DN1241 Numerical Methods, Basic Course III 7.5 credits

Basic concepts and ideas: algorithm, local linearization, iteration, extrapolation, discretization, convergence, stability, condition.

Reliability assessment: parameter sensitivity, experimental perturbations, precision.

Numerical methods for: linear systems of equations, nonlinear equations and systems of equations, interpolation, model-fitting with the method of least squares, optimization, quadrature, differential equations.

The application of mathematical software in the solution of scientific and engineering problems, numerical experimentation, and the presentation of effective algorithms.

An overlying goal with the course is the realization of the necessity of numerical methods in order to simulate technological and scientific processes based on mathematical models.

After completing this course, the students should be able to

• identify various mathematical problems and reformulate these in a way suitable for numerical treatment
• select a suitable numerical method for the treatment of the given problem
• motivate the choice of a method by describing its advantages and limitations
• select an algorithm leading to efficient computation and implement this in a programming language, suitable for scientific computing, e.g. Matlab
• present the results in a relevant and illustrative way
• provide an estimate of the accuracy of the results
• utilize standard functions from e.g. Matlab's library for calculation, visualization and efficient programming.

For single course students: completed upper secondary education including documented proficiency in Swedish corresponding to Swedish B, English corresponding to English A. Furthermore: 15 hp in mathematics and 6 hp in computer science or programming technics.

For those studying at KTH: mandatory first year courses in mathematics and a course in computer science or programming.

G. Eriksson: Numeriska algoritmer med Matlab, CSC/Nada 2002.

T. Sauer: Numerical Analysis, Pearson 2006.

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

• LABA - Laboratory Work, 1.5 credits, grading scale: P, F
• LABB - Laboratory Work, 3.0 credits, grading scale: P, F
• TEN1 - Examination, 3.0 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 all the regulations of the code of honor at the School of Computer science and Communication apply, see: http://www.kth.se/csc/student/hederskodex/1.17237?l=en_UK.

A written examination (TENl; 3 university credits.).
Computer assignments (LABA; 1,5 university credits.).
Computer assignments with oral and written presentation (LABB; 3 university credits.).

• 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.

DN2220 Applied Numerical Methods I or DN2250 Applied Numerical Methods II, DN2225 Numerical Solution of Differential Equations I, DN2266 Mathematical Models, Analysis and Simulation, Part I or DN2252 Numerical Algebra, DN2264 Parallel Computations for Large-Scale Problems part 1.

The course cannot be counted towards the degree if the student also has taken any of the courses 2D1210, 2D1212/DN1212, 2D1213/DN1213, 2D1214/DN1214, DN1215, 2D1240/DN1240.