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Mathematical Analysis (MAT310)

The course covers fundamentals of mathematical analysis with focus on complex analysis.


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

Facts
Course code

MAT310

Version

1

Credits (ECTS)

10

Semester tution start

Autumn

Number of semesters

1

Exam semester

Autumn

Language of instruction

English

Content
Elements of mathematical logic, basic topological notions, analytic and harmonic functions of a complex variable, Cauchy-Riemann conditions, Cauchy's integral theorem and integral formulas, Taylor and Laurent series representations, classification of isolated singularities and residue theory.
Learning outcome
Upon completing this course students should be able to:
  • Clearly understand what is meant by a mathematical proof, and how to communicate mathematical arguments clearly in the form of a mathematical proof.
  • Understand basic topological notions (closed, open, connected and compact sets, convergence, continuity).
  • Get operational knowledge of analytic and harmonic functions, including maximum principle and integral representations.
  • Determine Taylor and Laurent series of elementary analytic functions, find their zero points and singularities, and get knowledge of residue theory and its applications. 
Required prerequisite knowledge
MAT100 Mathematical Methods 1
Recommended prerequisites
MAT200 Mathematical Methods 2, MAT210 Real and Complex Calculus, MAT300 Vector Analysis
Exam
Form of assessment Weight Duration Marks Aid
Written exam 1/1 4 Hours Letter grades No printed or written materials are allowed. Approved basic calculator allowed

Course teacher(s)
Course coordinator: Alexander Rashkovskii
Head of Department: Bjørn Henrik Auestad
Method of work
6 hours lectures/problem solving per week.
Overlapping courses
Course Reduction (SP)
Mathematical Analysis (BMA100_1) 5
Mathematics 5 - Complex analysis (ÅMA310_1) 5
Open for
Mathematics and Physics, Bachelor's Degree Programme Admission to Single Courses at the Faculty of Science and Technology Mathematics and Physics, Five Year Integrated Master's Degree Programme Exchange programme at Faculty of Science and Technology
Course assessment
Questionary and/or discussion.
Literature
The syllabus can be found in Leganto