Department of Biophysics · Subjects · Biomathematics 1

Data

Official data in SubjectManager for the following academic year: 2020-2021

Course director

Dr. László GRAMA

associate professor,
Department of Biophysics
laszlo.grama@aok.pte.hu

Number of hours/semester

lectures: 0 hours

practices: 28 hours

seminars: 0 hours

total of: 28 hours

Subject data

Code of subject: OPA-B1G-T
2 kredit
Pharmacy
Basic modul
autumn

Prerequisites:

Course headcount limitations

min. 1

Topic

Introduction into fundamentals and methods of mathematical analysis. Applications in the fields of physics, chemistry and biology. The course focuses on the acquisition of the basic knowledge of mathematics and special courses will introduce the special applications.
Topics discussed during the course: Definition, type and discussion of the functions. Derivatives of elementary functions, geometrical interpretation, differentiation rules and applications. Integration. Solving basic integral problems and differential equations. Examples from physics, chemistry and biology.

Lectures

Practices

1. Introduction: a biological example. Variables and functions
2. Introduction: a biological example. Variables and functions
3. Properties of functions: monotonic, periodic, exponential and log functions. Family of standard functions
4. Properties of functions: monotonic, periodic, exponential and log functions. Family of standard functions
5. Limits and continuity of functions
6. Limits and continuity of functions
7. Sequences and series. Infinite series, test of convergence
8. Sequences and series. Infinite series, test of convergence
9. Rate of change and its limit. Derivatives of elementary functions. Rules of differentiation
10. Rate of change and its limit. Derivatives of elementary functions. Rules of differentiation
11. Higher order derivatives. Taylor's expansion of functions
12. Higher order derivatives. Taylor's expansion of functions
13. Maximum and minimum of functions. Applications for physical problems
14. Maximum and minimum of functions. Applications for physical problems
15. Indefinite integrals: basic integrals. Techniques of integration
16. Indefinite integrals: basic integrals. Techniques of integration
17. Integration by parts and substitutions, composite functions
18. Integration by parts and substitutions, composite functions
19. Definite integral. Newton-Leibniz's rule. Applications
20. Definite integral. Newton-Leibniz's rule. Applications
21. Differential equations. Types of differential equations. Separable differential equations
22. Differential equations. Types of differential equations. Separable differential equations
23. Solution of first-order differential equations
24. Solution of first-order differential equations
25. Application of differential equations: chemical reactions, enzymatic reactions
26. Application of differential equations: chemical reactions, enzymatic reactions
27. Higher order differential equations. Compartment models
28. Higher order differential equations. Compartment models

Seminars

Reading material

Obligatory literature

Literature developed by the Department

http://biofizika.aok.pte.hu

Notes

József Belágyi, László Mátyus, Miklós Nyitrai: Mathematics, textbook
Péter Hajdu, László Grama: Selected Problems in Mathematics, problems booklet

Recommended literature

Conditions for acceptance of the semester

Maximum of 25 % absence allowed

Mid-term exams

Making up for missed classes

Exam topics/questions