Basic Numerical Methods

Basic Numerical Methods

Upon completing this module, the students will acquire the basics of numerical mathematics and numerical simulation methods. This includes the theoretical understanding of how a computer calculates with finite floating-point numbers and what kind of errors and inaccuracies may arise from these, and how to reduce or control them same. They will be familiar with basic numerical methods for modelling and simulating statistical models, linear algebra models, and ordinary and partial differential equations. They will be able to estimate the approximation errors of the methods and determine the algorithmic intensity, and will be able to implement these methods themselves.


Contents

Floating point arithmetic, rounding errors, cancellation, numerical interpolation (Lagrange, Newton, Splines), Taylor developments, finite differences and their approximation errors, explicit and implicit time integrators, qudrature, direct and iterative algorithms for matrix inversion, matrix decomposition (LU), solution for the Poisson equation.


Program / Module

M.Sc. Computational Modeling and Simulation
Module: CMS-COR-NUM - Basic Numerical Methods


Time/Place
Winter Term

Lecture: Mondays, 5. DS (14:50-16:20) ONLINE / FIRST LECTURE: OCT 26, 2020
Exercises: Thursdays, 3. DS (11:10-12:40) ONLINE / FIRST TUTORIAL: OCT 29, 2020

LECTURES AND EXERCISES WILL BE ENTIRELY ONLINE FOR THE WHOLE SEMESTER. They will be held as Zoom live screen-casts with the possibility to ask questions. Recurrent links (i.e., the same every week) are announced here below. In order to keep this as close as possible to a real lecture experience, the webcasts are not recorded.

Webcast link for the lectures (recurrent, same every week): https://us02web.zoom.us/j/88336989253?pwd=WVQ1TkxyM2JKempOZ2w1dXlPeHRUUT09
Meeting ID: 883 3698 9253
Password: 164596

Webcast link for the exercise tutorials (recurrent, same every week): https://us02web.zoom.us/j/84364851860?pwd=d09OcURPeU5hUzc0ZnBWeU9yempmUT09
Meeting ID: 843 6485 1860
Password: 667585


Format

2 SWS lecture, 2 SWS exercise, self-study

5 credits


Exam

Online exam in OPAL (exceptionally due to Covid-19 situation and special decision by university Senate and Rectorate) of 90 minutes duration. Time and date to be announced.

Proper registration to the exam in SELMA is mandatory. Only registered students will receive a link and code to participate in the online exam. This is an open-book exam. All sources and means of help are allowed to be used, but the exam must be completed alone and by yourself without the help of any third person.


Grade scale:

All exams are graded in absolute terms w.r.t. the following pre-defined grade scale that remains constant over the years:

  • The top grade of 1.0 is reached with 80% of the maximum possible points
  • Half of that, i.e., 40% of the maximum possible points, are required to pass
  • Below 40%, or no-show, is a fail.
Between the top grade and the passing threshold, the grading scale is linear. In the end, grades are rounded to the nearest allowed grade according to the exam regulations: 1.0, 1.3, 1.7, 2.0, 2.3, 2.7, 3.0, 3.3, 3.7, 4.0, 5.0. The grades 0.7, 4.3, and 4.7 are not allowed. Any grade above 4.1 is a fail (see exam regulations). The maximum number of points that can be reached in the exam is given by the number of minutes the exam lasts (i.e., a 90 minute exam yields maximum 90 points). Points are distributed amongst the exam questions to reflect the number of minutes a good student would need to solve the problem. This provides some guidance for your time management in the exam. In order to reduce the risk of correction mistakes, all exams are checked by at least two independent, qualified assessors (typically professors or teaches with officially conferred examination rights). The exam review session (see below) is for you to come look at your exam paper and report correction mistakes you found.


Exam Review winter term 2020/21

Exam Review dates and details are going to be announced after completion of the exam.

IMPORTANT: All students attending an exam review must fill in and sign the exam review form they are going to receive during the review. Undocumented exam reviews are not permitted. You must participate in person.


Registration to the course

For students of the Master program "Computational Modeling and Simulation: via CampusNet SELMA

For students of the Computer Science programs: via jExam


Teachers

Lecture: Prof. Ivo F. Sbalzarini
Exercises: Abhinav Singh


Instruction language: ENGLISH


Lecture notes are available as PDF here.
Below is the weekly syllabus and the exercise/solution handouts: