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 2015-2016. Merk at det kan komme endringer.
Semesters
Fakta
Emnekode
MAT210
Vekting (stp)
10
Semester undervisningsstart
Spring
Undervisningsspråk
English, Norwegian
Antall semestre
1
Vurderingssemester
Spring
Timeplan
Content
Functions of several variables, complex numbers and functions, analytic functions, series, Taylor series, Laurent and 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 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 and Laurent 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 |
|---|---|---|---|---|---|---|---|
| 1/1 | 4 Hours | Letter grades | Compilation of mathematical formulae (Rottmann), Specified printed and hand-written means are allowed. Definite, basic calculator allowed | — | — | — |
Definite, basic calculator allowed.
Fagperson(er)
Head of Department:
Bjørn Henrik AuestadHead of Department:
Bjørn Henrik AuestadCourse coordinator:
Tyson RitterMethod 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.
The course description is retrieved from FS (Felles studentsystem). Version 1