Course detail

Mathematical Applications in Chemistry II

FCH-BC_PCM2Acad. year: 2022/2023

Content of the subject is approximation of function (both discrete and continuous) using selected function (polynomial, exponential function, etc.) and selected criteria (least squares method, splines, etc.). Examples are selected from seminars of other, chemistry related subjects. Subject further involves integrals of real functions of one and two variables (calculation of area, volume, length of a curve) and solution of differential equations. These are solved using different methods with focus on numerical methods using ode functions in MATLAB. Examples are based on problems solved in subjects physical chemistry and chemical engineering. Lessons utilize mathematical software MATLAB, which is used to solve tasks analytically, numerically and graphically.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

Ing. Dušan Navrátil

Department

Institute of Physical and Applied Chemistry (ÚFSCH)

Learning outcomes of the course unit

Knowledge, abilities and competence of students is expected to be seen in following areas:
a) making relevant approximation of function quickly and easily
b) evaluating definite integrals
c) solving differential equations using different methods, knowing their advantages and disadvantages
d) using functions ode23 and ode45 in MATLAB to solve differential equations
e) creating simple m-files, that solve given task with given input values
f) modifying existing m-files to solve different tasks

Prerequisites

Knowledge of calculus and approximation of functions is expected. Knowledge of symbolic and numeric calculations in MATLAB and ability to create 2D graphs in this software is expected as well.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Theoretical knowledge, examples of solutions and applications of tasks in chemistry are presented in lectures. Seminars are used to practise selected tasks and their applications. Students can study from distance learning text: MATLAB počítačová cvičení z matematiky pro chemické aplikace. Additional study material, guides and tasks for practise are provided in LMS Moodle.

Assesment methods and criteria linked to learning outcomes

Students take three tests during the semester. During the first test (approximations), students submit one m-file and they can receive up to 32 points. At least 16 points have to be achieved, otherwise the result is considered unsatisfactory. During second test (application of integrals) up to 32 points can be gained. Numerical result has to be calculated and at least 16 points gained. During the third test (application of differential equations), appropriate number of m-files is submitted. Result is satisfactory, when numerical result is correct and at least 18 points from a maximum of 36 are achieved. As long as students have satisfactory result on all three tests and do not have an unexcused absence they will be awarded course-unit credit. If any of the tests is unsatisfactory and it is not retaken during the semester, student has to either retake this test during thefirst week at the exam period. Classification is made using ECTS scale.

Course curriculum

Week 1: Lecture - Approximation in 2D in Chemistry, part 1 - least squares method
Week 2: Seminar - Practising approximations of measured data sets
Week 3: Lecture - Approximation in 2D in Chemistry, part 1 - other approximation methods
Week 4: Seminar - Approximations
Week 5: Lecture - Application of integrals
Week 6: Seminar - Practising selected examples
Week 7: Lecture - Application of differential equations, part 1
Week 8: Seminar - Application if integrals
Week 9: Lecture - Application of differential equations, part 1
Week 10: Seminar - Practising tasks with differential equations found in physical chemistry and chemical engineering
Week 11: Lecture - Differential of real function of two real variables
Week 12: Seminar - Correction tests
Week 13: Lecture - Final lecture. Evaluation of achieved results in subject

Work placements

Not applicable.

Aims

Subject's goal is to introduce students to advanced methods of solving mathematical tasks (Mathematics I and Mathematics II). These methods are necessary for studying chemistry. Students are going to learn basics of mathematical informatics and will be prepared for its application in other subjects, especially in subjects with focus on chemistry. This is one of the key competencies according to Bologna conference on European higher education area.

Specification of controlled education, way of implementation and compensation for absences

Seminars will be held for two hours every two weeks in specialized IT classroom. Attendance on seminars is mandatory and will be checked. Lectures will be held two hours every two weeks. Attendance on lectures is recommended but not mandatory.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

POLCEROVÁ, Marie. Doprovodný text k počítačovým cvičením Matematika I. Brno: Fakulta chemická, Vysoké učení technické v Brně, 2001. (CS)
POLCEROVÁ, Marie. MATLAB počítačová cvičení z matematiky pro chemické aplikace. Brno: Fakulta chemická, Vysoké učení technické v Brně, 2018. (CS)

Type of course unit

Lecture

13 hod., optionally

Teacher / Lecturer

Ing. Jiří Hvožďa

Computer-assisted exercise

13 hod., compulsory

Teacher / Lecturer

Ing. Martin Chabičovský, Ph.D.
Ing. Jan Komínek, Ph.D.
Ing. Dušan Navrátil

Elearning

eLearning: currently opened course