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On my web page (http://folk.uio.no/iliamu/) the final exams of the last four years (2007 - 2010) are now available.

The progarm of the last lectures:

• Maximum Principles for the explicit and implicit finite difference scheme (sections 6.2.3 & 6.2.4)
• Maximum Priniciple for the non linear heat equation (section 6.3)
• Harmonic Functions (section 6.4)
• Discrete Harmonic Functions (section 6.5)
• Poisson equation in 2D-space dimensions (sections 7.1 & 7.2)
• Divergence Theorem (section 7.3)
• Mean Value Property of the Harmonic Functions (section 7.4)

Exercises: 6.5, 6.6, 6.8, 6.9, 6.10, 6.12, 6.13, 7.1, 7.2, 7.4, 7.5, 7.7, 7.9, 7.17, 7.18.

The lecture of today at 10 has been cancelled. The course will be finished in two more lecture: tomorrow at 14:15 as normally scheduled and the day after, Wednesday 11 of May, from 10:15 to 12 in GA06 2458 Seminarrom Postscript.

The last Group sessions with Kristina will be on Wednesday 18 and 25 of May from 2:15pm to 5pm in GA06 2423 Seminarrom Java.

The second Assignment for the course is now and can be download from the web: http://folk.uio.no/iliamu/ . It should be sent to Kristina by Monday 16 of May 1pm.

In the lecture of Tuesday 26 of April:

• Stability Analysis of the wave equation (section 5.3.1)
• Maximum principle for the two point boundary value problem (section 6.1)
• Maximum principle for the linear heat equation in the continuous case (section 6.1: 6.2.1 and 6.2.2)

For next Monday work on the following exercises: 5.9, 5.10, 6.1, 6.2, 6.3, 6.4.

Results for the Midterm Exam:

CANDIDATE - RESULT (20 points)

321 - 19/20

327 - 12/20

328 - 13/20

329 - 6/20

330 - 19/20

331 - 20/20

332 - 9/20

333 - 14/20

336 - 10/20

339 - 15/20

342 - 10/20

345 - 14/20

347 - 8/20

349 - 6/20

351 - 19/20

352 - 19/20

In the lecture of Tuesday the 12 of April:

• Derivation of the wave equation (download "wave equation.pdf" from my web page)
• Wave Equation solution in the continuous and discrete case (section 5.1, 5.2 and 5.3 from the textbook). The last topic, the stability analysis, is missing and will be done during the next lecture on Tuesday 26 of April.

For the next Group session, Thursday 28 of April, work on the following exercises: 5.1, 5.2, 5.3, 5.4, 5.7, 5.8.

IMPORTANT: The results of the midterm exam will become available immediately after Easter, by Tuesday 26 of April.

In the lecture of today:

• Von Neumann's Stability Analysis (section 4.3)
• An Implicit Scheme (section 4.4)
• Numerical Stability by Energy Argument (section 4.5)

For next Monday work on the following exercises: 4.5, 4.6, 4.8, 4.10, 4.12, 4.14, 4.18, 4.22

Here an updated plan for the remaining part of the course:

• Tuesday 5 of April Lecture 11: Second part of the Discretized Heat Equation (Section 4.3 - 4.5)
• Monday 11 of April: Exercise session
• Tuesday 12 of April Lecture 12: Wave equation, derivation, analytic + discretized solution (notes on derivation + Chapter 5)
• Tuesday 26 of April Lecture 13: Maximum Principles (Chapter 6)
• Thursday 28 of April: Exercise session
• Monday 2 of May: Exercise session + Mandatory Assignment pubblication
• Tuesday 3 of May: Lecture 14
• Monday 9 of May: Lecture 15
• Tuesday 10 of May: Lecture 16
• Monday 16 of May: Exercise session + Hand in Mandatory Assignment (I chance)
• Monday 23 of May: Exercise session + Hand in Mandatory Assignment (II chance)
• Monday 30 of May: Exercise session
• Wednesday 8 of June: Final Exam

More detailed informations to come.

In the lecture of today:

• Explicit scheme to discretize the Heat Equation (Section 4.1)
• Fourier Analysis of the numerical solution (Section 4.2)

For next Monday work o exercises: 4.1, 4.2, 4.4, 4.6.

The files of the old exams for the year 2007 and 2008 (INF-MAT3360v07mtENG.pdf and INF-MAT3360v08mtENG.pdf) are now on line to be download from my web page. Also the files on the heat equation and the solution of exercises of the 14 of march are now available to be downloaded.

During the lecture of yesterday I went through the following program:

• Eigenvalue/Eigenfunction problem (section 2.4 of the textbook)
• Fourier coefficients for the heat equation (sections 3.4 and 3.6.3 of the textbook)
• Energy Argument (section 3.7)

Exercises regarding this lecture, for the Group session on Monday 28, are: 2.25, 2.26, 2.28, 3.14, 3.16, 3.17, 3.20.

IMPORTANT: For some problem with the server the files "heat equation.pdf" and "Exercises Solutions 14.3.pdf" do not download. I am not able to solve the problem until Friday 25 when I will get back to the office. If you need the files before that email me (ilia.musco@cma.uio.no) and I will send them directly to yuo.

IMPORTANT CHANGES: To help the students with the work on the Assignment no exercise session net Monday 21 of March. Monday 21 is the deadline to hand in the Assignment Monday at 3pm by email to Kristina (kristrd@math.uio.no) or personally to her at the Room B601 on the 6th floor of the Abel Building.

NEXT EXERCISE LECTURE THURSDAY 24 OF MARCH, from 2:15pm to 5pm where Kristina will work on the exercise assigned for the previous lecture and for those ones that will be assigned tomorrow after the next lecture. She will also bring the Assignments marked and give some suggestions to those that will need the second chance to try to pass.

During the lecture of today the following program has been done:

• Derivation of the Heat Equation from basic physical concepts. For this see the file (heat equation.pdf) on my web page.
• Solution of the heat equation with the separation of variables method for both the Dirichlet and Neumann boundary conditions. For this see the file (heat equation.pdf) on my web page plus section 3.1, 3.2, 3.3, 3.5 and 3.6 (up to 3.6.2) from the text book.

Next Lecture on Friday, between 14:15 and 16 at the usual room. Chapter 3 will be finished with the explicit calculation of the Fourier coefficients going through the eigenvalue/eigenfunction problem (section 2.4, 3.4 and 3.6.3). We will also try to start chapter 4 introducing the Fourier discrete analysis of the heat equation.

For next Monday work on exercises: 3.1, 3.2, 3.4, 3.5, 3.8, 3.9, 3.12, 3.13. For some of these you need to know how to calculate expl...

The solutions of the exercises assigned for the today Group session are now on line on my web page: Exercise Solutions 14.3.pdf

The solutions of Project 1.1 are now on my web page: http://folk.uio.no/iliamu/

In the two lectures of this week (Monday 7 and Tuesday 8 of March) the following program has been done:

• Boundary conditions of PDEs (page 73 to 87 from the file PDEextrachapter5.pdf that you can find on my web page)
• Two Boundary value Problems (Chapter 2 of the textbook) from page 39 to page 65. Last section 2.4 about Eingenvalue problems will be done during the solution of the heat equation next week.

Next week the exercise session will be of 3 hours, on Monday 14 of March, from 9 to 12 on the following exercises:

• From the text book 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.11, 2.14, 2.19, 2.23 and Project 2.1.
• From the file PDEExerciseBC.pdf on my web page 5.13 and 5.16

On my web page you can download the Assignment for the mid term Exam. At the end of this one exercise has been canceled. Substitute this with exercise 5.14, 5.15, 5.17 from the file PDEExerciseBC.pdf on my web page....

Lecture 6 supposed to be on Friday 25/2 has been cancelled at last moment because I was sick.

For the Exercise session on Tuesday 1 of March, keep working on the exercises already assigned including Project 1.1

The evolution of the course in March will have the following schedule:

• Monday 28/2: Exercise 4
• Tuesday 1/3: Exercise 5
• Monday 7/3: Lecture 6
• Tuesday 8/3: Lecture 7 & Mandatory Assignment posted
• Monday 14/3: Exercise 6&7 (3 hours session between 9:15 and 12)
• Tuesday 15/3: Lecture 8
• Friday 18/3: Lecture 9 (between 14:15 and 16)
• Monday 21/3: Exercise 8 (Hand in to Kristina the Assignment)
• Thursday 24/3: Assignment Results (1 hour session, time and room to be fixed)
• Monday 28/3: Exercise 9 & Hand in 2nd chance of the Assignment
• Tuesday 29/3: Lecture 10
• Thursday 31/3: MID TERM EXAM

Here the exercises to work on for next Monday.

• from the file PDEextrachapter1.pdf: 1B.4, 1C.1, 1C.6, 1D.1, 1D.3
• from the file PDEextrachapter4.pdf: 4.1 (only (a), (b) and (c)) and 4.2, both at the end of the chapter.

The exercises for Tuesday will appear on Friday after the next lecture.

FILES NOW UPLOADED ON MY WEB PAGE!

For the next lecture on Friday the 25 have a look at PDEextrachapter5.pdf, we re going to spend one hour on it while the second hour will regard section 2.1 of the textbook.

Program of the lectures done the 14 and 15 of February:

• D'Alambert solution of the wave equation (section 1.4.3 of the text book).
• Intruction of the Laplace and Poisson equation. See the file (PDEextrachapter1.pdf) uploaded on my web page.
• Properties of of Linear PDE: functions & vectors; linear operators; eigenvalues, eigenvectors & eigenfunctions; Homogeneous & Non Homogeneous. (PDEecxtrachapter4.pdf)
• Physical derivation the Poisson equation for the Gravitational Field using the divergence theorem (see Poisson.pdf) on my web page.

For the Monday 21 work on the following exercises from the text book: 1.8, 1.14, 1.15, 1.16, 1.17.

NEW SEMINAR ROOM FOR THE LECTURE/EXERCISE SESSION ON MONDAY: Caml, Room number 3438, in the middle of the building.

Yesterday I introduced the Fourier Law and the Heat equation in 1 and then in n-dimensions. See for this the file (PDE_extra.pdf) upload on my web page: http://folk.uio.no/iliamu/. Then I used the characteristics method to work out the solution of the heat equation in 1-d under simple initial condition (See section 1.4.4 from the text book)

In my web page look also at the file with the calendar of the courses . It has been updated with some changes. In particular, for the next 3 weeks we have: next week no exercise session because we will have lecture both Monday 14 and Tuesday 15. The week after the lecture is moved from Tuesday the 22nd to Friday the 25th, same time and same room as Tuesday. Finally The first week of March exercise both on Monday the 28th and Tuesday the 1st of March.

Exercises for the next group sessions will be assigned after the lecture of Tuesday the 15th.

On the second lecture of the 1st of February we have seen in details, with some explicative examples, the Forward Euler Method (section 1.3 of the book) and the characteristic method to solve first-order homogeneous and non homogeneous equations (section 1.4.1 and 1.4.2 from the text book).

For next Monday work on the following exercises: 1.5, 1.6, 1.7, 1.8. Start also to work on the remnant time of the Exercise sessions on Project 1.1 and keep going on with this also during the following weeks.

On my webpage it now possible to download the tentative program of all the lectures and exercise sessions that will be given during the ongoing semester, based on the teaching done last year.

http://folk.uio.no/iliamu/INF-MAT%203360%20Calendar%202011.pdf

Changes are of course possible, and will be always announced with a message. The program really done and the exercises given for the group session will always be specified with a new message after the lecture.

In the first lecture, Tuesday 24 I gave a general overwiew of the course: ODEs, PDEs etc¡­ Sections 1.1 and 1.2 from the text book. For Monday 31 work on exercises 1.1, 1.2, 1.3 and 1.4 from the text book.