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.
SF1683 Differential Equations and Transforms 9.0 credits
Information per course offering
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Information for Autumn 2025 Start 25 Aug 2025 programme students
- Course location
KTH Campus
- Duration
- 25 Aug 2025 - 12 Jan 2026
- Periods
- P1 (5.0 hp), P2 (4.0 hp)
- Pace of study
33%
- Application code
50280
- 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]
- Schedule
- Part of programme
Contact
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus SF1683 (Autumn 2019–)Headings with content from the Course syllabus SF1683 (Autumn 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
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.
Literature
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
Examination
- 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.
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