SF1523 Analytical and Numerical Methods for Differential Equations 7.5 credits

Analytiska och numeriska metoder för differentialekvationer

Please note

The information on this page is based on a course syllabus that is not yet valid.

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.

  • Education cycle

    First cycle
  • Main field of study

    Technology
  • Grading scale

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

Course offerings

Spring 19 CDEPR1 for programme students

Spring 20 CDEPR1 for programme students

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.

Course main content

  • 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.

Eligibility

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

Literature

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

Examination

  • LABA - Laboratory Works, 2.5, grading scale: P, F
  • TEN1 - Examination, 5.0, grading scale: A, B, C, D, E, FX, F

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. 

Offered by

SCI/Mathematics

Contact

Mattias Sandberg (msandb@kth.se)

Examiner

Mattias Sandberg <msandb@kth.se>

Version

Course syllabus valid from: Autumn 2019.
Examination information valid from: Autumn 2014.