## ING2301 Functions, Differential Equations and Numerical Methods

The course deals with the most important functions in mathematics, their properties and applications. It also addresses models formulated with simple differential equations of the first and second order, as well as the solution of such equations. Furthermore, the course will give an introduction to basic concepts and techniques in programming, which are then used to solve equations numerically.

The course is planned to be given by a civilian university.

Knowledge

After completing the course, the cadet is able to:

- explain where and how derivation and integration is used
- explain the properties of trigonometric functions and exponential/logarithmic functions
- understand the theory and meaning of complex numbers
- explain how the relationship between these, the trigonometric functions and the exponential function in complex form leads to the development of Fourier series
- Understand how programming is used to solve mathematical problems

Skills

After completing the course, the cadet is able to:

- use solid computing skills to solve tasks involving basic problems from engineering mathematics
- use a relevant mathematical symbol and formula system to manipulate symbols and formulas
- think and reason mathematically, that is, set up mathematical models, solve mathematical problems, both analytically and numerically, and evaluate and account for his/her results
- use mathematical methods and tools

General competences

After completing the course, the cadet is able to:

- explain how mathematics can be used to solve practical and technical problems
- recognise and manage mathematical models that other courses and personal professional development can build on
- formulate mathematical models within an engineering framework
- use a relevant system of formulas and communicate about mathematics, both orally and in writing

The course is coordinated with the other technical courses.

Emphasis is placed on using examples from these and from service in the Navy.

Approximately 16 hours of work per week is expected (lectures, problem solving, project work, independent study).

Examination is carried out according to the Regulations for Admission, Studies and Examinations (in Norwegian, “Forskrift om opptak, studier og eksamen”) at the Norwegian Defence University College.

- Berle, E., Langholm, T. & Meen, K. (2019).
*Innføring i Programmering*. Sjøkrigsskolen. - Croft, A., Davison, R., Hargreaves, M. & Flint, J. (2013).
*Engineering Mathematics – A Foundation for Electronic, Electrical, Communications and System Engineers*(4. utg.). Harlow: Pearson-Education.- Numbersystems: Chap. 1.3
- Engineering functions: Chap. 2
- Trigonometric functions: Chap. 3
- Logical ports: Chap. 5
- Complex numbers: Chap 9.1 – 9.5, 9.7 – 9.9
- Diferentiation: Chap. 10 – 12
- Integration: Chap. 13 – 15 and 16.3
- Ordinary differential equations: Chap. 19
- Numerical methods to solve differential equations: Chap. 20.5 – 20.6
- Fourier series: Chap 23.1 – 23.3 and 23.5

Form of assessment | Grouping | Duration | Type of duration | Grading scale | Proportion | Oral examination | Comment | Supported materials |
---|---|---|---|---|---|---|---|---|

Mappevurdering | Individual | 1 | Semesters | A-F | 100 % | Not required | The portfolio consists of assignments, tests and project in connection with oral presentation. Details will be announced at the beginning of the term. | Textbook, table of formula, calculator |