Course

Real and Complex Calculus (MAT210)

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


Dette er emnebeskrivelsen for studieåret 2018-2019. 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

Content

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

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 derivate elementary analytical functions. Understand the concepts of analytic and harmonic functions, and be able to understand and use the necessary conditions for differentiability. Understand and use basic properties of analytic and harmonic functions. Be able to determine Taylor series of elementary analytical functions. 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

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 exercises 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

Mathematics - One Year Foundation Programme at the Faculty of Science and Technology.

Bachelor studies at the Faculty of Science and Technology.

Master studies at the Faculty of Science and Technology.

Emneevaluering

Use evaluation forms and/or conversation for students' evaluation of the course and teaching, according to current guidelines

Litteratur

Text book: Adams & Essex: Calculus. (Pearson). Detailed description of syllabus will be given at the semester start.

Erwin Kreyszig, Advanced Engineering Mathematics. Last edition.

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