YMX8150 Applied Mathematics

2nd part of the course

Numerical methods for equations of mathematical physics

(weeks 7 – 11 of the academic semester).

Topics to be studied are: finite difference, finite elements and finite volume methods to solve boundary value problems of mathematical physics in 1d and 2d cases as well as explicit and implicit finite difference schemes to solve initial boundary value problems in 1d case. Presentation of the material follows the book

V. Ruas, Numerical methods for partial differential equations. Wiley, 2016 

that can be electronically accessed in the university network. The URL is:

http://ebookcentral.proquest.com/lib/tuee/detail.action?docID=4517661&query=Ruas%20Numerical%20methods%20for%20partial%20differential%20equations

In case you have problems to access this book, please contact me:

jaan.janno@taltech.ee

Some supplements are given by the lecturer, too: slides of lectures.

Excercises are solved by means of Matlab, alternatively the software GNU Octave can be used. Solution of homework problems by means of other software (e.g. C, Python) is also accepted. An exception is only MS Excel, homeworks done by Excel are not accepted.

Our university has acquired Total Academic Headcount (TAH) individual licence of Matlab that includes all modules. Instructions for installation are here:

https://confluence.ttu.ee/it-info/it-arvuti-ja-oppetoeoekoht/tarkvara/matlab

Each student must choose two problems from the list of homework problems and present solutions.

The grade of this part of the course is computed on the basis of sum of credits of homeworks and theoretical test. Maximal credits:

First homework: 30

Second homework: 30

Theoretical test: 40.

Algorithm for computing the grade on the basis of sum of credits.

0 – 50    “0”

51 - 55   “0.5”

56 - 60    “1”

61 – 65   “1.5”

66 – 70   “2”

71 – 75   “2.5”

76 – 80   “3”

81 – 85   “3.5”

86 – 90   “4”

91 – 95   “4.5”

96 – 100  5”

Questions for theoretical test are  here .

Plan of classes (Fall 2021):

7. week

Tuesday: Matlab basics (variables, functions, scripts, loops, operations with arrays, graphics) – students acquainted with matlab may skip this class

Thursday: introductory material (solving linear systems of algebraic equations, approximate computation of derivatives, classical problems of mathematical physics) and beginning of the main material

8. week:

Tuesday (19 October) the class will not take place

Thursday: main material

9 – 11. weeks:  main material

We will arrange an additional time for the theoretical test on 12. week.

 

Material of classes (to be updated!):

Scripts of 1st class (Matlab basics)

Problems solved in class with Matlab scripts.

Times for retaking the theoretical test:

6.01.2022 12.00 U05-402

13.01.2022 12.00 U05-402

17.01.2022 12.00 U05-402