Mathematics 2 (2024)

Course manager

Laust Tophøj

Semester schedule

Autumn (13-week period)

ECTS

5

Language of instruction

English

Course type

Elective

Qualifications

Competences corresponding to participation in the disciplines – Mathematics 1 and Statistics (previously Mathematics 2) together with Mathematical modelling (previously Applied mathematics 1), Chemical engineering, and Chemical unit operations – are recommended.

Objectives

Computer-based calculation methods are largely used in connection with engineering modelling and analyses of complex physical, chemical, biotechnological, and process technological contexts. In order to derive full advantage of these methods of calculation, it is important to possess detailed knowledge about their theoretical background. Mathematics 2 is directed at familiarizing the students with the branch of mathematics that constitutes the foundation for these advanced computer-based calculation methods.

Content

• Parametrization of planes/surfaces and spaces
• Integration of scalar functions over surfaces and spaces
• Integration of vector functions
• Matrix analysis
• Partial differential equations

Learning targets

On completion of the course, the student is expected to be able to:

Knowledge

• Understand and explain the principles of SVD
• Understand and explain the principles and application of partial differential equations 
• Understand and explain the principles of integration in multiple dimensions and coordinate systems

Skills

• Be able to use SVD for analysis of data
• Parametrization of elementary planes/surfaces and spaces
• Integrate scalar functions in Cartesian, cylindrical, and spherical coordinates
• Solve partial differential equations numerically

Competences

• Translate physical conditions into a mathematical model as represented by a partial differential equation
• Analyze stability of dynamic systems
• Be able to get an overview of large data sets
• Master handling of scalar fields in various geometries 

Teaching method

Seminars, podcasts, and problem solving

Qualifications for examination participation

• Approval of all written assignments

Each assignment will be performed and submitted subject to guidelines set out by the course manager.

Examination and aids

Written examination. Duration of the examination: 4 hours.

Permitted aids: Textbook, notes and mathematical program/spreadsheet. No access to the internet.

The form of examination at a 2nd attempt may vary from the above.

Marking 

External

Grading

The 7-point grading scale