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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 2021-2022

Course code




Credits (ECTS)


Semester tution start


Number of semesters


Exam semester


Language of instruction

English, Norwegian

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.
Functions of several variables, complex numbers and functions, analytic functions; series, Taylor series, Fourier series; residues.
Required prerequisite knowledge
Recommended prerequisites
MAT100 Mathematical Methods 1
MAT100 1 Mathematical Methods 1
Form of assessment Weight Duration Marks Aid
Written exam 1/1 4 Hours A - F Basic calculatorCompilation of mathematical formulae (Rottmann)

Course teacher(s)
Course coordinator: Alexander Ulanovskii
Head of Department: Bjørn Henrik Auestad
Method of work
6 hours lectures and exercises per week
Open for
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
Overlapping courses
Course Reduction (SP)
Mathematical Methods 2b (MAT220) 1
Mathematical Methods 2 (ÅMA260) 5
Mathematical methods 2b (ÅMA270) 1
Mathematical methods 2c (ÅMA330) 5
Mathematics 5 - Complex analysis (ÅMA310) 5
Mathematical Methods 2 (MAT200) 5
Mathematics 5 - Complex analysis (ÅMA310) 6
The syllabus can be found in Leganto