KE551: Mathematical applications

Students taking the course are expected to:

• Have knowledge of chemistry and mathematics at the level of 1^st year
• Be able to use chemistry and mathematics at the level of 1^st year

The
course builds on the knowledge acquired in the courses on 1st year in
chemistry and mathematics, and gives an academic basis for studying many
topics as for example quantum chemistry, spectroscopy and physical
chemistry that are part of the degree.

In relation to the
competence profile of the degree it is the explicit focus of the course
to enable the student to analyze problems in inorganic chemistry, spectroscopy, physical chemistry and theoretical chemistry with a
mathematical approach and to perform calculations on typical
mathematical-chemical problems.

The learning objectives of the course are that the student demonstrates the ability to:

1. Describe
   typical mathematical problems in chemistry using mathematics and
   possess an overview of the basic concepts of the mathematical methods
   used in chemistry.
2. Formulate and reformulate typical mathematical models in chemistry for the description and analysis of chemical problems.
3. Choose a computational approach and perform basic practical alculations related to mathematical-chemical problems.

The following main topics are contained in the course:

1. Chemical
   analysis of relevant mathematical functions of one or more variables
   and their partial derivatives and total differentials.
2. Integration of chemically relevant functions with applications in particular to thermodynamics and quantum chemistry.
3. Sequences and series with special focus on the use of application of Taylor series in chemistry.
4. Introduction to complex functions.
5. Differential
   equations with applications to chemical problems such as chemical
   reaction kinetics, the harmonic oscillator and particle in a box.
6. Linear
   algebra (vectors, matrices, solution linear systems of equations,
   determinants, eigenvalues and eigenvectors) and its application in
   chemistry and especially quantum chemistry, spectroscopy and symmetry.

• Erich Steiner: The Chemistry Maths Book, Oxford University Press, 2. Udgave.

See itslearning for syllabus lists and additional literature references.

The teaching activities result in an estimated work effort of an average student in the following way:  

• Intro phase (lectures) - number of hours: 12
• Training phase: number of hours: 32, of which 16 hours is computer exercises.
  

The intro phase will consist of 2 elements: 1) A video (approx. 15 min. duration) which provides an introduction of the topic to be worked on. It is assumed that the students have watched this video before the introductory class. 2) In the intro class itself, there will be an opportunity to ask questions about the video. Otherwise, elaborate questions / assignments must be worked on that support the material reviewed in the video.

The training phase will also be divided into two elements: 1) Training in enabling the student to choose a calculation method and perform basic practical calculations. 2) Give an introduction to Maple as an auxiliary tool when performing calculations on mathematical-chemical problems.

Activities in the study phase:

• Reading the textbook material
• Problem solving
• Mini project
• Video review of the textbook material