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MAT310_1

Mathematical Analysis

This is the study programme for 2020/2021.


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

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, argument 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.

Contents

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.

Required prerequisite knowledge

MAT100 Mathematical Methods 1
MAT100 Matematiske metoder 1

Recommended previous knowledge

MAT200 Mathematical Methods 2, MAT210 Real and Complex Calculus, MAT300 Vector Analysis
MAT210 Real and Complex Calculus or MAT200 Mathematical methods 2MAT300 Vector Analysis

Exam

Weight Duration Marks Aid
Written exam1/14 hoursA - FNo 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

5-6 hours lectures/problem solving per week.

Overlapping courses

Course Reduction (SP)
Mathematical Analysis (BMA100_1) 5
Mathematics 5 - Complex analysis (ÅMA310_1) 5

Open to

Mathematics and Physics - Bachelor's Degree Programme
Admission to Single Courses at the Faculty of Science and Technology
Mathematics and Physics, 5-year integrated Master's Programme

Course assessment

Questionary and/or discussion.

Literature


Link to reading list


This is the study programme for 2020/2021.

Sist oppdatert: 22.09.2020

History