Mathematics for engineering 3 B

Integration

Double integrals in cartesian and polar coordinates. Triple integrals in cartesian, cylinder and spherical coordinates. Surface integrals and line integrals. Numerical methods for calculation of integrals. Calculation of mass, mass centre and moment of inertia.

Vector fields

Divergence and curl, conservative fields and potentials. Work, circulation and flux. Green's Theorem, Stokes' Theorem and the Divergence Theorem.

Partial differential equations

Calculation of vector fields. Conservation laws. Numerical solution by the finite volume method, with emphasis on calculation with computer.

Knowledge

The candidate has good knowledge about:

• Numerical calculations with computer tools
• The central concepts from vector analysis
• The connection between vector analysis and engineering applications

Skills

The candidate:

• Can perform numerical calculations in vector analysis using computer
• Can calculate vector fields using computer and the finite volume method
• Can formulate relevant applied problems, solve these with computer and interpret the results
• Can use computer to analyse mathematical problem

General Competencies

The candidate:

• Knows and can apply relevant mathematical languate in order to communicate engineering problems
• Has experience with applying mathematical methods and digital tools on problems from their own and neighboring subjects
• Is able to connect mathematical concepts and methods to models encountered in and outside their studies.

Lectures, exercises, compulsory tasks.

Compulsory tasks include both analytical and numerical solution methods, and includes problems that are solved using digital tools.