Fall and Spring
Course is given in three different schedules dependent on study
programme.
Scheme A: E1A, E2 og F1A, F2 Scheme B: E3A, E4 og F3A, F4 Scheme C:
E5, E3B og F5, F3B

Location:

Campus Lyngby

Scope and form:

Per week: 2 lectures, 3h tutorials and 3h groupwork. Moreover
thematic exercises and projectwork in some weeks.

Decide with teacher, Closing tests: The 5th of
Dec 2015 for the fall and the 13th of May 2017 for the
spring

Type of assessment:

Written examination and
reports
4 parts equally weighted: 1) 6 homework assignments, 2) Tests in
fall curriculum, 3) 3-week project exercise and 4) Tests in spring
curriculum. Precise description:
http://01005.mat.dtu.dk/info/eksamensregler/

The course content is the mathematical basis for a broad range of
technical fields and also provides a starting point for further
studies in mathematics and applied mathematics. The dominating
theme of the course is linearity. The goal is to give students the
ability to employ fundamental tools of mathematics in theoretical
studies as well as in applied thematic exercises and projects. The
use of modern computer software supports both of these
aspects.

Learning objectives:

A student who has met the objectives of the course will be able to:

use the algeraic and the geometric representation of complex
numbers including the complex exponential.

use matrix algebra and Gaussian elimination for solving systems
of linear equations.

analyse and explain the linear structure of solution sets in
vector spaces.

perform calculations with the elementary functions including
their inverse functions.

use Taylor's formulas for approximizations and limits.

solve elementary first and second order differential equations
and systems of differential equations.

calculate extremas for multivariate functions, especially on
domains with boundary.

parameterise elementary curves, surfaces and massive solids and
calculate elementary curve, surface and volume integrals.

use Gauss's and Stokes's theorems in simple
applications.

use mathematical terminology and reasoning in oral as well as
written presentation.

coordinate joint work in groups around thematic exercises and
applications.

use computer algebraic systems (at present Maple) for solving
and visualisation of mathematical problems.

Content:

Linear equations and linear maps. Matrix algebra. Vektor spaces.
Eigenvalue problems. Symmetric and orthogonal matrices. Complex
numbers. Linear differential equations. Standard functions.
Functions of one and several real variables: linear approximations
and partial derivatives, Taylor expansions and quadratic forms,
extrema and level curves, line, surface and volume integrals.
Vector fields, Gauss' and Stokes' theorem.
Applications of MAPLE in the above areas. Examples of applications
in the engineering sciences.

Remarks:

The course is a two-semester course for students following one of
the preliminary four-semester programs:
Scheme A for the programs Biotechnology, Environmental Engineering,
Medicine & Technology, Human Life Science Engineering,
Quantitative Biology.
Scheme B for the programs Architectural Engineering, Civil
Engineering, Earth and Space Physics and Engineering, Mathematics
and Technology, Mechanical Engineering and Physics and
Nanotechnology.
Scheme C for the programs Electrical Engineering, Design and
Innovation, Network Technology and IT, Software Technology and
Strategic Analysis and Systems Design.

Green challenge participation:

Please contact the teacher for information on whether this course
gives the student the opportunity to prepare a project that may
participate in DTU´s Study Conference on sustainability, climate
technology, and the environment (GRØN DYST). More infor
http://www.groendyst.dtu.dk/english