# 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.

Course description for study year 2022-2023. Please note that changes may occur.

Facts
Course code

MAT210

Version

1

Credits (ECTS)

10

Semester tution start

Spring

Number of semesters

1

Exam semester

Spring

Language of instruction

English, Norwegian

Time table
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.
• Understand the notion of residue and use it for computing contour integrals.
• Be able to find the Fourier series of a given simple function.
Content
Functions of several variables, complex numbers and functions, analytic functions; series, Taylor series, Fourier series; residues.
Required prerequisite knowledge
None
Recommended prerequisites
MAT100 Mathematical Methods 1
Exam
Course teacher(s)
Course coordinator: Alexander Ulanovskii