Mathematics 1

Limits, continuity, differentiation and integration of functions of one variable.

Intermediate-value theorem, maximum and minimum values, l'Hopital rule, Newton's method, and Taylorpolynomial with remainder.

Techniques of integration and numerical integration.

Volume, arc length, area of surfaces of revolution, moments, and centeroids.

First and second order linear differential equations. Separable differential equations.

Numerical solution of differential equations: Euler's method and Runge-Kutta.

Complex numbers and the complex exponential function.

Systems of linear equations, Gauss-Jordan elimination, row echelon form, matrix algebra, and determinants.

Learning outcome - Knowledge.
The candidate has
- established a basic knowledge and understanding of mathematics as field that other subjects can build on.
- thorough knowledge of the core topics of differentiation, integration, and differential equations with applications.
- good knowledge of complex numbers.
- good knowledge of numerical computations and their possibilities and limitations.

Learning outcome - Skills.
The candidate
- knows the relevant mathematical symbols and formulas.
- can manipulate symbols and formulas.
- can reason mathematically.
- can formulate engineering problems in mathematical form.
- have good numeracy skills.
- can identify connections between mathematics and engineering applications.
- can understand and use mathematical descriptions of problems.
- solve problems using both analytic and numerical methods.

Learning outcome - Competence.
The candidate
- understand that change and change per unit of measurement can be measured, calculated, added and included in equations.
- understand 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 and exercises 

Compulsory exercises and / or written homework