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

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.

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.

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

• 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) 

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

• 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.

Anders Szepessy

• 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.