26 - Homework #4
Homework #4 has been posted (see homework page). It is due on Wednesday, September 2 in class.

One of the problem of this homework is focused on the solution of Ordinary Differential Equations, a topic we will start covering today and cover mostly on Monday. However, to work on this homework problem you do not need the material of the lecture as the schemes used are given to you explicitely.


Tuesday, August 25 - Final exam
I remind you that the final exam will take place on Friday, September 4 from 3p to 6p. Please make necessary arrangements to be present on that day at that time. Make-up exams will only be provided for medical reasons with proper documentation.

The room hasn't been assigned yet and I will send another email as soon as I am notified of the room.

I have posted on the website an example of final exam that was given in previous years (see Assignments page) . This year's final will consist of problems of the same style as this sample and as the midterm exam. I strongly encourage you to look at these examples, try to work on them without looking at the solution, and then compare your work with the solution, and come to office hours or discussion session if you have any question.


Tuesday, August 25 - Quizz #3 and M-files
Quizz 3 and its solutions have been posted on the web (see Assignments page)

I have also posted the M-files I used during lecture yesterday (see Lectures page) to illustrate the dangers of extrapolation and the problem of oscillations when you interpolate with a high-order polynomial. I have also added some Matlab functions that perform interpolation using splines (linear, quadratic and natural cubic). I encourage you to look at them and understand them in the light of Chapter 16 of the textbook.


Wednesday, August 19 - Homework #3
Homework #3 has been posted (see homework page). It is due on Wednesday, August 26 in class.


Friday, August 14 - Midterm infos
I have posted a sample Midterm and its solutions for you to have an idea of the type of problems I will give you on Wednesday. The number and exact questions of the problems will however differ and I also encourage you to review the problems in Homework assignments 1 and 2.

I remind you that the Midterm will cover all Lectures from 1 through 5 (this means that it does include next Monday's lecture) as well as all reading assignments, class notes and files or programs presented in lecture.
It will be a closed-book and closed-notes exam. No calculator or computer allowed. Only pens, pencils and paper.


Friday, August 14 - Operation count on Thomas algorithm
On Monday, we discussed Thomas algorithm to solve efficiently a tridiagonal system. I would like to attract your attention on the cost of this algorithm. For a square tridiagonal matrix of size n, the cost is approximately 8n (at leading order), contrary to the higher cost I provided in class on Monday. Please make a correction in your notes. I encourage you to do the calculation yourself by looking at the code (see Problem 5 of the sample Midterm) and then look at the correction.
This very low cost (it varies linearly with the size of the matrix) is to be compared to the cost of full Gauss elimination (~2n³/3).


Thursday, August 13 - Homework #1 Solutions - new files posted
The solution of Homework #1 has been posted (see homework page).
I have also posted the M-files that I used yesterday in class (see Lectures page). I encourage you to look at them and try to understand what operations they are doing. You should be able to write your own function to solve a system of linear equations iteratively using any of the three methods (Gauss Seidel, Jacobi and SOR).


Wednesday, August 12 - Homework #2
Homework #2 has been posted (see homework page). It is due on Wednesday, August 19 in class.


Monday, August 10 - New files posted
I have posted today's lecture slides on the website as well as the three Matlab routines that I used to solve linear systems using Gauss elimination with or without partial pivoting, and linear tridiagonal systems using Thomas algorithm (see Lectures page)

Quizz #1 and its solution have also been posted (see Assignments page)



Thursday, August 6 - New files posted
I have posted on the Lectures page a brief review of Taylor Series. Please read it carefully and I encourage you to look back at your notes from previous classes on Taylor Series.



Wednesday, August 5 - New files posted
I have posted on the website the M-files that I used in the presentation of MATLAB today.

I have added a script file to illustrate the Taylor Series discussion: this script file taylor_exp.m computes the Taylor series of f(x)=exp(x) in 0 with increasing order and plots this approximation. You can observe how closer the match is as the order is increased.

I have also added a set of exercises on MATLAB with solutions for you to get familiar with the basic commands of MATLAB.
All these files can be downloaded from the Lectures page.


Wednesday, August 5 - Homework #1
Homework #1 has been posted (see homework page). It is due on Wednesday, August 12 in class.



Tuesday, August 4 - Linear Algebra exercises and Matlab introduction
To complete yesterday's review on Linear Algebra, I have put online a brief review of how to compute determinants, matrix inverse and eigenvalues/eigenvectors (see Lectures page). I have also included some exercises (with solutions) in each case for you to make sure you remember what these different concepts are and how to use them.

During tomorrow's lecture, I will give a quick demonstration on how to use the basic commands of Matlab before giving you the basic informations you will need to program Matlab routines (as soon as next week in Homework #1).
I have placed a document as required reading that summarizes the minimum you need to know about Matlab and programming with Matlab. This document complements the reading of Chapters 2 and 3 of the textbook. Try to have a first reading of this document before tomorrow to get the most out of tomorrow's lecture.




Monday, August 3 - Lecture 1 notes
The lecture slides from today's lecture are now online (see Lectures page or here)


Monday, August 3 - Session Group Assignment
The group assignments have been modified and the final group compositions are available now. (Group assignments  & session schedule)
At this point I won't be able to make further changes in the group composition, unless someone is willing to switch group with you. Please check carefully which group you are in (particularly those of you who have been assigned to Group A and whose first session is tomorrow evening!)


Monday, August 3 - Session Group Assignment
The session groups have been assigned. Please carefully check and remember the group you have been assigned to.



Thursday, July 30
Students registered for the class should have received an email regarding the organization of the discussion sessions. Please respond before Monday if you have a schedule conflict with one of the session schedule so you can be assigned in a different group (session schedule).
The group assignments will be posted on the website on Monday.

If you haven't received this email but are registered for the class please send me an email.



Friday, July 24
The first lecture of the session will be held on Monday August 3 in Center Hall Room 105.

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