# SF1634 Differential Equations II 9.0 credits

#### Differentialekvationer II

Basic course in differential equations, Fourier series, Fourier and Laplace transforms.

### Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

## Course information

### Content and learning outcomes

#### Course contents *

ODEs of order 1: Basic notions and theory. Modelling. Direction fields and solution curves. Autonomous equations, stationary solutions and their stability. Separable equations. Linear equations.

ODEs of higher order: Basic teori. Methods for solving linear equations with constant coefficients. Oscillations.

Systems of linear ODEs: Basic notions and theory. The eigenvector method (homogenuous linear systems), The method of variation of parameters (particular solutions of nonhomogenuous linear systems).

Generalized functions as a tool to represent signals.

The Laplace transform with applications.

Fourier series and Fourier transforms with applications.

Linear partial differential equations: Separation of variables. Solution of some classical equations (the wave equation, the heat equation, the Laplace equation) with transform methods.

#### Intended learning outcomes *

After passing the course the students should

• have basic knowledge of the theory of ordinary differential equations (ODE),
• be able to solve some types of (systems of) ODEs with standad methods,
• -be able to examine (systems of) ODEs with elementary geometric and with qualitative methods,
• be able to determine Fourier and Laplacetransforms,
• be able to determine the Fourier series representation of periodic continuous-time signals,
• be able to solve separable partial differential equations and determine solutions to boundary value problems with Fourier and transform methods,
• be prepared for deeper studies in fields relevant for their future education,
• be able to use relevant software for solving problems of the type mentioned above with symbolic as well as with geometric methods,
• be able to apply this knowledge of modelling problems.

#### Course Disposition

No information inserted

### Literature and preparations

#### Specific prerequisites *

SF1624/SF1663/SF1666/SF1667/SF1675 + SF1625/SF1664/SF1668 + SF1626/SF1665/SF669 or corresponding courses.

#### Recommended prerequisites

No information inserted

#### Equipment

No information inserted

#### Literature

Zill-Cullen/Differential Equations with Boundary-Value Problems

Råde-Westergren/Mathematics Handbook for Science and Engineering.

### Examination and completion

#### Grading scale *

A, B, C, D, E, FX, F

#### Examination *

• INLA - Assignments, 3.0 credits, Grading scale: P, F
• TENA - Examination, 6.0 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.

#### Other requirements for final grade *

(TEN1, 6 cr). One examination test,
(INL1, 3 cr), One report.

#### Opportunity to complete the requirements via supplementary examination

No information inserted

#### Opportunity to raise an approved grade via renewed examination

No information inserted

### Further information

#### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF1634

SCI/Mathematics

#### Main field of study *

Mathematics, Technology

First cycle