Mathematics for Quantum Chemistry

Studiewijzer 2015/2016

Globale inhoud

The main purpose of this course is to substantially increase the mathematics level of the chemistry students. Particular attention is devoted to develop formal skills, focusing on mathematical tools that are absolutely necessary for chemical physics and theoretical/computational chemistry, but also very useful for all other chemistry disciplines.

Leerdoelen

• Taylor series and polynomials. How to approximate a complicated function around a certain point by means of simple polynomials? As you will learn, this makes it possible to greatly simplify equations and provides good approximations in many important limiting situations. The concept of series expansion will be also generalized to matrices in the Linear Algebra part of the course.
• Linear Algebra: matrices, matrix operations, linear vector spaces, eigenvalues and eigenvectors, diagonalization of matrices. In quantum mechanics, the operators can be 3 represented in matrix form and wave functions as vectors. Being able to perform matrix operations and understanding the properties of matrices and vector spaces is therefore essential. General linear vector spaces that appear in computational and theoretical chemistry will be also explained.
• Fourier series and Fourier transforms. You will learn how a complicated periodic function can be expressed as a sum of simple sinusoidal functions. Also, you will learn how to transform functions into momentum space and understand the advantages of using this powerful tool.
• Partial derivatives. Multidimensional integrals. One-variable calculus is good for learning the basic concepts, but in the real world many properties are expressed as functions of several variables. We therefore need to generalize concepts such as derivatives or integrals in order to do calculus with such functions.
• Vector analysis. Once you understand the concepts of partial derivative and multidimensional integral, you will be able to learn calculus theorems for higherdimensional spaces.
• Ordinary and partial differential equations. Partial differential equations are everywhere in Chemistry. For example, the Schrödinger equation, central in quantum chemistry, is a partial differential equation. You will learn the basic concepts behind the strategies to solve these equations

Onderwijsvormen

Hoorcolleges en werkcolleges.

Verdeling leeractiviteiten

Toetsing

Assignments

Five assignments during the course will be given, in the first 5 weeks of the course. Each assignment will be given on a Friday (via blackboard). The solution has to be handed to the instructor on the following Thursday, at the beginning of the lecture. The rules are: - In making assignments, collaboration of 2 people is allowed (not 3 or more). Each person 5 should write and understand his/her own results. Indicate with whom you collaborated if you did. In contrast to common assumptions, deviations from this rule are noticed fairly quickly. - Assignments cannot be handed in after the deadline. - The final mark for the assignments is the average of the best four.

Assessment

We will have a final written exam to assess if you have met the objectives of the course. The structure of this exam and the material that you can use in it will be explained during the course. The final mark of the course is based on the results of the assignments and of the written exam in the following way: - If the result of the written exam is equal to or less than 5 then this is the final result. - If the result of the written exam is more than 5, the final result is based on both the written exam and the assignments. The weighting factor of the written exam is 3/4 and of the assignments is 1/4.

Opdrachten

Assignments

• 5 written assignments

Onderstaande opdrachten komen aan bod in deze cursus:

•    Naam opdracht 1 : beschrijving 2
•    Naam opdracht 2 : beschrijving 1
•    ....

Fraude en plagiaat

Dit vak hanteert de algemene ‘Fraude- en plagiaatregeling’ van de UvA. Onder plagiaat of fraude wordt verstaan het overschrijven van het werk van een medestudent dan wel het kopiëren van wetenschappelijke bronnen (uit bijvoorbeeld boeken en tijdschriften en van het Internet) zonder daarbij de bron te vermelden. Uiteraard is plagiaat verboden. Hier wordt nauwkeurig op gecontroleerd en streng tegen opgetreden. Bij verdenking van plagiaat wordt de examencommissie van de opleiding ingeschakeld. Wanneer de examencommissie overtuigd is dat er plagiaat gepleegd is dan kan dit maximaal leiden tot een uitsluiting van al het onderwijs van de opleiding voor een heel kalenderjaar. Zie voor meer informatie over het fraude- en plagiaatreglement van de Universiteit van Amsterdam.www.uva.nl/plagiaat

Weekplanning

Rooster