Course detail

Mathematical Applications in Chemistry I

FCH-BC_PCM1Acad. year: 2022/2023

The course deals with solving tasks using computer technology. Chosen topics of secondary school mathematics and subject Mathematics I (calculation of values of elementary functions, substitution into formulas, modification of terms, solution of nonlinear equations, systems of equations, graphs in 2D, differentials of real functions of one real variable, matrices, determinants) are taught and exercised using computer technology and applied to chemistry. Mathematical software MATLAB is used in lessons 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) using advanced methods to solve basic mathematical tasks quickly and easily
b) effectively solving practical tasks with applications in chemistry
c) ability to present solution with appropriate graphical representation in 2D
d) combining symbolic, numerical and graphical methods in their solutions
e) verifying solutions using alternative methods
f) creation of simple m-files, that solve given task with given input values
g) modification of existing m-files to solve different tasks

Prerequisites

Knowledge of mathematics, computer science and chemistry at the secondary school level is expected.

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 (elementary functions), students submit one m-file and they can receive up to 24 points. At least 12 points have to be achieved, otherwise the result is considered unsatisfactory. During second test (calculations in chemistry) up to 36 points can be gained. Accurate or approximate result has to be calculated and at least 18 points gained. During the third test (course of function), at least one m-file is submitted. Result is satisfactory, when graph of function is correct and at least 20 points from a maximum of 40 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 the first week of the exam period. Each test is possible retake twice. Classification is made using ECTS scale.

Course curriculum

Week 1: Lecture - Elementary functions in MATLAB
Week 2: Seminar - Use of elementary functions in MATLAB
Week 3: Lecture - Calculations in chemistry, part 1 - analytical and numerical calculations
Week 4: Seminar - Test n. 1: Elementary functions in MATLAB
Week 5: Lecture - Calculations in chemistry, part 2 - non-linear equations
Week 6: Seminar - Calculations in chemistry
Week 7: Lecture - Graphs of functions in 2D, part 1 - course of a function
Week 8: Seminar - Test n. 2: Calculations in chemistry,
basics of graph creation
Week 9: Lecture - Graphs of functions in 2D, part 2
Week 10: Seminar - Course of a real function of one real variable
Week 11: Lecture - Use of differentials in chemistry, matrices, determinants
Week 12: Seminar - Test n. 3: Course of a function
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 (secondary school and Mathematics I). 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.

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

Elearning

eLearning: currently opened course