Mathematical solutions (traditional and using MATLAB) of differential equations in physical chemistry – basic use of functions ode23 and ode45)

Mathematical solutions (traditional and using MATLAB) of differential equations in physical chemistry – basic use of functions ode23 and ode45)

Paper in proceedings (conference paper)

The objective of the computer-aided teaching of Mathematics I and Mathematics II is to make students learn to apply the acquired knowledge and mathematical skills in technical subjects. For this reason, in Mathematics II each student has to solve individually given application task using differential equations. Students have to solve this task from physical chemistry first generally by traditional manual calculations. Then they can substitute a specific given value and calculate exact and approximate solutions. Students should check both of these results using MATLAB. Then they find, independently of this solution, specific approximate solution using predefined functions ode23 and ode45 in MATLAB and calculate absolute error of their approximate solution. In this paper this unusual way of solving problems from reaction kinetics is analyzed on three examples of basic use of functions ode23 and ode45. First example deals with calculation of current concentration of resulting product, given initial concentration of two reactants, rate constant and reaction time. The second example deals with calculation of speed of chemical reaction and includes explanation of the possibility of setting the maximum step for both of the above mentioned functions. The third example shows process of solution of subsequent reactions. This paper does not deal of following because it would have exceeded the maximum number of pages allowed: cases where it is not possible from the general solution to explicitly express the function of current concentration of the final product or not generally express current quantity for example of salt in the second tank, even when rate constant, reaction time, or neither is not known.

The objective of the computer-aided teaching of Mathematics I and Mathematics II is to make students learn to apply the acquired knowledge and mathematical skills in technical subjects. For this reason, in Mathematics II each student has to solve individually given application task using differential equations. Students have to solve this task from physical chemistry first generally by traditional manual calculations. Then they can substitute a specific given value and calculate exact and approximate solutions. Students should check both of these results using MATLAB. Then they find, independently of this solution, specific approximate solution using predefined functions ode23 and ode45 in MATLAB and calculate absolute error of their approximate solution. In this paper this unusual way of solving problems from reaction kinetics is analyzed on three examples of basic use of functions ode23 and ode45. First example deals with calculation of current concentration of resulting product, given initial concentration of two reactants, rate constant and reaction time. The second example deals with calculation of speed of chemical reaction and includes explanation of the possibility of setting the maximum step for both of the above mentioned functions. The third example shows process of solution of subsequent reactions. This paper does not deal of following because it would have exceeded the maximum number of pages allowed: cases where it is not possible from the general solution to explicitly express the function of current concentration of the final product or not generally express current quantity for example of salt in the second tank, even when rate constant, reaction time, or neither is not known.

Mathematics, differential equations, physical chemistry, MATLAB, ode23, ode45

Mathematics, differential equations, physical chemistry, MATLAB, ode23, ode45

POLCEROVÁ, M.

2016

15.06.2015

Univerzita Obrany, Brno

Brno

978-80-7231-998-5

Matematika, informační technologie a aplikované vědy

první

NEUVEDENO

199

205

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