Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBMA02305 
Vaknaam  Numerical Mathematics 2 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Numerical Mathematics 2  
Leerdoelen  The student is able to: 1. describe the methods mentioned in the course description, 2. reproduce basic concepts and theorems from Numerical Analysis related to the subjects mentioned in the description, 3. apply techniques from vector analysis and linear algebra to analyze the treated numerical methods, 4. create an algorithm from a given numerical method and to implement it in MATLAB, 5. assess some of the difficulties that may come up when solving a problem on a computer by a specific algorithm, specifically, the difficulties arising from finite precision computations (propagation of roundoff errors), limited memory availability, and finite computation speed (complexity of the algorithm), 6. make a judicious choice from the discussed methods for a particular problem. 

Omschrijving  In this course, we will treat both the theory and algorithms of advanced numerical methods. Advanced methods are built on advanced theoretical considerations. Hence, the theory will play an important role in this course. We will study tools for solving the following problems: • Linear systems: Under which conditions can a linear system be solved safely, i.e. without rounding errors destroying the solution? What to do with under and overdetermined system? • (Generalized) eigenvalue problems: How can one determine all the eigenvalues of a system? How can one find the most interesting eigenvalues of a matrix? Among others, we will discuss the Lanczos method. • Approximation, Interpolation, and Integration problems: o A leastsquares problem can be solved elegantly when the approximating polynomial is constructed with orthogonal polynomials, like Gauss Legendre and Chebyshev polynomials. o As a spinoff, orthogonal polynomials learn us how to choose the interpolation points in interpolation problems. o Moreover, since numerical integration methods are based on interpolation they lead to the very accurate Gauss and Chebyshev integration methods. 

Uren per week  
Onderwijsvorm 
Hoorcollege (LC), Werkcollege (T)
(The Lab Sessions are mandatory. Deadlines will be set; not meeting a deadline will result in zero points for the associated exercise.) 

Toetsvorm 
Practisch werk (PR), Tussentoets (IT)
(The course will be subdivided into three units. Each unit will consist of a practical and a test, which both will be marked, say PRi and Ti for the ith unit. Each PRi and Ti should be 5 or higher to pass. The final mark will be (2*PR1+3*PR2+3*PR3+3*T1+4*T2+5*T3)/20, and should before rounding be 5.5 or higher to pass. Each nopass can be repaired. For the practical, this is during the next unit and for the test, this is in the reexamination. A pass mark for a practical cannot be upgraded by a repair. In case the final mark is 5.5 or higher, a pass mark for a test cannot be upgraded by repair) 

Vaksoort  bachelor  
Coördinator  dr. ir. F.W. Wubs  
Docent(en)  dr. ir. G. Tiesinga ,dr. ir. F.W. Wubs  
Verplichte literatuur 


Entreevoorwaarden  Prior knowledge: Knowledge and skill in handling basic numerical techniques and programming in MATLAB as taught in the course Numerical Mathematics I and good knowledge of linear algebra and vector analysis is necessary.  
Opmerkingen  This course prepares for advanced courses on Numerical Mathematics  
Opgenomen in 
