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01005 Advanced Engineering Mathematics 1

Danish title:

Matematik 1

Language:

Point( ECTS )

20

Course type:

BSc
Taught under single-course student
??

Schedule:

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.

Duration of Course:

13 weeks + 13 weeks

Date of examination:

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:

Exam duration:

Aid:

Evaluation:

Not applicable together with:

General course objectives:

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

Responsible:

Karsten Schmidt , Lyngby Campus, Building 321, Ph. (+45) 4525 5856 , ksch@dtu.dk
Michael Pedersen , Lyngby Campus, Building 303B, Ph. (+45) 4525 3012 , micp@dtu.dk

Department:

01 Department of Applied Mathematics and Computer Science

Home page:

http://01005.mat.dtu.dk/

Registration Sign up:

At CampusNet
Last updated: 11. maj, 2016