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SF1683 Differential Equations and Transforms 9.0 credits

About course offering

For course offering

Autumn 2024 Start 26 Aug 2024 programme students

Target group

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Part of programme

Degree Programme in Engineering Physics, åk 2, Mandatory

Degree Programme in Information and Communication Technology, åk 3, Conditionally Elective

Degree Programme in Medical Engineering, åk 2, Conditionally Elective

Master of Science in Engineering and in Education, åk 3, MAFY, Mandatory


P1 (5.0 hp), P2 (4.0 hp)


26 Aug 2024
13 Jan 2025

Pace of study


Form of study

Normal Daytime

Language of instruction


Course location

KTH Campus

Number of places

Places are not limited

Planned modular schedule


For course offering

Autumn 2024 Start 26 Aug 2024 programme students

Application code



For course offering

Autumn 2024 Start 26 Aug 2024 programme students


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Course coordinator

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Headings with content from the Course syllabus SF1683 (Autumn 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

First order differential equations. Second order linear equations. The Laplace transform. Systems of differential equations. Qualitative methods for non-linear differential equations. Long term behaviour. Stability of critical points. Existence and uniqueness theorems. Fourier series, inner product rooms, orthogonal systems of functions. Sturm-Liouville problems. The Fourier transform. Distributions. Partial differential equations. Separation of variables. Applications to ordinary and partial differential equations. Introduction to analytical functions of one complex variable. Basic theory of power series. Elementary analytical functions.

Intended learning outcomes

After the course the student should be able to

  • use theorems and methods to solve solutions to problems within the parts described by the course content,
  • demonstrate av basic understanding of the mathematical concepts within the course content,
  • read and comprehend mathematical text and show the ability to explain mathematical reasoning.

For higher grades, the student in addition should be able to:

  • demonstrate a deeper understanding of the course content by describing proofs,
  • be able to solve more complex problems within the problem areas of the course descibed by the course content.

Literature and preparations

Specific prerequisites

Completed basic course SF1626 Calculus in Several Variable or SF1674 Multivariable Calculus.

Recommended prerequisites

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Announced no later than 4 weeks before the start of the course on the course web page.

Examination and completion

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

Grading scale

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


  • TEN1 - Exam, 5.0 credits, grading scale: A, B, C, D, E, FX, F
  • TEN2 - Exam, 4.0 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.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability. The examiner may allow another form of examination for re-examination of individual students.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Ethical approach

  • 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.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study


Education cycle

First cycle

Add-on studies

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