Biomathematics 1 - Theory

Data

Official data in SubjectManager for the following academic year: 2019-2020

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

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

Practices

Seminars

Reading material

Obligatory literature

Literature developed by the Department

htp://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

http://biofizika.aok.pte.hu
The criterion of admission to the exam is the successful completion of the practice carried out in paralell (midsemester grade with the result different from ?failed?).

Examiners

• Dr. Bugyi Beáta
• Dr. Grama László
• Tempfliné Pirisi Katalin Erzsébet

Instructor / tutor of practices and seminars