Courses – Fakultet tehničkih nauka u Novom Sadu

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

Type of studies	Title
Master Academic Studies	Mathematics in Engineering (Year: 1, Semester: Summer)

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
A. Babloyantz,	MOLECULES, DYNAMICS, AND LIFE, An Introduction to Self-Organization of Matter,	1986	John Wiley & Sons,	English
Quarteroni, A., Formaggia, L., Veneziani, A.	Complex Systems in Biomedicine	2006	Springer, Milano	English
2. Jon Mathews, R.L. Walker,	MATHEMATICAL METHODS OF PHYSICS,	1969	w.a. Benjamin, Inc., Menlo Park, California,	English

Course activity	Pre-examination	Obligations	Number of points
Test	Yes	Yes	10.00
Final exam - part two	No	No	25.00
Exercise attendance	Yes	Yes	2.00
Final exam - part one	No	No	25.00
Test	Yes	Yes	10.00
Test	Yes	Yes	10.00
Written part of the exam - tasks and theory	No	Yes	50.00
Project	Yes	Yes	15.00
Lecture attendance	Yes	Yes	3.00