Course content

The course includes a general introduction to modelling and computer simulation as tools in materials science and engineering, "advanced" use of spread sheets (Excel), and basic skills in programming and program development. Some important types of problems that will be treated are: Analysis and representation of experimental data, numerical integration and derivation, root finding and numerical methods to solve differential equations, random numbers and Monte-Carlo methods. The topics will be presented by means of relevant examples related to modelling and simulation of processes and reactions in materials science and materials engineering. The examples are among others related to casting and solidification, heat conduction, recrystallization and grain growth, diffusion, melt treatment and thermo-mechanical treatment and transformation kinetics (C-curves).

Learning outcome

After the course is finished, and to successfully pass the course, the students must be able to:

- Identify and describe key elements of mathematical modelling of processes and reactions in materials science and engineering, and shortly be able to account for why and in which connections mathematical/numerical modelling is useful.

- Apply adequate algorithms for smoothing, numerical derivation and integration in work sheets (Excel), in order to process and analyze experimental data, including graphical representation of results.

- Account for the principles of model fitting/regression and be able to apply them in Excel to perform calculations to determine relevant model parameters.

- Analyze and reformulate mathematical equations and simple models into a form which is suitable for numerical solutions in a computer.

- Make use of basic principles and algorithms to create effective and user friendly computer codes for numerical calculations and simulations, including use of repetitive control structures (loops), conditional control structures (if, while) and functions, as well as simple/useful methods for input/output.

- Implement and perform relevant calculations which involve algorithms for numerical derivation and integration, iterative techniques for solving equations (root finding), numerical solutions to ordinary and partial differential equations (incl. Euler's method, Runge-Kutta methods and Finite Difference methods).

- Make use of random numbers and Monte Carlo methods to solve deterministic problems and specifically to perform evaluations of definite integrals.

- Analyze and discuss accuracy of the results obtained by relevant numerical calculations and be able to modify the calculations in order to achieve the required accuracy.

- Present data, both experimentally measured and numerically computed, in well-organized plots/graphs/charts with scientific publication quality.

- Create well-documented and well-organized Python code so that, in principle, it can be further used and modified by another user

Learning methods and activities

The course and the teaching will be centered around 10-12 relevant computer problems/exercises. The problems/topic of the exercises and knowledge and skills required to solve the problems will be presented in the lectures. The exercises will be based on the use of spread sheet (Excel) and Python programming language. Total amount of work load for the whole semester (incl. independent home work) is ~200 hrs.

Recommended previous knowledge

The course TDT4110 - Information Technology, Introduction, or courses that give similar knowledge and skills about computers and use of basic computer tools. Basic knowledge and skills related to numerical methods, e.g. TMA4125 Calculus 4N is recommended. Also, it is preferential, although not absolutely necessary with an introductory course to materials science and engineering.

Required previous knowledge

More than 2/3 of the course (computer exercises) is based on programming in Python. The course therefore requires basic knowledge of Python and some experience with programming, or equivalent previous knowledge to be assessed by the course responsible to be satisfactory.

Course materials

No ordinary textbook. An overview of the course material is presented at the start of the semester and will be made available electronically throughout the semester.

Credit reductions