Mathematical Simulation
Course Overview 
Level of study
	Bachelor Degree	
Workload	ECTS: 3
Total Hours: 108
Contact Hours: 48
•	Lectures: 16
•	Labs: 0
•	Seminars: 32
	
Course Code		
Semester
	Winter /Summer	
Prerequisites
	Higher Mathematics, Computer Science.	
Course Objectives	Quantitative Reasoning and Mathematics: quantitative reasoning and mathematics will be characterized by logic, critical evaluation, analysis, synthesis generalization, modeling, and verbal, numeric, graphical, and symbolic problem solving.

-Ability to model situations from a variety of settings in generalized mathematical forms;
- Ability to express and manipulate mathematical information, concepts, and thoughts in verbal, numeric, graphical and symbolic form while solving a variety of problems;
- Ability to solve multiple-step problems through different (inductive, deductive and symbolic) modes of reasoning;
- Ability to properly use appropriate technology in the evaluation, analysis, and synthesis of information in problem-solving situations;
- Ability to shift among the verbal, numeric, graphical and symbolic modes of considering relationships;
- Ability to extract quantitative data from a given situation, translate the data into information in various modes, evaluate the information, abstract essential information, make logical deductions, and arrive at reasonable conclusions;
- Ability to employ quantitative reasoning appropriately while applying scientific methodology to explore nature and the universe;
- Ability to discern the impact of quantitative reasoning and mathematics on the sciences, society, and one's personal life.	
Learning Outcomes
	- The student will be able to identify the relevant parameters and relationships for real-world problems and hence guide experimental design.
- The student will be able to exploit dimensional analysis to construct realistic scaled models.
- Given schematic diagram of vibration system, the student will be able to write the differential equation(s) describing the dynamics of the system.
- Given few fit a model to experimental data, the student will be able to choose which model best fits the data (Model fitting).
- Given experimental data, the student will be able to create model and to predict other experimental results (Model interpolation).
- Given a mathematical model, the student will be able to determine, what is the ‘best’ possible output (Optimization).	
Syllabus
	Topic 1. Mathematical Modelling. Basic definitions and concepts 
Topic 2. Dimensional Analysis. 
Topic 3. Similitude. 
Topic 4. Modeling with differential equations
Topic 5. Mathematical processing of experimental data. Fitting Data
Topic 6. Mathematical processing of experimental data. Interpolation. 
Topic 7. Optimization parameters of mathematic model.	
Labs
	-	
Projects
	-	
Assessment
	Credit Test	
Resources
	Resource type: Background textbook
Alexander A. Samarskii, Alexander P. Mikhailov. Principles of Mathematical Modelling: Ideas, Methods, Examples. - 2001

Resource type: Background textbook
Nguyen V.M. Man, Ph.D., Mathematical Modeling and Simulation.-2010

Resource type: Background textbook
Stephen L. Campbell, Jean-Philippe Chancelier, Ramine Nikoukhah. Modeling and Simulation in Scilab/Scicos.- 2000

Resource type: Background textbook
Chen K., Giblin P., Irving A., Mathematical Explorations with MATLAB. - 2008

Resource type: On-line resources
Students will be provided a list of classic papers which are available on-line which they will be expected to read in order to gain an overview of the field, and also have access to a range of textbooks which help them prepare for the assessed seminars and tests.
http://stud.lms.tpu.ru/course/view.php?id=1039
	
Instructors
	Deryusheva Valentina Nikolaevna
http://portal.tpu.ru:7777/SHARED/v/VDERUSHEVA/eng
	
Примечание: пример описания дисциплины можно посмотреть по ссылке: http://www.ecs.soton.ac.uk/module/COMP6233#overview