SF1675 Applied Linear Algebra 13.5 credits

Basic ideas and concepts in linear algebra: vectors, matrices, systems of linear equations, Gaussian elimination, matrix factorization, complexity, vector geometry with scalar product and vector product, determinants, vector spaces, linear independence, bases, change of basis, linear mappings, eigenvalue, eigenvector, the least squares methods, orthogonality, Gram-Schmidt's method.

Calculation and programming technical aspects: MATLAB programming with control and data structures, file management, functions, visualization, numerical solution of systems of linear equations with Gaussian elimination and LU factorization, experimental determination of complexity in solving linear equation systems, numerical calculation of condition numbers, assessment of accuracy, graphical illustration of results.

After the course the student should be able to

• use concepts. theorems and methods to solve and present solutions to problems within the parts of linear algebra described by the course content,
• use Matlab to solve problems within the parts of linear algebra and numerical analysis described by the course content,
• read and comprehend mathematical text.
• use basic control and data structures in Matlab for problem solving

in order to

• develop a good understading for basic mathematical concepts within linear algebra and to use these for mathematical modeling of engineering and scientific problems,
• develop a skill, with the help of computers, to illustrate key concepts and solve applied problems with Matlab as well as to visualize and present the results in a clear manner.

Basic requirements.

If the course is discontinued, students may request to be examined during the following two academic years.

• LAB1 - Laboratory Sessions, 1.5 credits, grading scale: P, F
• LAB2 - Laboratory Sessions, 2.0 credits, grading scale: P, F
• PRO1 - Project, 1.0 credits, grading scale: P, F
• TEN1 - Examination, 1.5 credits, grading scale: P, F
• TEN2 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

In this course, the code of honour of the school is applied, see: http://www.sci.kth.se/institutioner/math/avd/na/utbildning/hederskodex-for-studenter-och-larare-vid-kurser-pa-avdelningen-for-numerisk-analys-1.357185

Katarina Gustavsson

Mats Boij

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Written examination: 

 Four re-exams for both TEN1 and TEN2 are offered for two years after the last course edition was given.

TEN1 will be given at two opportunities during the corresponding autumn semester and TEN2 will be written tigeter with TEN1 of the new course SF1694 Applied Linear Algebra that replaces the course SF1675.

Approved oral and/or written presentation of homeworks

Lab2 of the course SF1675 can be finalized within the new course SF1694. The deadlines for submission and presentation of lab work in SF1694 apply also for students who intend to finalize their lab work in the course SF1675.

For other lab work of SF1675 that cannot be finalized within the course SF1694, the examiner will provide one opportunity per academic year that will be scheduled immediately after an edition of SF1694 has been given.

PRO1 can be finalized within the new course SFSF1694. Possible deadlines of SF1694 apply also for students who will finalize their project work of SF1975.