Beskjeder
Syllabus for the final exam: Heat equation:- Explicit solutions with the Fourier method with different boundary conditions, energy estimates, Explicit and Implicit schemes, Von-Neumann stability analysis, Maximum principles.
Wave equation: Explicit solutions by Fourier method, Energy estimates, explicit finite difference schemes and their stability.
Corrected sheets of the first Obligatory exercises will be distributed in class tomorrow, Please collect it. Group lesson on friday will involve solving 5.2, 5.3, 5.7, 5.8 and 5.11
Obligatory exercise set 2: Some typographical errors in exercise 2.d. Corrected version now on
folk.uio.no/siddharm/Oblig2.pdf
Obligatory exercise set 2 is now available on
folk.uio.no/siddharm/Oblig2.pdf
Due date is the 24th of May.
For group lessons this friday, he will do exercise number 4.15, 4.18, 1.8,1.9, 5.1 and 5.2 from the book.
Solutions to midterm can be download from
folk.uio.no/siddharm/INF-MAT3360v07_mtNOR.pdf
Group lesson tomorrow. He will cover exercises 3.4, 3.5. 3.13, 3.17 and 3.20
Today, i started analysing the convergence of the numerical scheme for heat equation. In the next lecture, i will continue with the analysis and introduce Von-Neumann Analysis and Implicit schemes for heat equation.
No class on 29-03-2007: Mid-term Exams.
No class on 05-04-2007: Easter holiday.
No group lessons on 30 March, 6 April.
PDF file with answers to Mid-term exam will be updated soon.
Special Group lessons tomorrow -- for both groups. One group lesson at 1015 and another at 1415. I will summarize the exam syllabus and answer questions.
Today, i proved uniqueness and stability for solutions of the heat equation by the energy method. I also derived an explicit finite difference scheme and showed some of its properties.
Assignment 1: Errata.
1. In exercise 2.1, substitute $\Delta t/2$ instead of $\Delta t$ in the Taylor expansion hint.
2. In Exercise 4, switch $0 < x < y$ to $0 < y <x$ in the first line of definition of the Green's function $G(x,y)$.
Sorry for the errors
Today, i covered the use of the Fourier method to solve heat equation with both Dirichlet and Neumann Boundary conditions. In the next lecture, i will start with numerical methods for the heat equation.
Group lesson tomorrow morning: He will continue with exercises from Chapter 2 and start with Chapter 3 if he has time. The link to answers and hints for exercises is folk.uio.no/haakonah/infmat3360
First Obligatory exercise set will be distributed in Class tomorrow. Please collect it either in class or from me in room no B905 Nils Henrik Abel Hus or download it from
folk.uio.no/siddharm/Oblig1.pdf
The due date for submitting completed answers is 18th April.
Group lesson tomorrow from 1015 to 1200 at C309, VB -- he will continue with exercises in chapter 2.
Today, i derived the heat equation and explained how to obtain solutions of it by using the Fourier series. In the next lecture, i will continue with Fourier series solutions for the Neumann problem and also derive energy estimates for the heat equation.
2 group lessons tomorrow: First at 1015-1200 at C309, VB house and Second at 1415-1600 at C311, VB house.
Today, i covered convergence of numerical method for poisson's equation and eigenvalue problem for the same equation. I will start with Fourier Series solutions of the heat equation in the next lecture
In the next lecture, i will prove convergence of the numerical method for Poisson's equation and study eigenvalue problems. Next group lesson will be about exercises in Chapter 2. A selection of problems from 2.2 to 2.15 will be done.
In the last two lectures, i continued the coverage of Poisson's equation. We have studied properties of the solution by using the Green's function, derived a numerical method, solved matrix equations using Gaussian elimination and seen some properties of the continuous and discrete solution operators.
Next lecture will be about properties of solutions of Poisson's equation by using the Green's function. We will also derive a numerical method for Poisson's equation.
Today, i covered solving advection equations with method of Characteristics. I also started with Poisson equations in 1-D by deriving the Green's function representation of the solution.
Updated Syllabus: Chapters 1 to 7 of the Book introduction to PDE by A. Tveito and R. Winther
No Group lessons tomorrow (9th Feb, 2007). First group lessons are on 16th Feb, 2007. Cover exercises 1.1 to 1.7 and project 1.3. Your group teacher is Haakon A. Hoel (haakonah@student.matnat.uio.no)
Today, i covered solutions of ODE, stability of solutions, Numerical Methods (Forward Euler) to compute solutions of ODE and introduced method of characteristics for advection equation.