# SF1676 Differential Equations with Applications 7.5 credits

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Headings with content from the Course syllabus SF1676 (Spring 2020–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

• First order ordinary differential equations: Fundamental theory and concepts, separable and linear equations, modeling.
• Linear ordinary differential equations of higher order and systems of linear ordinary differential equations: Fundamental theory, finding solutions in specific cases, in particular the case of constant coefficients, discussion of properties of solutions.
• Autonomous systems: Fundamental concepts, stationary solutions and their stability, applications to dynamical systems and scientific modeling.
• Integral transforms: Laplace transform and Fourier series, and their application to differential equations.
• Introduction to partial differential equations: Solution of classical boundary value problems.
• Group project: Application to concrete problems connected to the construction area and the built environment.

### Intended learning outcomes

After passing the course, the students should be able to

• use concepts, theorems and methods to solve, and present the solution to, problems within theparts of the theory of differential equations that are described by the course content;
• apply and combine in the form of a group project the methods of differential equations to apractical problem connected to the construction area and the built environment;
• read and comprehend mathematical text.

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

Completed basic course SF1626 Calculus in Several Variable

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### 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.

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

### Examination

• PRO1 - Project, 1.5 credits, grading scale: P, F
• TEN1 - Exam, 6.0 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.

### Other requirements for final grade

Written exam, possibly with continuous examination. A project with presentation.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### 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 web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF1676

Technology

First cycle