Course

Real and Complex Calculus (MAT210)

Introduction to the theory of functions of one complex and several real variables, including convergence/divergence of series, both real and complex.


Dette er emnebeskrivelsen for studieåret 2023-2024. Merk at det kan komme endringer.

See course description and exam/assesment information for this semester (2024-2025)

Semesters

Fakta

Emnekode

MAT210

Vekting (stp)

10

Semester undervisningsstart

Spring

Undervisningsspråk

English, Norwegian

Antall semestre

1

Vurderingssemester

Spring

Timeplan

Vis timeplan

Litteratur

Pensumlisten finner du i Leganto

Content

Functions of several variables, complex numbers and functions, analytic functions; series, Taylor series, Fourier series; residues.

Learning outcome

  • Understand the concept of limit, and be able to define continuity and differentiability of functions of several real variables and of one complex variable.
  • Understand the concepts of convergence and divergence of series and power series of functions of one real and one complex variable, and be able to use different convergence tests, especially for finding the radius of convergence and area of convergence of a power series.
  • Get operational knowledge of the basic concepts of multi-variable analysis. Be able to solve extremal value problems in several variables.
  • Be able to calculate with complex numbers in Cartesian, polar and exponential form, find powers and roots of complex numbers.
  • Be able to define and know basic properties of the complex exponential and logarithmic functions and complex trigonometric functions, and to differentiate elementary analytical functions.
  • Understand the concepts of analytic and harmonic functions, and be able to understand and use the necessary conditions of differentiability.
  • Understand and use basic properties of analytic and harmonic functions. Be able to determine Taylor series of elementary analytical functions.
  • Understand the notion of residue and use it for computing contour integrals.
  • Be able to find the Fourier series of a given simple function.

Forkunnskapskrav

Ingen

Anbefalte forkunnskaper

Mathematical Methods 1 (MAT100)

Exam

Form of assessment Weight Duration Marks Aid Exam system Withdrawal deadline Exam date
Written exam 1/1 4 Hours Letter grades Basic calculator, Compilation of mathematical formulae (Rottmann), Specified printed and hand-written means are allowed. Definite, basic calculator allowed — — —


Vilkår for å gå opp til eksamen/vurdering

2 compulsory assignments
3 compulsory assignments must be approved to have access to the exam.

Fagperson(er)

Head of Department:

Bjørn Henrik Auestad

Head of Department:

Bjørn Henrik Auestad

Course coordinator:

Tyson Ritter

Method of work

6 hours lectures and problem-solving classes per week

Overlapping

Emne Reduksjon (SP)
Real and Complex Calculus (MAT210_1) , Mathematical Methods 2b (MAT220_1) 1
Real and Complex Calculus (MAT210_1) , Mathematical Methods 2 (ÅMA260_1) 5
Real and Complex Calculus (MAT210_1) , Mathematical methods 2b (ÅMA270_1) 1
Real and Complex Calculus (MAT210_1) , Mathematical methods 2c (ÅMA330_1) 5
Real and Complex Calculus (MAT210_1) , Mathematics 5 - Complex analysis (ÅMA310_2) 5
Mathematical Methods 2 (MAT200_1) , Real and Complex Calculus (MAT210_1) 5
Real and Complex Calculus (MAT210_1) , Mathematics 5 - Complex analysis (ÅMA310_1) 6

Åpent for

Battery and Energy Engineering - Bachelor in Engineering Civil Engineering - Bachelor in Engineering Computer Science - Bachelor in Engineering Computer Science - Bachelor in Engineering, Part-Time Electrical Engineering, Vocational Path - Bachelor's Degree Programme Electrical Engineering - Bachelor's Degree Programme, part-time Electrical Engineering - Bachelor's Degree Programme Energy and Petroleum Engineering - Bachelor in Engineering Geosciences and Energy Resources - Bachelor in Engineering Environmental Engineering - Bachelor in Engineering Mechanical Engineering - Bachelor in Engineering Mathematics and Physics - Bachelor's Degree Programme Medical technology - Bachelor in Engineering Medical Technology - Bachelor in Engineering - part time Geosciences Engineering - Bachelor in Engineering
Admission to Single Courses at the Faculty of Science and Technology
City and Regional Planning - Master of Science Degree Programme, Five Years Industrial Economics - Master of Science Degree Programme, Five Year Industrial Automation and Signal Processing - Master's Degree Programme - 5 year Structural and Mechanical Engineering - Master of Science Degree Programme. Five Years Advanced teacher education for level 8-13 in science Mathematics and Physics - Five Year Integrated Master's Degree Programme Petroleum Engineering - Master of Science Degree Programme, Five Years
Exchange programme at Faculty of Science and Technology
Mathematics - One-Year Programme Science and Technology - one-year programme

Emneevaluering

There must be an early dialogue between the course supervisor, the student union representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital subject evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.

Litteratur

Book Calculus : a complete course Adams, Robert A., Essex, Christopher; Adams, Robert A., Ontario, Canada, Pearson, xvii, 1086 sider, 96 sider, 2021, isbn:9780135732588, Book Advanced engineering mathematics Kreyszig, Erwin, Norminton, E.J.; Kreyszig, Herbert, Hoboken, N.J., Wiley, XV, 1001, 97, 27 s., cop. 2011, isbn:9780470646137,

Kontakt

Head of Department:

Bjørn Henrik Auestad

Head of Department:

Bjørn Henrik Auestad

Course coordinator:

Tyson Ritter

Tilbys av

Faculty of Science and Technology

Department of Mathematics and Physics

The course description is retrieved from FS (Felles studentsystem). Version 1