# SF1682 Analytical and Numerical Methods for Differential Equations 11.0 credits

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Headings with content from the Course syllabus SF1682 (Autumn 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

• Equations: First and higher order ordinary differential equations and systems of these, partial differential equations (e.g. for heat and waves).
• Transforms: Fourier transform, Laplace transform and Fourier series.
• Analytical concepts: Initial value problems, boundary value problems, existence and uniqueness of solutions, autonomous equations, direction fields, phase portraits, solutions curves, oscillation phenomena, general solution, particular solution, stationary/critical points, stability, linearization of systems, the delta function, generalized derivatives.
• Numerical concepts: Apprximation, discretization, convergence, conditional number, accuracy, local linearization, stability, stiff systems, implicit and explicit methods, adaptivity.
• Analytic methods: Integrationg factor, separation of variables, variation of parameters, eigenvalue methods, transforms, spectral methods.
• Numerical methods: Newton's method for non-linear systems, Euler forward, Euler backwards, Runge_kutta methods, finite difference methods, spectral methods, fast Fourier transform (FFT), computational complexity.

### Intended learning outcomes

After the course the student should be able to

• use concepts. theorems and methods to handle questions in analysis and numerical aspects of differential equations and transforms described by the course content,
• use analytical and numerical methods to solve the the differential equations described by the course content, and gain insights into the possibilities and limitiations of methods.
• 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

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

• INLA - Assignments, 5.0 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. The examiner may allow another form of examination for re-examination of 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

### 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 SF1682

SCI/Mathematics

Technology

First cycle