Mathematical Modeling

• Apply a mathematical model to solve a problem
• Explain the components of a mathematical model
• Judge area of validity of a mathematical model
• Use statistics to summarize the obtained results
• Implement numerical algorithms using Matlab or Python
• Set up test scenarios and collect data
• Explain the model parameter’s influence on the model
• Interpret the calculated results of the model
• Visualize data and results graphically
• Evaluate the relevance of the results for the analyzed problem
• Write a stringent and structured report that precisely describes the model and analysis of the calculated results

The main content of the course is to solve specific cases with associated problems. For each case a problem has to be analyzed, the mathematical model must be described and implemented on a computer, and calculations and simulations must be done, which illustrates the relevance of the model. All of this has to be reported in a structured manner. The methods will fall within discrete mathematics, image analysis, differential equations, materials science, operations research, and scientific computing. The course include peer grading of other students reports, which is a prerequisite for being examined

01025/01035/02601/02403/02402/02002/02525/02631/10018/10022, Knowledge of mathematical analysis, linear algebra and numerical analysis. Fundamental physics including mechanics. Knowledge of statistics and Matlab or Python programming. It will be an advantage to have knowledge of image analysis.

Lectures, exercises and reports

The course is a prerequisite for the following advanced courses: 02610 Optimization and datafitting, 02614 High performance computing, 02616 Large-scale modeling, 02623 Finite element methods for partial differential equations, 02685 Scientific computing for differential equations. The course is reserved for students from Mathematics and Technology and General Engineering, and other students are welcome if there are available seats.