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SF1692 Analytical and Numerical Methods for Ordinary Differential Equations 5.5 credits

SF1692 is a basic course in ordinary differential equations. The course includes mathematical analysis, computational methods and modeling.

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 Mathematics, åk 2, Mandatory


P1 (5.5 hp)


26 Aug 2024
27 Oct 2024

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


Sara Zahedi,


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Course coordinator

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Headings with content from the Course syllabus SF1692 (Autumn 2021–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Course contents

  • First order ordinary differential equations, fundamental theory and concepts, separable and linear equations, variation of parameters, modeling.
  • Existence- and uniqueness theorems, Picard iterations, convergence, condition, accuracy, explicit and implicit numerical methods.
  • Linear ordinary differential equations of higher order and systems of linear ordinary differential equations, basic theory, finding solutions in specific cases, discussion of properties of solutions.
  • Autonomous systems, qualitative properties and stability analysis for linear and non-linear systems, with applications in dynamical systems including modeling.
  • Integral transforms, Laplace transform and applications to differential equations and Green functions.

Intended learning outcomes

After completion of the course the student should be able to:

  • apply concepts, theorems, and methods included in the course to solve and present solutions to problems within parts of the theory of differential equations;
  • apply, implement, and evaluate the numerical methods included in the course to solve ordinary differential equations and show insight about the possibilities and limitations of the methods;
  • read and comprehend a mathematical text and present mathematical results.

Literature and preparations

Specific prerequisites

  • Completed basic course in multivariable calculus (SF1674 or equivalent)
  • Completed basic course in linear algebra (SF1672 or equivalent)
  • Participated in a basic course in numerical methods (SF1550 or equivalent)

Recommended prerequisites

  •  Completed basic course in calculus in one variable (SF1673 or equivalent)


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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


  • PRO1 - Project, 2.5 credits, grading scale: P, F
  • TEN1 - Written exam, 3.0 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.

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

No information inserted


Sara Zahedi,