Course code Mate5018

Credit points 2

Total Hours in Course80

Number of hours for lectures16

Number of hours for seminars and practical classes16

Independent study hours48

Date of course confirmation19.10.2022

Responsible UnitDepartment of Mathematics

Matemātikas katedra
## Svetlana Atslēga

Dr. math.

Mate5017, Interdisciplinary Computing I

In this course the approximation and interpolation of functions, interpolation polynomials, splines, discrete and continuous distributions are studied at advanced level. It encourages mathematical thinking, and provides insight into various mathematical applications in information technologies and other fields. In addition, students will acquire skills in working with appropriate software such as Matlab.

After successful completion of this course the student:

1. knows and is capable of proving knowledge and critical understanding of interpolation of functions, interpolation polynomials, splines, discrete and continuous distributions, their applicability for describing the real-world processes considered in their specialty. – tests

2. is able to show understanding of relevant concepts and regularities, to perform necessary actions and operations. The student is able to use the appropriate software to make calculations. While working in a group or doing work independently, student is able to apply mathematical calculations corresponding to the problem of the specialty, to perform the intermediate results of the calculations and professional evaluation and interpretation of the final results, to apply knowledge in calculations for their branch of research, summarize and analytically describe the results. - independent works.

1. Approximation of functions. Interpolation. Parabolic interpolation. (4 h)

2. Lagrange interpolation. Newton interpolation. Computation and constraction of interpolation polynomial using Matlab. (4 h)

3. Hermite interpolation

4. Spline interpolation. Spline interpolation using Matlab: General Spline Interpolation, Cubic Spline Interpolation. (4 h)

5. 1st test: Interpolation (2 h)

6. Mathematical Modelling. Mathematical Modelling in Nature: mathematical modelling of forest stands. (3 h)

7. Random variables. Probability density function and its properties. Cumulative distribution function and its properties. Continuous distributions: normal distribution, exponential distributions. Random variables and simulations. (4 h)

8. Imitation Monte Carlo methods. The computer simulation of Monte Carlo methods and some random processes: functions random, norm and exp. (4 h)

9. History of biosystems and biosystems today. Bioinformation databases and its analysis, biological statistics. (4 h)

10. 2nd test: Mathematical Modelling. Random variables. Applications of Monte Carlo method (2 h)

The requirement is – passing the test.

The following independent works must be completed and credited, both in writing and using the appropriate application software:

1st Independent Work: Parabolic interpolation. Lagrange interpolation.

2nd Independent Work: Newton interpolation. Hermite interpolation.

3rd Independent Work: Spline interpolation.

4th Independent Work: Random variables.

5th Independent Work: Monte Carlo methods.

The student can receive the accumulative exam if:

- all independent works are completed (all tasks are executed correctly);

- during the semester each test score is at least 4.

Failed tests can be repeated.

The student may overwrite unsuccessfully written test work during the study process, at times specified by the teaching staff.

The accumulative exam mark is the average mark of all tests.

The written exam can be arranged at the time indicated by the lecturer, if all the independent works are defended (all tasks are performed correctly)..

1. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika II daļa. Rīga: Zvaigzne, 1988. – 527 lpp.

2. Buiķis A. Matemātiskās fizikas vienādojumi. Pamatjautājumi. Rīga: Latvijas Universitāte, 2003. – 57 lpp.

3. Anthony J. Wheeler, Ahmad R. Ganji. Introduction to Engineering Experimentation: International Version, 3/E. Pearson Higher Education, 2010, 480 pp. [skatīts 17.04.2019.] Pieejams:

http://vig.pearsoned.co.uk/catalog/academic/product/0,1144,0135113148-TOC,00.html

1. Christian P. Robert, George Casella. Monte Carlo statistical methods. Springer, 2004. – 645 p.

2. Said Elnashaie, Frank Uhlig. Numerical techniques for Chemical and biological engineers using MATLAB. A simple bifurcation approach. Springer, 2007. – 590 p.

3. Veerarajan T. Probability, Statistics and Random Processes. Tata MCGraw-Hill,2009. - 595 p.

Course for master study programme “Information Technologies”.