Faculty of Technical Sciences

Subject: Mathematical methods in biomedical sciences (17.OM539)

General information:
 
Category Professional-applicative
Scientific or art field
  • Teorijska i primenjena matematika
  • Physics
ECTS 5

Preparing the students to be capable for abstract thinking and gaining the basic knowledge from mathematical tools important for quantitative description of biomedical phenomena. After finishing of this subject students are enable to perform the sophisticated quantitative evaluation of statistical processes involved in cellular dynamics. This includes the application of Boltzmann’s, Maxwell’s and Gibbs’s statistics. Besides, the methods of nonlinear equations leading to appearance of solitonic waves will be elaborated. These waves serve as signal mechanisms within the functional dynamics of living cells.

The acquired knowledge the student uses in the future education and in the other subjects by constructing and solving the adequate mathematical models.

Theoretical study: The statistical thermodynamic distributions; Boltzmann’s, Maxwell’s and Gibb’s statistics and Arhenius law. The diffusion equations; The fluctuation-dissipation theorem. Langevin’s equations. The nonlinear differential equations which describe the mechanism of action potential in nerv-axon cells. (The Hodgkin-Huxley equation and the Fitzhugh-Nagumo equation). The solitonic waves as signaling mechanisms in living cells. Nonlinear differential equations of electrical transmission lines leading to the localized pulses of ionic currents in living cells.Practical classes (exercise): the exercises are performed with appropriate examples of theory that practicing a given material and therefore contribute to the understanding and practice of a given material.

Lectures. Numerical and calculation practice. Consultations. Lectures are organized in combined form. The presentation of the theoretical part is followed by the corresponding examples which contribute to better understanding of the theoretical part. During the practice classes which follow the lectures, the subject matter is supported by charactristic examples to provide futher practice and better understanding In addition to lectures and practice classes there are regular consultations. There is a possibility of taking partial examinations which cover certain logical units during the course.

Authors Title Year Publisher Language
2. Jon Mathews, R.L. Walker, MATHEMATICAL METHODS OF PHYSICS, 1969 w.a. Benjamin, Inc., Menlo Park, California, English
Quarteroni, A., Formaggia, L., Veneziani, A. Complex Systems in Biomedicine 2006 Springer, Milano English
A. Babloyantz, MOLECULES, DYNAMICS, AND LIFE, An Introduction to Self-Organization of Matter, 1986 John Wiley & Sons, English
Course activity Pre-examination Obligations Number of points
Written part of the exam - tasks and theory No Yes 50.00
Lecture attendance Yes Yes 3.00
Final exam - part two No No 25.00
Final exam - part one No No 25.00
Test Yes Yes 10.00
Project Yes Yes 15.00
Test Yes Yes 10.00
Test Yes Yes 10.00
Exercise attendance Yes Yes 2.00
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Prof. Lončarević Ivana

Full Professor

Lectures

Assoc. Prof. Nedović Maja

Associate Professor

Lectures
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Assoc. Prof. Ilić Dušan

Associate Professor

Practical classes
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Assoc. Prof. Ilić Dušan

Associate Professor

Computational classes

Faculty of Technical Sciences

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Phone:  (+381) 21 450 810
(+381) 21 6350 413

Fax : (+381) 21 458 133
Emejl: ftndean@uns.ac.rs

© 2024. Faculty of Technical Sciences.