Course detail

Mathematic application in chemstry II

FCH-BC_PCM2Acad. year: 2018/2019

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.

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.

Recommended optional programme components

Not applicable.

Recommended or required reading

POLCEROVÁ, Marie. MATLAB počítačová cvičení z matematiky pro chemické aplikace. Brno: Fakulta chemická, Vysoké učení technické v Brně, 2018. (CS)
MATLAB CREATIVE TEAM. MATLAB The Language of Technical Computing. USA: Natick, The MathWorks, Inc., November 2000. Fifth printing. MA 01760-2098 USA. (CS)
POLCEROVÁ, Marie. Doprovodný text k počítačovým cvičením Matematika I. Brno: Fakulta chemická, Vysoké učení technické v Brně, 2001. (CS)

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, or complete a written exam during the last seminar (for up to 100 points). This exam can be retaken once during exam period. Classification is made using ECTS scale.

Language of instruction

Czech

Work placements

Not applicable.

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

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.

Classification of course in study plans

  • Programme BPCP_CHCHT Bachelor's

    branch BPCO_SCH , 1. year of study, summer semester, 2 credits, compulsory

  • Programme BKCP_CHCHT Bachelor's

    branch BKCO_SCH , 1. year of study, summer semester, 2 credits, compulsory
    branch BKCO_CHTOZP , 1. year of study, summer semester, 2 credits, compulsory-optional

  • Programme BPCP_CHCHT Bachelor's

    branch BPCO_CHTOZP , 1. year of study, summer semester, 2 credits, compulsory-optional
    branch BPCO_CHMN , 1. year of study, summer semester, 2 credits, compulsory-optional

  • Programme BKCP_CHCHT Bachelor's

    branch BKCO_CHM , 1. year of study, summer semester, 2 credits, compulsory-optional

  • Programme BPCP_CHCHT Bachelor's

    branch BPCO_CHM , 1. year of study, summer semester, 2 credits, compulsory-optional

  • Programme BPCP_CHTP Bachelor's

    branch BPCO_BT , 1. year of study, summer semester, 2 credits, compulsory-optional

  • Programme BKCP_CHTP Bachelor's

    branch BKCO_BT , 1. year of study, summer semester, 2 credits, compulsory-optional
    branch BKCO_PCH , 1. year of study, summer semester, 2 credits, compulsory-optional

  • Programme BPCP_CHTP Bachelor's

    branch BPCO_CHP , 1. year of study, summer semester, 2 credits, compulsory-optional

  • Programme AKRED_neaktuální Bachelor's

    specialization () , 1. year of study, summer semester, 2 credits, compulsory-optional
    specialization --- , 1. year of study, summer semester, 2 credits, compulsory-optional

Type of course unit

 

Lecture

13 hours, optionally

Teacher / Lecturer

seminars in computer labs

13 hours, compulsory

Teacher / Lecturer