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.
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Content and learning outcomes
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.
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.
Literature and preparations
Active participation in SF1625 Calculus in one variable and SF1522 Numerical Computations.
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.
- LABA - Laboratory Works, 2.5 credits, grading scale: P, F
- TEN1 - Examination, 5.0 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.
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.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
- 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 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 SF1523