 COURSE SYLLABUS

Mathematics Space 7.5 Credits

Matematik Ry
First cycle, M0046M
Version
Course syllabus valid: Autumn 2018 Sp 1 - Spring 2020 Sp 4
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 Courses M0029M, M0030M, M0031M, M0032M, or equivalent.

Selection

The selection is based on 1-165 credits.

Course Aim
After completed course, the student should:
• be able to use the Laplace transform as a tool for solving ordinary differential equations with initial conditions.
• be able to solve systems of differential equations using diagonalization and matrix exponential.
• be able to compute Fourier series and Fourier transforms for some elementary functions and distributions.
• manage concepts as transfer function, LTI-systems, causality, stability, impulse response and convolution integrals for linear systems.
• have gained knowledge about distribution theory and be able to use distributions such as the dirac delta function to model certain physical phenomena.
• be able to formulate a few common partial differential equations, boundary- and initial conditions, starting with problems from physics and be able to solve these with variable separation techniques.

Contents
Linear systems, Laplace transform, Fourier series, Fourier transform, use of transforms för solving differential equations. Systems of differential equations. Distributions. Mathematical models for diffusion, heat transfer, wave propagation. Solution of PDEs with variable separation.

Realization

Examination

Examiner
Johan Byström

Literature. Valid from Spring 2018 Sp 3 (May change until 10 weeks before course start)
1) B.P. Lathi: Linear systems and signals, 2nd edition, Oxford University Press, 2010.
2) Handed out material

Course offered by
Department of Engineering Sciences and Mathematics

Items/credits