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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.

Information per course offering

Termin

Information for Autumn 2024 Start 26 Aug 2024 programme students

Course location

KTH Campus

Duration
26 Aug 2024 - 27 Oct 2024
Periods
P1 (5.5 hp)
Pace of study

33%

Application code

52121

Form of study

Normal Daytime

Language of instruction

Swedish

Course memo
Course memo is not published
Number of places

Places are not limited

Target group
No information inserted
Planned modular schedule
[object Object]

Contact

Examiner
No information inserted
Course coordinator
No information inserted
Teachers
No information inserted
Contact

Sara Zahedi, sara.zahedi@math.kth.se

Course syllabus as PDF

Please note: all information from the Course syllabus is available on this page in an accessible format.

Course syllabus SF1692 (Autumn 2021–)
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)

Equipment

No information inserted

Literature

No information inserted

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

Examination

  • 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

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

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

Technology

Education cycle

First cycle

Add-on studies

No information inserted

Contact

Sara Zahedi, sara.zahedi@math.kth.se