Based on a mathematical model, simulate technical and scientific processes. The course addresses how to structure the problem, rewrite the problem in a form that is suitable for numerical treatment, select the appropriate numerical method, implement the method, visualize and present a solution, and estimate the reliability of the results.
The course deals with:
- numerical methods for linear systems of equations, non-linear systems of equations, optimization, interpolation, the least squares method, and integration with deterministic and probabilistic methods.
- basic ideas and concepts such as algorithm, computational cost, iteration, local linearization, interpolation, extrapolation, discretization, order of accuracy, convergence, complexity, condition, and stability.
An overall goal of the course is to provide the student with insight into how numerical methods, analysis, and programming techniques can be used to make reliable and efficient simulations of technical and scientific processes based on mathematical models.
After completing the course, the student should be able to
- given a mathematical model for a technical or scientific problem, identify and classify the mathematical subproblems that need to be solved, rewrite them in a form suitable for treatment with numerical methods and select appropriate numerical methods.
- describe key concepts and basic ideas used in the numerical methods included in the course and be able to use these concepts and ideas to describe advantages and limitations of the methods.
- describe, apply, implement, and evaluate the numerical methods included in the course.
- estimate the reliability of numerical results and investigate properties of numerical methods using analytical procedures included in the course.
- present, discuss and summarize problem statements, solution approaches, and results when solving problems.
