## ING1502 Mathematical methods 1

Course code:
ING1502
Course name in Norwegian Bokmål:
Matematiske metoder 1
Program of study:
Bachelor i ingeniørfag, studieretning telematikk
Credits:
15
Level of study:
Bachelor
Teaching semester:
2021 Autumn
Assessment semester:
2021 Autumn
Language of instruction:
Norwegian / English
Person in charge:
Kirsi Helkala
Course content

Mathematical methods 1 will give the students knowledge and understanding of specific mathematical concepts, problems and solution methods. The course provides an introduction to basic mathematical modelling. The course will also teach the student how mathematics can be integrated in engineering and interdisciplinary problem solving. The course forms the basis for further studies of the courses at Norwegian Defence Cyber Academy (NDCA) and gives the student a system of concepts and understanding that is necessary to perform the profession.

Course topics
• Number systems
• Complex numbers
• Functions
• Derivation
¨• Integration
• First and second order differential equations
• Vector algebra and vector-valued functions
• Functions with two and three variables
• Partial derivatives, linear approximations, the chain rule, directional derivatives and gradient
• Dual integrals and triple integrals
• Polar coordinates, cylindrical coordinates, spherical polar coordinates and general change of variables
• Vector field
• Conservative fields and potentials
• Line integrals and work, surface integrals and flux
• Green’s, Gauss’ and Stokes’ theorems

Special conditions related to the assessments
A bonus percentage of up to 5% is given depending on the number of tasks the student has registered as completed in the course.
There is no requirement to pass for individual sub-evaluations. Any resit as a result of failing the overall grade is given in form of a written examination that covers the whole syllabus, that counts 100% on the final grade. In case of reassessment of examination grade all tests will be evaluated, after final assessment is given.

Learning outcome

Knowledge
After completion of the course, the cadet is able to:
• demonstrate understanding of the mathematical concepts, problems and solution methods that are a part of the course’s topics
• point out basic relationships between mathematics and engineering applications.

Skills
After completion of the course, the cadet is able to:
• calculate with symbols and formulas
• apply derivation and integration to simple practical problems
• compose and solve simple differential equations
• solve simple equations with complex numbers as solution
• apply mathematical representations
• describe curves, surfaces and spatial areas through equations and differences, by using different types or coordinates, and by using parameter representations
• setting up and calculating the different integrals of scalar and vector fields that are part of the course’s topics; including using being able to use the connections between the various types of integrals in Green’s, Stokes’ and Gauss’ theorems
• recognize a conservative field and calculate a potential function for the field

General competence
After completion of the course, the cadet is able to:
• use own words to describe the application and significance of mathematics for engineering problems
• point out connections between mathematics and the courses “Physics,” “Chemistry” and “Electronics”, as well as Electronic Warfare

Working and learning activities

Lectures, flipped classroom, tests, group work, student presentations and exercises

Sensor system

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.

Curriculum

Lorentzen, L., Hole, A. & Lindstrøm, T.L.. (2015). Kalkulus med èn og flere variable​. (2. utg.). Universitetsforlaget.

Mandatory courseworkCourseworks givenCourseworks requiredPresence requiredComment
Øvinger RequiredIt is mandatory to have completed 1/3 of the exercises given before each written examination, in order to have permission to take the written examination.
Obligatoriske arbeidskrav:
 Mandatory coursework: Øvinger Courseworks given: Courseworks required: Presence required: Required Comment: It is mandatory to have completed 1/3 of the exercises given before each written examination, in order to have permission to take the written examination.