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SF1693 Analytical and Numerical Methods for Partial Differential Equations and Transforms 11.0 credits

SF1693 is a basic course on partial differential equations and transforms. The course focus on methods for mathematical analysis, computation, modeling and programming related to partial differential equations.

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Choose semester and course offering to see information from the correct course syllabus and course offering.

Headings with content from the Course syllabus SF1693 (Autumn 2021–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Equations: Time-independent elliptic partial differential equations, time-dependent parabolic and hyperbolic partial differential equations, with application to diffusion, linear and non-linear waves, eigenvalue problems and optimization.

Areas of application are selected from: heat conduction, diffusion, solid mechanics, fluid mechanics, electromagnetics, quantum mechanics, acoustics and vibrations.

Concepts: wellposedness, Hilbert space, orthogonality, regularity, boundary value and initial value problems, fundamental solution, convergence, condition number, stability, weak and strong solutions, distributions, entropy conditions.

Analytical methods: characteristics, Fourier series, separation of variables, Fourier transform, variational methods, calculus of variation, maximum principles.

Numerical methods: the finite element method, finite difference methods, iterative methods, optimization methods, adaptive methods, fast Fourier transform, interpolation theory, quadrature.

Intended learning outcomes

A general goal is that the course should provide the student with skills to handle methods of mathematical analysis, computation, modeling and programming related to partial differential equations.

After the course the student should be able to:

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

Course disposition

No information inserted

Literature and preparations

Specific prerequisites

  • Completed basic course in multivariable calculus (SF1674 or equivalent)
  • Completed basic course in numerical methods (SF1550 or equivalent)  

Recommended prerequisites

  • Completed basic course in linear algebra (SF1672 or equivalent)
  • Completed basic course in calculus in one variable (SF1673 or equivalent)
  • Completed basic course in in ordinary differential equations (SF1692 or equivalent) 
  • Completed basic course in fundamentals of programming (DD1331 or equivalent) 

Equipment

No information inserted

Literature

No information inserted

Examination and completion

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

Grading scale

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

Examination

  • LAB1 - Laboratory work, 5.0 credits, grading scale: P, F
  • TEN1 - Written 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.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Profile picture Anders Szepessy

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 SF1693

Offered by

SCI/Mathematics

Main field of study

Technology

Education cycle

First cycle

Add-on studies

No information inserted

Contact

Sara Zahedi, sara.zahedi@math.kth.se