Studyinfo subject DAVE3700 2022 HØST
DAVE3700 Mathematics 3000 Course description
 Course name in Norwegian
 Matematikk 3000
 Study programme

Bachelorstudium i ingeniørfag  data / Bachelorstudium i ingeniørfag  elektronikk og informasjonsteknologi / Bachelorstudium i ingeniørfag  energi og miljø i bygg / Bachelorstudium i ingeniørfag  bioteknologi og kjemi / Bachelorstudium i ingeniørfag  maskin / Bachelorstudium i ingeniørfag  bygg
 Weight
 10 ECTS
 Year of study
 2022/2023
 Curriculum

FALL
2022
 Schedule
 Programme description

Bachelorstudium i ingeniørfag  data / Bachelorstudium i ingeniørfag  elektronikk og informasjonsteknologi / Bachelorstudium i ingeniørfag  energi og miljø i bygg / Bachelorstudium i ingeniørfag  bioteknologi og kjemi / Bachelorstudium i ingeniørfag  maskin / Bachelorstudium i ingeniørfag  bygg
 Course history

Introduction
In technological and scientific courses, we use mathematics to create models of reality. This enables engineers and natural scientists to calculate the outcome of complicated processes.
Among other things, the course covers mathematics for describing gas and liquid flows in process plants, and air flows in ventilation systems. The methods are also used to describe electromagnetic field propagation in the atmosphere and in conductors. Some of the techniques can be used to calculate the flow volume running through a pipe or watercourse. The Norwegian physicist Vilhelm Bjerknes was a pioneer in the use of this type of mathematics to forecast the weather.
The course deals with subjects that form part of engineering programmes all over the world. An understanding of these subjects will enable students to communicate with other engineers, to participate in professional discussions where the use of mathematics is assumed, and to read specialist literature where mathematics is used. The course also provides a formal background for continued studies leading up to a master’s degree in several fields. The course builds on Mathematics 1000 and Mathematics 2000.
The elective course is initiated provided that a sufficient number of students choose the course.
Recommended preliminary courses
Passed Mathematics 2000 (all study programmes).
Required preliminary courses
No requirements over and above the admission requirements.
Learning outcomes
After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence:
Knowledge
The student can:
 use the chain rule to calculate d f / d t where f = f (x (t), y (t))
 give a geometric interpretation to the use of the chain rule
 use the substitution method to calculate the largest and / or smallest value of a function under one constraint
 give a geometric description of the idea behind Lagrange's method with one constraint, and be able to use the method
 set up Lagrange's equations when there are multiple constraints
 parametrize a curve in the plane and in space in Cartesian coordinates
 calculate position, speed or acceleration when one of the three is known
 calculate curve length, curvature, tangent vector and normal vector for a curve
 describe a curve in the plane in polar coordinates
 sketch a vector field in the plane
 calculate gradient, divergence and curl
 explain the concept of potential for a gradient field
 determine an expression for the line element d s of a parametrized curve
 calculate the line integral for a scalar and a vector field and interpret the answers
 determine when a vector field is conservative
 use the properties of a conservative field to simplify calculations
 calculate double and triple integrals with given boundaries, and give geometric interpretations of the results
 determine the boundaries of double integrals when the integration region is described in Cartesian coordinates or in polar coordinates
 determine the boundaries of triple integrals when the integration region is described in Cartesian coordinates, cylindrical coordinates or spherical coordinates
 compute using Green's theorem
 use Green's theorem to calculate the circulation of a vector field
 use Green's theorem to derive the divergence theorem in the plane
 calculate the flux of a vector field through a curve
 use the divergence theorem to calculate the flux through closed curves
 explain surface integrals, and be able to calculate surface integrals when it is easy to calculate d S and when the area is the graph of z = f (x, y)
 calculate flux through surfaces when it is easy to calculate and when the surface is the graph of z = f (x, y)
 use the divergence theorem to calculate the flux through closed surfaces
 compute using Stokes' theorem
Skills
The student can:
 discuss the chain rule for a function of two variables, and explain how to determine the largest and / or smallest values for functions of several variables under constraints
 discuss how to describe the movement of particles in the plane and in space
 discuss the concepts of gradient, divergence and curl
 compare line integrals of scalar and vector fields, and discuss the concept of conservative field
 discuss differences and similarities in methods and techniques used to calculate double and triple integrals and be able to interpret the results
 discuss the concept of flux for two and threedimensional vector fields, and explain the calculation techniques used to calculate flux.
General competence
The student can:
 based on the theory on functions of one variable, can generalize the knowledge of the derivative as a measure of instantaneous change to functions with several variables
 based on the theory of definite integrals for functions of one variable, can generalize this to the integration of functions with several variables
 evaluate their own and other students' academic work, and formulate written and oral assessments of these works in a scientifically correct and accurate manner
 write precise explanations and reasons for procedures, and demonstrate the correct use of mathematical notation
Teaching and learning methods
The teaching is organised as scheduled work sessions. During the work sessions, the students shall practise using the material with which they are presented. Exercises consist of group discussions, individual practice in solving assignments, formulating and solving problems and assessing their own and others’ assignments submitted for weekly assessment.
The students shall learn how to assess their own and others’ scholarly works and formulate assessments of them in such a way that the assessment can serve as advice on further studies. These practical exercises will take place in the scheduled part of the work sessions. Students will therefore carry out weekly assessments of exercises set for the week. Information about how the weekly assessment will take place will be given in the lectures.
The students are required to complete exercises between work sessions. The proposed exercises will be directly linked to the course goals. Selfassessment of answers will give students insight into whether they have achieved the goals.
Course requirements
There are no coursework requirements in this course.
Assessment
Individual written exam, 3 hours.
The exam result can be appealed.
Permitted exam materials and equipment
All printed and written aids.
A handheld calculator that cannot be used for wireless communication or to perform symbolic calculations. If the calculator’s internal memory can store data, the memory must be deleted before the exam. Random checks may be carried out.
Grading scale
Grade scale AF.
Examiners
One internal examiner. External examiners are used regularly.