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, 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) in SCH-A316 (Georg-Schumann-Bau) / FIRST LECTURE: OCT 14
Exercises: Thursday, 3. DS (11:10-12:40) in HSZ/003 (Hörsaalzentrum). 17.10.2019: VMB/0E02/U (von-Mises-Bau)


Format

2 SWS lecture, 2 SWS exercise, self-study

5 credits


Exam

Monday, February 10, 2020, 09:20-10:50h, M13/DÜLF/U (Dülfersaal, Mensa Mommsenstr. 13)

Since there are more than 10 registered students, the module examination consists of a written examination with a duration of 90 minutes.

At the exam, the following may be used:

  • 4 A4 sheets (8 pages if you print duplex) of hand-written summary. We recommend writing the summary by hand, but it can also be machine-written. In the latter case, the font size must be 8 points or larger throughout.
  • A standard pocket calculator (devices with network or bluetooth access, as well as devices capable of storing and displaying documents are not allowed)
Items not adhering to these guidelines will be confiscated in their entirety at the beginning of the exam.


Exam Review

You can come and look at your exam, and ask questions about its correction and the answers given during the exam review times. Due to the current travel and contact restrictions, we offer three exam review dates: one in June, one during the summer break, and one around the beginning of the winter semester 2020/21. The dates and modalities for the latter two are yet to be determined, but you are invited to participate in the June date if you happen to be around:


  • June 18, 2pm, Outdoors at the pond between the BAR building and the Mensa (Maps Link). The review only takes place if there is no rain. In case of rain, a new date will be found. In order to participate, You MUST wear a face mask and you are only allowed to come forward one by one.
  • July 20, 2pm, Outdoors in the seating area in front of the Center for Systems Biology Dresden, Pfotenhauerstr. 108 (Maps Link). The review only takes place if there is no rain. In case of rain, a new date will be found. In order to participate, You MUST wear a face mask and you are only allowed to come forward one by one.
  • October 19, 2pm. Location to be announced, depending on how the Covid restrictions develop
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.

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


Teaching language: ENGLISH


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