Course - Numerical Methods - TKT4140
TKT4140 - Numerical Methods
About
Examination arrangement
Examination arrangement: School exam
Grade: Letter grades
| Evaluation | Weighting | Duration | Grade deviation | Examination aids |
|---|---|---|---|---|
| School exam | 100/100 | 4 hours | A |
Course content
Initial- and boundary-value problems for ordinary differential equations using difference methods. Numerical solution of partial differential equations using difference methods.
Optimization techniques and algorithms.
Mathematical representation and implementation of artificial neural networks.
The examples and problems are primarily from the following fields: Solid mechanics, elasticity, dynamics, fluid mechanics and heat transfer. The principle teaching resource for the course will be a digital compendium which integrates theory, examples and python-programs.
Learning outcome
This course will provide an introduction to numerical methods which are revelant in the engineering fields of academic programs MTPROD, MTING and MTBYGG. The subject is mandatory for the program Industrial Mechanics.
The numerical methods of interest to this course are related to the numerical analyses of ordinary and partial differential equations, numerical optimization and machine learning techniques (artificial neural networks). Examples from the first 2-3 years of the study programs MTPROD, MTING and MTBYGG will be used as background for the use of these numerical methods.
The following abbreviations are used below :
ODE : Ordinary differential equation, PDE : Partial differential equation, IVP/BVP: initial and boundary value problem.
ANN : Artificial Neural Networks
Knowledge: The candidate will learn about:
- Numerical methods for solving ODEs and PDEs in IVP/BVP.
- Basic finite difference schemes for parabolic, elliptical and hyperbolic PDE classes.
- Accuracy, consistency and stability of numerical schemes for ODEs and PDEs.
_ Numerical optimization schemes, both constrained and unconstrained, single or multi-variables.
_ Gradient free, Gradient based and genetic algorithms for optimization.
_ Mathematical formulation of ANNs including their training and validation.
Skills: The candidate will be able to:
- Identify initial and boundary value problems for ODEs, choose a discretization strategy, implement the resulting ODE solver using python as a programing language.
- Discretise the three main types of PDEs using finite difference methods and program the resulting numerical scheme.
- Setup an optimization problem in python and select the appropriate optimization strategy for the problem at hand.
- Setup an ANN in python with the all the necessary steps for its training, validation and use
General competence: The candidate will have fundamental competence in:
- Programming (python) to be used later in the studies.
- Numerical methods for engineering applications as a foundation for more advanced numerical methods at later stages in the studies.
Digital competence: Extensive use of Python as a tool for problem solving i mechanics-related problems.
Learning methods and activities
Lectures and problem-solving supplemented with programming primarily in python. The lectures and exercises will be given in English if students not fluent in Norwegian are taking th course or if there are other practical reasons for doing so. If the lectures are given in English, the exam will be typed in English only. Students are free to to hand in their answers in Norwegian or English. Most of the teaching material is written in English.
Compulsory assignments
- Exercises
Further on evaluation
If there is a re-sit examination, the examination form may be changed from written to oral.
Recommended previous knowledge
Subject TDT4105 Information Technology, Introduction. Subject TMA4130, Mathematical Subjects, Advanced Course, is recommended, but not required.
Course materials
Digital compendium, downloadable example code, tutorials etc.
Credit reductions
| Course code | Reduction | From | To |
|---|---|---|---|
| SIO1054 | 7.5 |
No
Version: 1
Credits:
7.5 SP
Study level: Second degree level
Term no.: 1
Teaching semester: SPRING 2025
Language of instruction: English, Norwegian
Location: Trondheim
- Technological subjects
Department with academic responsibility
Department of Structural Engineering
Examination
Examination arrangement: School exam
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Spring ORD School exam 100/100 A INSPERA
-
Room Building Number of candidates - Summer UTS School exam 100/100 A INSPERA
-
Room Building Number of candidates
- * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"