Messages

The final results of the exam has been sent to the administration of the informatics department.

You can also contact me personally to know more in details the results of your exam.

Last Tutorial tomorrow where problems coming form the exams of the previous years will be solved, according with questions coming from the students and their necessity.

The program for the exam happening on the 7 of June is chapter 1, 2, 3, 4, 5, 6 and 7 + the derivation of the wave equation that is possible to download on my webpage.

In the last two lectures of Friday the 7 of May and Tuesday the 11 of May we went through the second part of the maximum principles chapter (section 6.3, 6.4 and 6.5) from the textbook. Exercises related to this part to work on are: 6.7, 6.9, 6.10, 6.12, 6.13.

Then we went through chapter 7 related to the the Poisson equation in 2 dimensions (from section 7.1 to section 7.3). Have also a look yourself to sections (7.4-7.6), only the main results without getting into the details of the calculation. For Chapter 7 work on the following results: 7.1, 7.2, 7.4, 7.5, 7.7, 7.9, 7.16, 7.18.

SUMMARY: The theoretical lecture of the course are finished. Starting with the next week there are 3 more exercise sessions with Nina Holden every Friday at 12:00. Work on the exercises listed above and on others coming from tha first 7th chapter of the textbook that you will find useful fot the exam happening the 7 of June. On the following link (down in the list to 24.03.2009) you...

Here you can download the second assignment to get to the final exam: http://folk.uio.no/iliamu/v10oblig2.pdf

NEXT LECTURE on Friday the 7 of May, Auditorium 2, from 2pm to 4pm.

In the lecture of today the first part of chapter 6 has been covered (sections 6.1 and 6.2): the maximum principles for the two-point boundary value problem and the linear heat equation, for both the continuos and discretized case.

Next lecture on Friday there will be no exercise lecture. Instead we will have a theory lecture at 2 pm, continuing with the maximum pronciples for the non linear heat equation and the harmonic functions. It is possible that the lecture will last until 5pm, depending on the needs of the program to be covered. I will announce as soon as possible the room of the lecture.

On Friday the assignement for the second part of the program will be given.

Ecxercises for the lecture of today: 6.1, 6.2, 6.5, 6.6, 6.8. The next exercise lecture to replace the one missed this week will be announced as soon as possible.

In the lecture of toady the Energy argument have been analized (sections 3.7, 4.5 and 5.2 from the text book). We have also started with the Maximum Principles (section 6.1).

For the next Friday exercise lecture work on 3.17, 3.19, 3.20, 4.23, 4.25, 5.3, 5.8.

IMPORTANT: Next Lecture will be on Tuesday the 4 of May and it is possible that it will last until 5pm instead of 4pm. In place of the exercise lecture of Friday the 7 of may ther will be a theory lecture. Time and place to be announced.

In the first part of the lecture of today I have explained the discretized wave equation with his solution and the sability analysis (5.3 from the text book).

In the second part of the lecture I have derived the form of the wave equation. You can download the material for this at the following link:

http://folk.uio.no/iliamu/wave.pdf

For the next exercise lecture of Friday work on 5.4, 5.7, 5.9, 5.10, 5.11.

IMPORTANT: Next week we will to see the Energy argument for both the wave and the heat equation (sections 3.7, 4.5 and 5.2 from the textbook). We will also see the Maximum Principles (Chapter 6). Therefore next lecture on Tuesday 27 of April will be long 3 hours, from 2pm to 5pm.

Here the results of the mid-term exam:

http://folk.uio.no/iliamu/INF-MAT3360%20RESULTS%20MID%20TERM%20EXAM.pdf

In the lecture of yesterday I have explained the implicit scheme to discetize the heat equation (section 4.4) and the analytic solution of the wave equation using the separation of variables method (section 5.1).

For the exercise lecture on Friday work on exercises 4.5(b), 4.8, 4.10(b), 4.12(b), 4.18, 5.1, 5.2, 5.5.

IMPORTANT: The next lecture on Tuesday the 20 of May is from 3pm to 5pm instead of 2pm to 4pm, always in Auditorium 4.

In the lecture of yesterday I have revised and completed all the discrete analisys with the Fourier method to discretize the heat equation with the explicit scheme. From the text book the first three sections of Chapter 4.

Next lecture, Tuesday the 13 of April, we will treat the implicit method, the discretization of the wave equation and the energy argumet for both.

For the next exercise lecture on Friday the 26 of March work on the following exercises: 4.4, 4.5(a), 4.6, 4.10(a), 4.12(a), 4.22, 4.23.

Here the link to the midterm exams of 2007 and 2008:

http://folk.uio.no/siddharm/INF-MAT3360v07_mtENG.pdf

http://folk.uio.no/siddharm/INF-MAT3360v08_mtENG.pdf

The mid term exam counts 20% of the total mark of the final exam.

By tomorrow students will be informed about the result of the assignement1 and who will fail will have time until next Tuesday to send us (me or Nina) a new solution to be then accepted to the mid term exam of Thursday.

In the lecture of yesterday we started to study the Discrete Fourier Method to solve the Heat equation. From chaper 4 of the text book section 4.1 and 4.2 until page 126 plus sub-section 2.4.2 whose result is useful in this context.

For the next exercise lecture on Friday some time will be spent to correct the first assiggment plus the following exercises: 3.9, 3.13, 3.20, 4.1, 4.2, 4.6.

The updated version of the Assigment, wih the corrected headings and deadline is available now here: http://folk.uio.no/ninahold/Assignment1.pdf. Exercises are the same as before.

In the lecture of yesterday we did some properties of matrix and eigenvalue problem from chapter 2. From the text book section 2.3.1, 2.3.2 and 2.4.1. On chapter 3 we finished the derivation of the Fourier method to solve the Heat Hequation, showing into details the mothod to derive the Fourier coefficients. From the text book section 3.4, 3.5 and 3.6.

In the Exercise lecture of this Friday sections 3.7 and 3.8 will be seen plus the following exercises: 2.14, 2.19, 2.23, 3.1, 3.2, 3.4, 3.8, 3.12, 3.14.

In the two lectures of Friday 26 of February and 2 of March we did the Gaussian elimination methid for a Tridiagonal system and some properties of the Diagonal Dominant Matrices (2.2.3 and 2.2.4 from the text book). We then started the solution of the Heat Equation using the Fourier Method: description of the general problems seeing the 4 steps of the solution using the Fourier Method, derivig in details the first two steps, the separation of variables and the superposition (3.1, 3.2 and 3.3 from the text book). For the Exercise lecture of tomorrow exercises 2.6, 2.7, 2.8, 2.9, 2.11, 2.14 and Project 2.1.

Here the obligation project to solve to access the mid-term exam: folk.uio.no/siddharm/v09Oblig1.pdf . Same one of last year, therefore do not consider the first lines referring to 2009. A new version correcting this will be soon provided. It should be hand in by Tuesday 16 of March to me or Nina Holden.

In today lecture we went carefully through the solution of the Laplace equation in 1D deriving the form of the Green Function to write the solution. We then studied the properties of the Green Function and the smoothness of the solution of the Laplace euquation. Finally we introduced the Finite Difference Scheme Approximation to study to work out a numerical solution of the Laplace equation. In the text book, from the beginning of chapter 2 until the end of paragraph 2.2.2. In the Next lecture we will start with the Gaussian Elimination method.

Solutions of some problems here: http://folk.uio.no/ninahold/Fasit.pdf

Tuesday, 16.02.2010 (14:15-16:00) Exercise Lecture with Nina Holden in Room C315

Friday, 26.02.2010 (12:15-14:00) Theory Lecture with Ilia Musco in Auditorium 2

In yesterday lecture we revised the characteristic method introducing the Transport Equation. Then we introduced in the general n-dimensional form the Laplace, Poisson and Heat Equation with some physical examples and derived the full solution in 1-dimension of the Heat and Poisson equation. This material is on chapetr 1 (1.4) and beginning of chpter 2 (2.1) of the text book. Additional material explained in the lecture on Laplace and Heat equation can be dowloaded from my home page:

http://folk.uio.no/iliamu/

Since now on next problem solving sessions will only consist of blackboard teaching and not independent work, so you are advised to look on the problems before class. For Friday exercise lecture solve 1.9, 1.10, 1.11, 1.12 and 1.13. Tuesday 16 of February Nina Holden will do an exercise lecture in my place (check this webpage to know the room) and for this solve exercises 1.14. 1.15, 1.16 and 1.17. For exercise...

The chapters of the book can be downloaded on the following website: http://www.springerlink.com/content/rx785w/

Today lecture I first exlained The Forward Euler Method. Then I introduced the Cauchy Problems, explaining in details, also with examples, the characteristic method for both homogeneous and non homogeneous first order partial differential equations. Finally I derived the d'Alambert solution of the wave equation. From the book paraghaph 1.3 and 1.4 (1.4.1, 1.4.2; 1.4.3). Next time we will finish to cover chapter 1 with the diffusion equation (paragraph 1.4.4) and start chapter 2 with the Poisson equation. Exercises assigned during this lecture for the tutorial of Friday 1.5, 1.6, 1.7, 1.8 together with the others assigned on the previous lecture.

Today's lecture: I gave a general overview of the course and its contents. I also introduced the general concepts of ODEs, PDEs, and stability of solutions of ODEs. From the book section 1.1 and 1.2. Exercise assigned for the tutorial: 1.1, 1.2, 1.3 and 1.4. from the book of the course.