Course
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 2020-2021. Please note that changes may occur.
Semesters
Facts
Course code
MAT210
Credits (ECTS)
10
Semester tution start
Spring
Language of instruction
English, Norwegian
Number of semesters
1
Exam semester
Spring
Time table
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 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.
Required prerequisite knowledge
None
Recommended prerequisites
Mathematical Methods 1 (MAT100)
MAT100 1 Mathematical Methods 1
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 | — | — | — |
Coursework requirements
2 compulsory assignments
Course teacher(s)
Head of Department:
Bjørn Henrik AuestadHead of Department:
Bjørn Henrik AuestadCourse coordinator:
Tyson RitterMethod of work
6 hours lectures and exercises per week
Overlapping courses
| Course | Reduction (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 |
Open for
Admission to Single Courses at the Faculty of Science and Technology
City and Regional Planning - Master of Science Degree Programme, Five Years
Industrial Economics - Master of Science Degree Programme, Five Year
Industrial Automation and Signal Processing - Master's Degree Programme - 5 year
Structural and Mechanical Engineering - Master of Science Degree Programme. Five Years
Advanced teacher education for level 8-13 in science
Mathematics and Physics - Five Year Integrated Master's Degree Programme
Petroleum Engineering - Master of Science Degree Programme, Five Years
Exchange programme at Faculty of Science and Technology
Mathematics - One-Year Programme
Science and Technology - one-year programme
Course assessment
Use evaluation forms and/or conversation for students' evaluation of the course and teaching, according to current guidelines
Literature
Book
Calculus : a complete course Adams, Robert A., Essex, Christopher, Don Mills, Ont., Pearson, XIX, 1060, A-85 s., cop. 2018, isbn:9780134154367,
Book
Advanced engineering mathematics Kreyszig, Erwin, Norminton, E.J.; Kreyszig, Herbert, Hoboken, N.J., Wiley, XV, 1001, 97, 27 s., cop. 2011, isbn:9780470646137,
The course description is retrieved from FS (Felles studentsystem). Version 1