Lecture

Dirac Delta Function and ODEs

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In course

CH-250: Mathematical methods in chemistry

This course consists of two parts. The first part covers basic concepts of molecular symmetry and the application of group theory to describe it. The second part introduces Laplace transforms and Fourier series and their use for solving ordinary and partia ...

Description

This lecture covers the Dirac delta function, its properties, and derivatives, as well as Laplace transforms for solving ordinary differential equations. It also discusses irreversible, reversible, and driven unimolecular reactions, emphasizing convolution, and the convolution theorem.

Instructors (2)

Ulrich Lorenz

Teaching & PhD PhD Students Jakub Hruby Past EPFL PhD Students Pavel Olshin, Gabriele Bongiovanni, Chengcheng Yan, Oliver Florian Harder, Mowry Nathan Junior, Constantin Richard Krüger

Jiri Vanicek

Teaching & PhD PhD Students Liam Oliver Marsh, Yeha Lee, Davide Barbiero, Yannick Calvino Alonso, Manas Nagda Past EPFL PhD Students Cesare Mollica, Ray Marcel Marin Florez, Marius Wehrle, Aurélien Patoz, Konstantin Karandashev, Tomislav Begusic, Julien Roulet, Seonghoon Choi, Roya Moghaddasi Fereidani, Zhan Tong Zhang, Eriks Kletnieks, Alan Scheidegger, Fabian Kröninger Courses Mathematical methods in chemistry CH-250 This course consists of two parts. The first part covers basic concepts

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Related concepts (31)

Molecularity

In chemistry, molecularity is the number of molecules that come together to react in an elementary (single-step) reaction and is equal to the sum of stoichiometric coefficients of reactants in the elementary reaction with effective collision (sufficient energy) and correct orientation. Depending on how many molecules come together, a reaction can be unimolecular, bimolecular or even trimolecular. The kinetic order of any elementary reaction or reaction step is equal to its molecularity, and the rate equation of an elementary reaction can therefore be determined by inspection, from the molecularity.

Homogeneous differential equation

A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.

Elementary reaction

An elementary reaction is a chemical reaction in which one or more chemical species react directly to form products in a single reaction step and with a single transition state. In practice, a reaction is assumed to be elementary if no reaction intermediates have been detected or need to be postulated to describe the reaction on a molecular scale. An apparently elementary reaction may be in fact a stepwise reaction, i.e. a complicated sequence of chemical reactions, with reaction intermediates of variable lifetimes.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Lindemann mechanism

In chemical kinetics, the Lindemann mechanism (also called the Lindemann–Christiansen mechanism or the Lindemann–Hinshelwood mechanism) is a schematic reaction mechanism for unimolecular reactions. Frederick Lindemann and J. A. Christiansen proposed the concept almost simultaneously in 1921, and Cyril Hinshelwood developed it to take into account the energy distributed among vibrational degrees of freedom for some reaction steps. It breaks down an apparently unimolecular reaction into two elementary steps, with a rate constant for each elementary step.

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