Single-Course Engelsk 5 ECTS

Mathematical Modeling

Overall Course Objectives

Mathematical modeling is a central component in the solution of most technical problems. Typically, the process begins with the formulation of a mathematical model, which is then implemented computationally and used to support laboratory-scale experiments and, eventually, the development of real-world solutions. The ability to formulate relevant mathematical models, implement them on a computer, and use them to obtain meaningful insight is therefore a fundamental competence in modern engineering. In this course, students will acquire tools for formulating mathematical models, carrying out simulations and calculations, and critically analyzing and reporting the results.

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Apply a mathematical model to solve a problem
Explain the components of a mathematical model
Assess the domain of validity of a mathematical model
Use statistics to summarize the obtained results
Implement numerical algorithms using Python
Set up test scenarios and collect data
Explain the model parameters’ 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 the analysis of the calculated results

The main content of the course is the solution of specific cases and their associated problems. For each case, the problem must be analyzed, the mathematical model described and implemented on a computer, and calculations and simulations carried out to illustrate the relevance and the applicability of the model. All of this must be documented in a structured manner. The methods applied may include discrete mathematics, image analysis, differential equations, materials science, operations research, and scientific computing. The course also includes peer grading of other students’ reports, and participation in this activity is a prerequisite for taking the exam.

01025/01035/02601/02403/02402/02002/02525/02631/10018/10022, Knowledge of mathematical analysis, linear algebra, statistics, and numerical algorithms. Fundamental physics including mechanics. Knowledge of Python programming.

Lectures, exercises, and reports

Mirza Karamehmedovic

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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 a programme-specific course for BSc Applied Mathematics. The course is reserved for students from Applied Mathematics and General Engineering, and other students are welcome if there are available seats.

See course in the course database.