Mathematics 3

Polar, spherical and cylindrical coordinates.
Parametric curves and polar curves.
Area calculations related to parametric curves.
Curves in space and their position, speed, and acceleration vectors.
Arc length differential and arc length of parametric curves.
Double and triple integrals over general areas and bodies and their use in calculating area, volume and moments.
Directional derivative, gradient, divergence, and curl.
Line integrals and surface integrals.
Green's, Gauss', and Stoke's theorems.
First and second order partial differential equations.
Separation of variables and d'Alembert's method.
One-dimensional heat equation and one-dimensional wave equation.
Two dimensional Laplace equation.

Learning outcome - Knowledge.
The candidate has
- established a basic knowledge and understanding of mathematics as field that other subjects can build on.
- knowledge about basic relationship between mathematics and engineering applications.
- knowledge of problem solving and modelling as a tool for solving engineering problems.

Learning outcome - Skills.
The candidate can
- use parametric curves in two and three dimensions.
- evaluate multiple integrals.
- use vector functions in two and three dimensions.
- use Green's, Gauss', and Stoke's theorems.
- use known techniques for solving first and second order partial differential equations.

Learning outcome - Competence.
The candidate
- known how to communicate engineering problems using mathematical language.
- know that change and change per unit can be measured, calculated, added and be part of equations.
- understands that it is the accuracy of mathematical language which makes it suitable for structuring engineering problems and enables solutions.
- have mathematical understanding which can provide a basis for lifelong learning.

Lectures.

Compulsory exercises and/or written homework.