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Biomathematics 1 - Practice

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Data

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

Course director

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

Department of Biophysics

Subject data

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

Prerequisites: -

Number of hours/semester

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

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

http://biofizika.aok.pte.hu

Examiners

Instructor / tutor of practices and seminars

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