Facts
Duration: 1 semester
Period: Spring Semester
Credits: 3 ECTS
Contact Hours: 64
Self-study: 152
Hours: 216
|
Main Objectives
This course is intended:
- for training Masters in Math to apply mathematical methods and modeling technique in their professional work;
- to give experience in the application of knowledge for development of the theoretical foundations of the methods of computational mathematics, for formation of practical skills development of numerical algorithms, for organization of computational experiment on the computer, for presentation of the results of calculations.
Learning Outcomes
In mastering the subject of Numerical analysis of PDEs the student will acquire the following knowledge: finite-differencing, finite-volume and finite element approaches for numerical solution of PDEs.
The course helps to form and consolidate the following professional skills:
- to be able to get into a stated problem;
- to be able to formulate and analyze the result;
- to be able to correctly choose and use an appropriate mathematical language in a required subject area;
- to understand the principal idea that the fundamental knowledge in Mathematics forms the bases for modern Computer Sciences.
Professor
Alexander Starchenko, PhD, Professor
Course annotation
Course unit code |
В.2.2 |
|||||
Course unit title |
Basic Professional |
|||||
Name(s), surname(s) and title of lecturer(s) |
Alexander Starchenko, PhD, Professor |
|||||
Semester |
2 |
|||||
ECTS credits |
6 |
|||||
Working hours |
Contact hours |
|||||
lectures |
32 |
|||||
labs |
32 |
|||||
Self-study |
152 |
|||||
Total |
216 |
|||||
Work placement |
Laboratory works in Computer class |
|||||
Prerequisites |
It is assumed that the students have mastered the following disciplines "Mathematical analysis", "Differential Equations", "Partial Differential Equations", "Theory of Probability", "Numerical Methods of approximate calculations" and "Computer Sciences". |
|||||
Language of instruction |
English (Russian) |
|||||
Objectives of the course |
Learning outcomes |
A student’s assessments methods |
||||
This course is intended for training Masters in Math to apply mathematical methods and modeling technique in their professional work. This course is intended to give experience in the application of knowledge for development of the theoretical foundations of the methods of computational mathematics, for formation of practical skills development of numerical algorithms, for organization of computational experiment on the computer, for presentation of the results of calculations. |
In mastering the subject of Numerical analysis of PDEs the student will acquire the following knowledge: finite-differencing, finite-volume and finite element approaches for numerical solution of PDEs. The course helps to form and consolidate the following professional skills: - to be able to get into a stated problem; - to be able to formulate and analyze the result; - to be able to correctly choose and use an appropriate mathematical language in a required subject area; - to understand the principal idea that the fundamental knowledge in Mathematics forms the bases for modern Computer Sciences. |
The current control of mastering the discipline includes three individual task and four reports on the labs. The final control – exam. |
||||
Teaching methods |
Lectures, Labs |
|||||
List of Topics |
Topic title |
Contact hours |
Assignments and independent study hours |
|||
Introduction. |
2 |
|||||
Finite difference schemes for elliptic equations |
8 |
Individual task 1 |
||||
Jacobi method and SOR method for solving of difference equations |
8 |
Lab 1 |
||||
Finite difference schemes for heat equation |
8 |
Lab 2 |
||||
Finite difference schemes for hyperbolic equation |
4 |
Individual task 2 |
||||
Quadrature method for solving integral equations |
6 |
Lab 3 |
||||
Convection-diffusion equation and its properties |
6 |
|||||
Basic finite-difference approximations of the diffusion-convection equation |
6 |
Individual task 3 |
||||
Finite Volume Method |
10 |
Lab 4 |
||||
Finite Volume Method on unstructured mesh |
2 |
|||||
Finite Element Method |
4 |
|||||
64 |
exam |
|||||
Assessment requirements |
In during the semester 70 points |
|||||
Assessment criteria |
Each lab 10 points and test 10 points |
|||||
The composition of final accumulative mark |
Exam 30 points. Examination ticket consists of two theoretical questions (10x2=20) and one exercise (10x1=10). |
|||||
Author of the course |
Alexander Starchenko |