TANA08 Numerical Methods II 2009

Study Guide@lith

Valid for year : 2009

TANA08	Numerical Methods II, 6 ECTS credits. /Numeriska metoder II/ For: COM ENG I Ii M Mat MMAT Y
OBS!	Overlapping course content: TANA48/TANA07
	Prel. scheduled hours: 44 Rec. self-study hours: 116
	Area of Education: Science Subject area: Mathematics
	Advancement level (G1, G2, A): A
	Aim: Within the area of scientific computing algorithms for solution of mathematical problems in science and technology are developed. The student should deepen his/her knowledge within the area. After this course the student should be able to use and analyse orthogonal transformations for the solution of eigenvalue problems, least squares problems and similar computational problems in linear algebra use and analyse Newton's and Gauss-Newton's methods for solving nonlinear equations use and analyse (with respect to accuracy and stability) one-step and multistep methods for integrating initial value problems
	Prerequisites: (valid for students admitted to programmes within which the course is offered) Numerical Methods I / Numerical Algorithms. A Basic Programming course. Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
	Organisation: The course consists of lectures, lessons and computer exercises.
	Course contents: Linear Algebra: LU-factorization. Perturbation Theory. The Singular Value Decomposition and the Pseudoinverse. Orthogonal transformations using the Householder and the Given´s methods. The QR decomposition and the Least Squares Problem. The Eigenvalue Problem: Normal forms. Perturbation Theory and error estimates. The Rayleigh quotient. The Power method and Inverse Iteration. Transformation to Hessenberg and tridiagonal form. The QR-algorithm. Systems of nonlinear equations and nonlinear least squares problems. The Newton and Gauss-Newton methods. Ordinary Differential Equations: Runge-Kutta methods. Multistep methods. Errror estimates and step lenght control. Difference equations. Stability and Convergence. Methods for stiff systems.
	Course literature: Michael T. Heath: Scientific Computing. An Introductory Survey, Second edition, McGraw Hill, 2002. Computer projects from the department.
	Examination:
	Written examination Laboratory work	4 ECTS 2 ECTS


Course language is Swedish/English. Department offering the course: MAI. Director of Studies: Torbjörn Larsson Examiner: Tommy Elfving Link to the course homepage at the department Course Syllabus in Swedish

Linköping Institute of Technology
Contact: TFK , val@tfk.liu.se Last updated: 02/06/2009