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Kursusbeskrivelse
Kursusnavn (dansk):Mathematical Analysis and Linear Algebra 
Kursusnavn (engelsk):Mathematical Analysis and Linear Algebra 
Semester:Forår 2013 
Udbydes under:cand.it., softwareudvikling og -teknologi (sdt) 
Omfang i ECTS:7,50 
Kursussprog:Engelsk 
Kursushjemmeside:http://learnit.itu.dk 
Min. antal deltagere:12 
Forventet antal deltagere:70 
Maks. antal deltagere:80 
Formelle forudsætninger:TBA 
Læringsmål:After the course the student should be able to:
• Define and calculate gradients and integrals of functions in several variables using the chain rule and Green’s theorem.
• Describe the underlying principles of finding minima and maxima of functions in several variables under constraints and calculate minima and maxima for given functions under given constraints.

• Describe Newton’s method and the theory behind it.
• Define the concept of vector field and describe properties of specific vector fields, e.g. judge if a given vector field is conservative or source free.
• Argue for convergence or divergence of a given infinite series.
• Describe Taylor series and calculate a Taylor expansion for a given function.
• Define and give a geometric interpretation of the concepts of vector spaces and subspaces. Define and compute dot and cross products of vectors.
• Solve systems of linear equations in several variables using row operations, inverses of matrices and least squares and determine possible number of solutions for a given system of linear equations.
• Define linear transformations, symmetric, quadratic, positive definite and similar matrices, singular value decomposition, elimination, eigenvalues and eigenvectors, orthogonality, orthonomality, and explain the importance of these concepts within linear algebra.
• Describe and calculate inverses, determinants, transposes of matrices 
Fagligt indhold:The course consists of two parts. In the first we study calculus of functions of several variables. Topics include
• A brief review of calculus of functions in one variable, including differentiation, integration, the fundamental theorem of calculus and Newton’s method
• Infinite series, the concept of convergence and techniques for proving convergence or divergence of series.
• A review of dot products and cross products of vectors.
• Curves in the plane and three dimensional space
• Partial derivatives of functions in many variables, directional derivatives and 
gradients, the chain rule in many dimensions. Finding maxima and minima 
under constraints.
• Multiple integrals and Fubini’s theorem.
• Vector calculus including line integrals and Green’s theorem, which is a 
generalization of the fundamental theorem of calculus to many variables.
• If time permits we will also cover surface integrals, the divergence theorem and Stoke’s theorem. 

The second part is about linear algebra and its applications.
Linear algebra and matrices is perhaps the branch of mathematics that has found most uses in practical applications. Matrices form the base for many models in economics, computer vision, graphics, games and various optimization problems.
Topics include:
• Fundamental properties of linear algebra, matrices and their relationship to linear functions.
• Methods for solving linear sets of equations.
• Methods for decomposing matrices and analyzing sets of linear equations
• Practical applications of matrices 
Læringsaktiviteter:14 ugers undervisning bestående af forelæsninger og øvelser

TBA 

Obligatoriske aktivititer:Der er ingen obligatoriske aktiviteter. Vær venlig KUN at ændre denne tekst når der er obligatoriske aktiviteter./
There are no mandatory activities. Please, change this text ONLY when there are mandatory activities. 
Eksamensform og -beskrivelse:X. experimental examination form (7-scale; external exam), 7-trins-skala, Ekstern censur

TBA  

Litteratur udover forskningsartikler:- Gilbert Strang: Calculus. Available for free download at
http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/
- Gilbert Strang: Introduction to Linear algebra, 4th edition

Mere info om den sidste er her
http://www.amazon.co.uk/Introduction-Linear-Algebra-Gilbert-Strang/dp/0980232716 
 
Afholdelse (tid og sted)
Kurset afholdes på følgende tid og sted:
UgedagTidspunktForelæsning/ØvelserStedLokale
Torsdag 12.00-13.50 Forelæsning ITU 4A16
Torsdag 14.00-15.50 Øvelser ITU 4A16

Eksamen afholdes på følgende tid og sted:
EksamensdatoTidspunktEksamenstypeStedLokale
2013-06-04 Tidspunkt oplyses senere Mundtlig eksamen ITU 3A54, 4A30
2013-08-27 RE-EKSAMEN - Contact course manager Mundtlig eksamen ITU 2A18
2013-08-27 RE-EKSAMEN Mundtlig eksamen ITU PREPARATION ROOM: 2A03