COURSE SYLLABUS

Linear Analysis 7.5 credits

Linjär analys
First cycle, M0018M
Version
Course syllabus valid: Autumn 2021 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

 Education level First cycle Grade scale G U 3 4 5 Subject Mathematics Subject group (SCB) Mathematics Main field of study Engineering Physics and Electrical Engineering

Entry requirements

In order to meet the general entry requirements for first cycle studies you must have successfully completed upper secondary education and documented skills in English language and The courses M0029M, M0030M, M0031M, or equivalent.

Selection

The selection is based on 1-165 credits.

Course Aim

After completing the course, the student expects be able to:

Knowledge and understanding

• Formulate and implement different convergence criteria for power series.
• Use the convergence criterion for Fourier series.
• Calculate Fourier series, Fourier transforms, Laplace transforms , and double-sided Laplace transforms of elementary functions and Diracfunction.
• Write down Laplace transform of exponential functions, sine and cosine functions, power functions with positive integer exponents and use formulas to calculate the Laplace transforms of products of these functions.
• Use and derive formulas for Laplace transforms , Fourier transforms and two-sided Laplace transforms.
• Use series and transforms to solve differential equations.
• Derive simple derivatives and formulas in the distributional sense by means of distribution theory and to solve differential equations containing simple distributions.
• olve systems of differential equations by using the eigenvalue method.
• Define and calculate the fundamental matrix / exponential matrix.

Competence and skills

• Independently solve differential equations and solve problems of convergence for series/powerseries by means of properties of series and transforms, within given limits of time.

Contents
• Convergence and divergence of series
• Powerseries
• Fourier series
• Fourier transform
• Laplace transform, double sided Laplacetransform
• Introduction to the theory of distributions (generalized functions)
• Solution of ordinary linear differential equations by means of power series and transforms.
• Solution of integral equations by means of transforms
• Solution of system of linear homogeneous differential equations by means of eigenvalue, eigenvector method.
• Exponential matrix
• Solution of linear non-homogeneous system of differential equations by means of method of undetermined coefficients and by means of variation of parameters.

Realization
Each course occasion´s language and form is stated and appear on the course page on Luleå University of Technology's website.

The course is of theoretical nature, and teaching are lectures and tutorials. The student assumes to be an active participant, and work with the prescribed problems. If the number of participants are too small the course will be given as a reading course.

Examination
If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided.

Knowledge and understanding including skills and abilities are examined by a written exam. The grade scale is U (failed), 3, 4 and 5 which is the highest grade.

Remarks

The preparation before this course is approximately half a year up to a year of studies in mathematics and for future use the course is a good and sometimes necessary preparation for many other subjects as eg. mathematics, elektronics, control theory, signal processing, image processing, mechanics, and mechanics of materials.

Examiner
Mikael Stenlund

Transition terms
The course M0018M is equal to MAM243

Literature. Valid from Autumn 2021 Sp 1 (May change until 10 weeks before course start)
Sven Spanne, Lineära system, kap. 11 kap. 14.1-14.9 including, solutions to kap. 11 and kap. 14.
Compendium, Franz Cech, Matematiska metoder inom elläran (a.k), KTH, V.T 1993.
Robert.A. Adams, Calculus a Complete Course, 7th ed, 8th ed, or 9th ed. Everything in the list above, except Adams, can be bought at the local office of ”teknologkåren” when the course begins.

Course offered by
Department of Engineering Sciences and Mathematics

Modules
0002Written examG U 3 4 57.50MandatoryA21

Study guidance
Study guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.

Syllabus established
The syllabus was approved by the department of mathematics and is valid from H07.

Last revised
by Head Faculty Programme Director Niklas Lehto 17 Feb 2021