(in Polish) Matematyka dla chemików II WM-CH-S1-E2-MCH2
Mathematics for Chemists 2 extends the fundamental concepts of calculus introduced in the first semester (limits, continuity, derivatives, and integrals). The course focuses on mathematical tools essential for modeling and analyzing chemical and physicochemical processes.
Course Content:
1. Advanced Integration Techniques
- integration by parts,
- substitution methods (including multiple and nonlinear substitutions),
- integrals involving exponential, logarithmic, and trigonometric functions.
Chemical applications:
- calculation of work and energy in thermodynamic processes,
- integration of rate laws,
- determination of average physical quantities (e.g., molecular energy or velocity).
2. Ordinary Differential Equations (ODEs)
- separable equations,
- first-order linear equations,
- simple dynamic models.
Chemical applications:
- chemical reaction kinetics (first- and second-order reactions),
- radioactive decay,
- time evolution of concentrations,
- simplified models of diffusion and relaxation processes.
3. Functions of Several Variables
- partial derivatives,
- gradient and direction of steepest ascent,
- higher-order derivatives,
- local extrema and necessary conditions.
Chemical applications:
- potential energy surfaces,
- molecular geometry optimization,
- dependence of thermodynamic quantities (e.g., energy, entropy) on multiple variables,
- phase and chemical equilibria.
4. Multiple Integrals
- double and triple integrals,
- change of variables (polar, cylindrical, spherical coordinates),
- geometric and physical interpretations.
Chemical applications:
- calculation of mass, charge, and energy for spatial distributions,
- distribution functions in molecular/statistical chemistry,
- modeling electron density,
- integration over volumes in physicochemical systems.
5. Introduction to Vector Calculus
- scalar and vector fields,
- gradient, divergence, and curl (conceptual level),
- line and surface integrals (introductory level).
Chemical applications:
- force fields (e.g., electrostatics),
(in Polish) Dyscyplina naukowa, do której odnoszą się efekty uczenia się
(in Polish) E-Learning
(in Polish) Grupa przedmiotów ogólnouczenianych
Subject level
Learning outcome code/codes
Type of subject
Preliminary Requirements
Course coordinators
Learning outcomes
Upon completion of the course, the student:
- applies integration techniques to solve physicochemical problems,
- solves basic differential equations describing chemical processes,
- analyzes functions of several variables and interprets their physical meaning,
- uses multiple integrals to describe spatial systems,
- understands fundamental concepts of vector calculus in the context of transport phenomena and fields.
Assessment criteria
Passing the classes requires passing short tests happening each week and oral exam. The proposed grade is dependent on the total amount of points gathered compared to the best result. The best student gets grade 4.5. The rest have the grades proposed according to the scheme:
>80%MAX => 4.5
>70%MAX => 4
>60%MAX => 3.5
>50%MAX => 3
The final grade is obtained after an oral exam at which the student can increase the proposed mark.
Practical placement
Not applicable
Bibliography
- Fichtenholz, G. M. (1964). Rachunek różniczkowy i całkowy, t. 1-3. Wydawnictwo Naukowe PWN, Warszawa;
- Rudin, W., Pierzchalski, A., & Walczak, P. G. (2009). Analiza rzeczywista i zespolona. Wydawnictwo Naukowe PWN;
- Leja, F. (1965). Rachunek rozniczkowy i calkowy. Panstwowe wydawnictwo naukowe;
- Krysicki, W., & Włodarski, L. (1999). Analiza matematyczna w zadaniach. Wydawn. Naukowe PWN;
- Banaś, J., & Wędrychowicz, S. (2020). Zbiór zadań z analizy matematycznej. Wydawnictwo Naukowe PWN.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: