MAMO2200 Advanced modeling and computing Course description

The course covers approximations and numerical methods that are central to analyzing, computing, and simulating mathematical models. Through implementation on a computer, students will learn to perform systematic numerical experiments. Examples and tasks are drawn from natural sciences, engineering, and economics. The topics addressed are intended to prepare and motivate students for further studies in applied and computational mathematics.

The course builds on

• MAMO1100 Introduction to modeling and computing
• DAFE1000 Mathematics 1000
• DAPE2000 Mathematics 2000 with statistics

None.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence.

Knowledge

The student can:

• explain methods for the numerical solution of nonlinear algebraic equations and differential equations.
• explain how and in which cases functions can be approximated with polynomials and trigonometric functions.
• explain standard methods and the use of stochastic simulations for estimating definite integrals.
• explain the fundamental properties of stochastic processes and Markov chain models.
• explain how the numerical methods can be implemented in Python.

Skills

The student can:

• use and implement methods for the numerical solution of equations, as well as analyze deviations.
• use and implement methods for numerical integration.
• approximate functions using Taylor polynomials to analyze deviations in numerical integrators.
• use and implement methods for the numerical solution of initial value problems.
• use and implement Markov chain models.
• implement numerical methods using Python programming.

General competence

The student can:

• read and understand texts and participate in discussions regarding modeling, computation, and implementation.
• assess the accuracy of numerical estimates and choose appropriate parameters to ensure the estimates are accurate enough.
• interpret and evaluate the results of numerical calculations.
• assess which algorithms should be used in different cases.

Lectures and exercise sessions with extensive use of software and computer coding. The exercises combine the use of pencil and paper with computational tools under the guidance of the instructor and/or student assistant.

The following coursework requirements must be approved to be eligible for assessment/exam:

Two out of three group assignments where

• each group shall consist of 1 to 4 students.
• each group assignment is submitted as a report of 8-15 pages.
• each assignment can be resubmitted once if it is not approved.

The purpose of the coursework is for students to gain practical experience with project work and to combine several of the learning outcomes in the process.

Individual oral exam of about 30 minutes consisting of a student-led presentation followed by questions.

The exam result cannot be appealed.

In the case of a new or postponed exam, a different examination format may be used.

The student may use his/her own computer for the presentation.

Grade scale A-F

Two internal examiners. External examiners are used regularly.