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# Real and Complex Calculus

This is the study programme for 2020/2021.

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

### 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 of 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.

### Contents

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

None.

### Recommended previous knowledge

MAT100 Mathematical Methods 1
MAT100 1 Mathematical Methods 1

### Exam

Weight Duration Marks Aid
Written exam1/14 hoursA - FBasic calculator.
Compilation of mathematical formulae (Rottmann).

### Course teacher(s)

Course coordinator
David Duncan Mcnutt

### Method of work

6 hours lectures and exercises per week

### Overlapping courses

Course Reduction (SP)
Mathematical Methods 2b (MAT220_1) 1
Mathematical Methods 2 (ÅMA260_1) 5
Mathematical methods 2b (ÅMA270_1) 1
Mathematical methods 2c (ÅMA330_1) 5
Mathematics 5 - Complex analysis (ÅMA310_2) 5
Mathematical Methods 2 (MAT200_1) 5
Mathematics 5 - Complex analysis (ÅMA310_1) 6

### Open to

Civil Engineering - Bachelor's Degree Programme
Computer Science- Bachelor's degree programme in computer science
Control Engineering and Circuit Design, Vocational Path
Control Engineering and Circuit Design - Bachelor's Degree Programme
Chemistry and Environmental Engineering - Bachelor's Degree Programme
Mathematics and Physics - Bachelor's Degree Programme
Geosciences Engineering - Bachelor's Degree Programme
City and Regional Planning - Master's Degree Programme
Industrial economics - Master's Degree Programme - 5 year
Industrial Automation and Signal Processing - Master's Degree Programme - 5 year
Mechanical and Structural Engineering and Materials Science- Master's Degree Programme - 5 years
Mathematics and Physics, 5-year integrated Master's Programme
Petroleum Engineering - Master`s Degree programme in Petroleum Engineering, 5 years

### Course assessment

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

### Literature

Literatur will be published as soon as it has been prepared by the course coordinator/teacher

This is the study programme for 2020/2021.

Sist oppdatert: 22.09.2020