SF1683 Differential Equations and Transforms 9.0 credits

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.

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.

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

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

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

• 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.

Mattias Dahl

• 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.