# SF1523 Analytical and Numerical Methods for Differential Equations 7.5 credits

This course gives  an overview and basic skills in differential equations solving and the related numerical methods for simulating technical and scientific processes based on mathematical models.

### Choose semester and course offering

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.

## Application

### For course offering

Spring 2025 Start 17 Mar 2025 programme students

### Application code

61051

Headings with content from the Course syllabus SF1523 (Autumn 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

• Equations: first and higher order scalar differential equations, systems of differential equations of first order, partial differential equations for heat conduction and waves,

• Concepts: discretization, approximation, convergence, condition numbers, linearization, stability,

• Methods: integrating factor, diagonalization, Fourier series, separation of variables, Fourier transform,

• Numerical method for integrals and differential equations: Eulers method, Runge-Kutta methods, the backward Euler method,  boundary value problems,  finite difference methods for heat conduction and waves,

• Numerical methods for optimization: Newton’s method, Lagranges method.

### Intended learning outcomes

A general aim with the course is to give the student the understanding that numerical methods and programming techniques are needed to make reliable and efficient simulations of technical and scientific processes based on mathematical models.

After the course the student should be able to

• Use concepts, theorems and methods to solve problems within analytical and numerical aspects of differential equations included in the course main content.
• Use analytical and numerical methods to solve differential equations included in the course main content, and show insight about possibilities and limitations for different methods.
• Read and assimilate mathematical text.

## Literature and preparations

### Specific prerequisites

Active participation in SF1625 Calculus in one variable and SF1522 Numerical Computations.

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

The course literature will be announced on the course homepage at least four weeks before the start of the course.

## 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

• LABA - Laboratory Works, 2.5 credits, grading scale: P, F
• TEN1 - Examination, 5.0 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.

In this course, the code of honour of the school is applied, see: http://www.sci.kth.se/institutioner/math/avd/na/utbildning/hederskodex-for-studenter-och-larare-vid-kurser-pa-avdelningen-for-numerisk-analys-1.357185

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability.

### 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 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.

Technology

### Education cycle

First cycle

No information inserted

### Contact

Ozan Öktem (ozan@kth.se)