Southern Federal University
Faculty of mathematics, mechanics and computer science
Milchakova str. 8a, Rostov-on-Don, 344090
Phone.: (863) 2975 111;
Fax: (863) 2975 113;
SYLLABUS
1-semester course
Modern Problems of Applied Mathematics and Informatics
for Masters Program Computational Mechanics and Biomechanics.
3 ECTS Credits
Aim of the course
The course “Modern problems in applied mathematics and informatics” is dedicated
to the overview of modern computer technologies for research and mathematical modeling
in biomechanics. The subject of the course is focused on the paradigms in information
technologies, program tools for natural science research and mathematical modeling some
biomechanics phenomena (mammalian skin, blood-vessels flow, bone replacement etc.).
The major emphasis is on the study of scientific computer FEM packages and their
utilization. Also this course deals with some additional computer-added techniques and
tools for research (research data visualization, scientific publications, scientific databases,
applied mathematics Internet portals, etc.).
2
Techniques, Skills, etc.
After completing the course, the students are expected to be able to:

compare different parallel and distributed computational systems;

choose and implement a suitable program tools for parallel coding;

compare different database and knowledge base systems;

compare different CAD/CAE systems;

utilize additional program tools for research (visualization systems, computer
packages for typesetting, etc.);

ascertain basic approaches for mathematical modeling in biomechanics;

understand and analyze the influence of approximation, calculations and
modeling errors;

utilize math packages (MATLAB, ANSYS etc.) for numerical experiments;

present coherent arguments to answer questions both orally and in writing.
Teaching
The following methods and forms of study are used in the course:

Lectures

Problem sets

Program packages utilization and coding

Self-study

Use of different reference books and Internet resources
At the end of the course the students are supposed to do case-study, make an oral
presentation and participate in discussion. Upon the successful completion, the students
will gain 3 credits.
Course content
3
#
Subject
№
1.
1
Introduction.
Form of
Duration
Lesson
(hrs)
Lecture
1
Lecture
1
Lecture
2
Cloud computing as Lecture
2
Course organization, its
aims and structure.
Information on core and
additional readings.
2.
Role of information
technologies and
2
computing tolls in applied
math, i.e. natural science
and engineering.
3.
Parallel and
Distributed computing
3
systems, their
classification. Program
tools for parallel coding.
Grid systems and grid
technologies
4.
distributed scalable virtual
4
services. Self service on
demand and resource
pooling. Private, public,
hybrid and community
clouds.
5.
Database and
Knowledge base systems,
5
their classification: cloud
database, data warehouse,
Lecture
2
Date
4
distributed database,
document-oriented
database, graph database,
hypermedia databases,
parallel database, real-time
database, spatial database.
Data models: hierarchical,
network, relational, object
and object relational.
Neural network.
6.
CAD/CAE systems. Lecture
2
Their classifications and
6
potential. Comparison of
CAD/CAE systems.
7.
Scientific
Lecture
2
Lecture
1
Colloquium
2
Self-study
16
computations and
7
computer algebra systems.
Algebraic algorithms and
symbolic computations
8.
Additional program
tools for research:
visualization systems and
image file formats,
8
computer packages for
typesetting, scientific
databases and Internet
portals
9.
9
10.
Essay presentation
1Mathematical model Lecture
4
5
10
for skin as soft tissue
11.
11
Two-phase
Lecture
4
1Mathematical model Lecture
4
mathematical model for
blood-vessel flow
12.
12
for quasi-one-dimensional
hemodynamics
13.
Mathematical
Lecture
4
Colloquium
2
Self-study
16
Lecture
4
Laboratory
3
Lecture
3
modeling of the hip
13
replacement
14.
Essay presentation
14
15.
Finite element
method and, its
15
foundations and technique
16.
Computer modeling
in mechanical and
16
biomechanical problems
with Maple and Maxima
17.
Computer modeling
in mechanical and
17
biomechanical problems
with Matlab
18.
Computer modeling
3
in mechanical and
18
biomechanical problems
with FlexPDE
19.
19
1Computer modeling
in mechanical and
biomechanical problems
Lecture
3
6
with ANSYS
20.
Computer modeling
Lecture
3
Colloquium
2
Self-study
22
in mechanical and
biomechanical problems
20
with Comsol
21.
21
Summarizing case-
study presentation
Requirements
During the session students are required to

attend class lectures;

write essays;

provide case-study;

represent the essays and case-study results in oral presentation at the
colloquium;

be prepared to participate in final course discussion.
Grade determination

Class participation - 40%

Written essay and its presentation – 15% (per each)

Case-study and its presentation – 20%

Participation in discussion – 10%
7
Literature
Core
1.
Encyclopedia of Computational Mechanics, Edited by Erwin Stein, Ren´e de
Borst and Thomas J.R. Hughes. Volume 1: Fundamentals. Volume 2: Solids and
Structures. Volume 3: Fluids. 2004. John Wiley & Sons.
2.
Biomechanics: principles and applications / edited by D. Schneck and J. D.
Bronzino. – CRC Press, 2003. – 300 p.
3.
Computer Methods in Biomechanics and Biomedical Engineering, J.
Middleton, University of Wales, Cardiff, Wales;
Gyan Pande, University of Wales
Swansea, Swansea, Wales, UK; M. L. Jones.
4.
Mathematical Problem Solving and New Information Technologies Research
in Contexts of Practice, Ponte, J.P.; Matos, J.F.; Matos, J.M.; Fernandes, D., 1992, XV,
346 p.
5.
Fundamentals of Mobile and Pervasive Computing, by Frank Adelstein,
Sandeep KS Gupta, Golden Richard III, and Loren Schwiebert, 2004
6.
Distributed Systems: Principles and Paradigms, by Andrew S. Tanenbaum
and Maarten Van Steen, 2006
7.
An introduction to numerical methods: A MATLAB approach / Abdelwahab
Kharab, Ronald B. Guenther.- 2nd ed.- Boka Raton, FL : Chapman & Hall/CRC, 2006.
8.
Neural networks: methodology and applications G. Dreyfus - 2005 // Springer
9.
Jiawei Han, Micheline Kamber & Jian Pei. Data Mining: Concepts and
Techniques (The Morgan Kaufmann Series in Data Management Systems), 2006, 800 p.
Additional
10.
Biomechanics: Mechanical Properties of Living Tissues Fung, Y. C., 1993,
11.
Fundamentals of Biomechanics: Equilibrium, Motion, and Deformation,
592 p.
Leger, Dawn L. Nordin, Margareta, 1999, XXII, 393 p.
12.
An Introduction to Biomechanics: Solids and Fluids, Analysis and Design
Humphrey, Jay D., DeLange, Sherry 2004, XVII, 631 p.
8
13.
Solving
PDEs
in
C++
(Computational Science and Engineering), Yair Shapira Yair Shapira
14.
Mobile
Computing
Principles:
Designing
and
Developing
Mobile
Applications with UML and XML, by Reza B'Far and Roy T. Fielding, 2004
15.
Cloud Computing: Implementation, Management, and Security, by John
Rittinghouse and James Ransome,2009
16.
Jamie MacLennan, ZhaoHui Tang, Bogdan Crivat . Data Mining with
Microsoft SQL Server. Wiley, 2008.- 672 p.
17.
Alan Dennis. Systems Analysis and Design with UML. Publisher: Wiley,
2007. 600 p.
Internet Resources
The World of Mathematical Equations. http://eqworld.ipmnet.ru/index.htm
MavicaNET - Multilingual Search Catalog. http://www.mavicanet.ru/directory/
Biomechanics and Movement Science Listserver. http://biomch-l.isbweb.org
Biomechanics Links. http://bones.ame.nd.edu/links.html
MathWorld. http://mathworld.wolfram.com