University College Dublin

 School of Mathematical Sciences

Master of Computational Science

computational science

Numerical Algorithms

Exercises & Assignments

Dr Derek O'Connor

First Semester 2006-2007

This page was last updated on July 18, 2009

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Exercises and Assignments

These exercises and assignments are an integral part of this course. The solution notes are particularly important because they discuss topics not covered in the lecture notes. The material covered in the lecture notes and solution notes are examinable. That is, any topic in these solution notes and the lecture notes may appear as an exam question. 

The exercises and assignments are not optional. Computational Mathematics is not a 'spectator sport' : you must compute.  Those who have little programming experience will need to work harder.

The exercises and assignments are designed to reinforce and complement the material covered in the lectures. Hence, they are synchronized with the lectures and so it is important that they are completed and submitted on time.

 In general, all exercises and assignments must be submitted as follows :

  1. A laser-printed report, typset in LaTeX. (MS Word will not do). This is to be handed in at the end of class on the due date.
  2. All  related files (.tex and .m, etc) must be emailed to me as a single zipped attachment.
  3. Please use the  LaTeX template file AssLabTempl.tex to typeset your Assignments and Lab. Exercises. It is in LatexNotes.zip.

See below for more details.

 

New assignments and exercises, and their links, will be added as we progress through the semester.

Exercises

After most classes you will be given a small set of problems which you will solve and hand in at the end of the next class.  These will require you to use  Matlab, and to a limited extent, Maple.  These exercises will count for 15% of the grade.

Lab Exercise 1 --  Calculating Constants : pi, e, gamma.

Lab Exercise 2  -- Function Evaluation : Sin(x)

Lab Exercise 3 ---  Matlab's Floating Point Number System

Lab Exercise 4  ---  Fixed Points and Iteration 

Lab Exercise 5  ---  Pivoting, Error, Residuals  

Lab Exercise 6  ---   LU Decomposition and Matrix Powers 

 

Assignments

It is virtually impossible to understand and appreciate algorithms without implementing them and using them in some program. For this reason 2  Matlab programming assignments will be given in this course. Assignments require more thought, reading, programming, and time than the exercises. These assignments will count for 15% of the grade.

Assignment  1.  Monte Carlo Methods  

Assignment  2.  Zero Finding Methods    Assign2.zip, multroot.zip

Submission of Reports

All assignments and lab exercises require you to submit a report. The submission has various parts :

  1. Paper Copy : This is the text of the report that is typset using LaTeX with the resulting PDF file printed on a laser printer. This should be handed to me at the end of class on the due date.  This paper copy will be marked and annotated by me and then handed back to you at the end of the next class.
  2. Digital Copy : This is a collection of the LaTex and PDF files along with the appropriate Matlab and data files used. All these files must be zipped into ONE file which is then emailed to me as an attachment. This is kept by me as a record of the work you have done. It is important that the paper and digital content be identical.

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