# TKT4140 - Numerical Methods

### Examination arrangement

Examination arrangement: School exam

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.

_ 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.

### 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.

• Exercises

### Further on evaluation

If there is a re-sit examination, the examination form may be changed from written to oral.

### Credit reductions

Course code Reduction From To
SIO1054 7.5
More on the course

No

Facts

Version: 1
Credits:  7.5 SP
Study level: Second degree level

Coursework

Term no.: 1
Teaching semester:  SPRING 2024

Language of instruction: English, Norwegian

Location: Trondheim

Subject area(s)
• Technological subjects
Contact information
Course coordinator:

Department of Structural Engineering

# Examination

#### Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Spring ORD School exam 100/100
Summer UTS School exam 100/100
• * 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.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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