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

**Dr. László GRAMA** (laszlo.grama@aok.pte.hu), associate professor

Department of Biophysics

Code of subject: **OPA-B1G-T** | **2** credit | **Pharmacy** | **Basic** module | **autumn**

Prerequisites: -

0 lectures + 28 practices + 0 seminars = total of 28 hours

min. 1

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.

- 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

http://biofizika.aok.pte.hu

József Belágyi, László Mátyus, Miklós Nyitrai: Mathematics, textbook

Péter Hajdu, László Grama: Selected Problems in Mathematics, problems booklet

Maximum of 25 % absence allowed

http://biofizika.aok.pte.hu

- Dr. Bugyi Beáta
- Dr. Grama László
- Karádi Kristóf
- Madarász Tamás
- Pirisi Katalin Erzsébet