# SF1682 Analytical and Numerical Methods for Differential Equations 11.0 credits

### Offering and execution

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## Course information

### 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

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### Literature and preparations

#### Specific prerequisites *

Completed basic course SF1626 Calculus in Several Variable.

#### Recommended prerequisites

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#### Equipment

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#### Literature

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

### Examination and completion

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

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

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### 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