# Programmes and lecture notes

## Course Programmes

Integration theory, given Spring 2018 (in Danish). Supplementary lecture notes can be seen here (NY pr. 20. april, endelig udgave for 2018).

Linear algebra with applications, given Autumn 2017 (in Danish). Supplementary lecture notes on unitary matrices and operators can be seen here.

Mini project: linear algebra on spaces of polynomials, 9--13 October 2017 (in Danish).

Integration theory, given Spring 2017 (in Danish). Supplementary lecture notes can be seen here.

### Previous programmes

Linear algebra with applications, given Autumn 2016 (in Danish).

Mini project: linear algebra on polynomials, 10--14 October 2016 (in Danish).

Integration theory, given Spring 2016 (in Danish).

Matematik 3, applied engineering mathematics (EN3+MP3), given Autumn 2015 (in Danish).

Details for Example 6.7.1..

Solutions by Jan-Otto Houghoudt: Exercise 6.2.11. Exercise 6.3.23. Exercise 6.7.19. Exercise 10.2.11. Exercise 10.4.5. Exercise 10.4.9.

Collected old examination problems from 2011-2016.

Solution of examination problems from January 2016, January 2015, August 2015, January 2014, January 2013.

Integration theory, given Spring 2015 (in Danish).

Matematik 3, analysis for engineering students (EN+MP), given Autumn 2014 (in Danish).

Matematik 3, analysis for engineering students (EN+MP), given Autumn 2013 (in Danish).

Collected old examination problems HERE.

Matematik 3, analysis for engineering, physics and nanoscience students, given Autumn 2012 (in Danish).

Optimisation, given autumn 2012 (in Danish).

Integration and Fourier theory, given Spring 2012 (in Danish).

Optimisation, as part of Mat3 and MatOk5, given Autumn 2011.

Linear Algebra and Dynamical Systems on Mat1, given Autumn 2010 (in Danish).

Optimisation as part of Mat3, given Autumn 2010 (in English).

Math1A, given autumn 2009 (in Danish).

Linear Algebra and Dynamical Systems on Mat1, given Autumn 2009 (in Danish).

Integration and Fourier theory, given Spring 2009 (in Danish).

Operator Theory and Functional Analysis, Spring 2009 (in Danish).

Math1A, given autumn 2008 (in Danish).

Linear Algebra and Dynamical Systems on Mat1, given Autumn 2008 (in Danish).

Math2A, Linear Algebra given spring 2008 (in Danish).

Integration and Fourier theory, given Spring 2008 (in Danish).

Linear Algebra and Dynamical Systems on Mat1, given Autumn 2007 (in Danish). Sketch of lectures.

Optimisation as part of Mat3, given Autumn 2007 (in Danish).

Math2A, Linear Algebra given spring 2007 (in Danish).

Math1A, Calculus given autumn 2006 (in Danish).
Examination problems are available at the web-site of the basis programme, with supplementary ones here: Problem A, Problem B, Problem C, Problem D.

Problems of Advanced Optimisation, given autumn 2006.
NB! The lecture notes on calculus of variations can be obtained further below on this page; the exercises are appended to these notes.

Integration and Fourier theory, given Spring 2006 (in Danish). ``Funktionalanalyse og Operatorteori'', Spring 2006 (in Danish).

``Samhørende og partielle differentialligninger'', given Spring 2006 (in Danish). Also available:

Optimisation, given Autumn 2005 (in Danish).

Older Programmes from Spring 2005 or earlier.

## Lecture notes

Notes on Optimisation under Constraints, used in the Mat3/MatOk5-course "Optimisation" Autumn 2011.

Notes on Calculus of Variations, used in the Mat3/MatOk5-course "Optimisation" Autumn 2011.

Convex Functions, an Elementary Approach, used in the Mat3/MatOk5-course "Optimisation" Autumn 2011.

Functional Analysis, these are supplementary notes to the course Operators on Hilbert spaces. Old version is available here

Om Riemann-integralet. Noter til matematik 1 (in Danish), these sum up the basic integration theory needed in Analysis 1.

Notat om eksponentialmatricer (in Danish). Here a general result on the entries in an exponential matrix is deduced for the purposes of Mathematics 1.

Notat om Lyapunovfunktioner (in Danish). Here the general stability results, based on Lyapunov functions, are deduced for the purposes of Mathematics 1.