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# Mathematical Analysis

This is the study programme for 2019/2020. It is subject to change.

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 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
Course teacher
Pavel Gumenyuk

### 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

Bachelor studies at the Faculty of Science and Technology. Master studies at the Faculty of Science and Technology

### Course assessment

Questionary and/or discussion.

### Literature

1. Frank Morgan, Real Analysis and Applications, American Mathematical Society, 2005.
2. E.B.Saff and A.D.Snider, Fundamentals of Complex Analysis. Engineering, Science, and Mathematics, Third Edition, Pearson, 2014.
OR
E.B.Saff and A.D.Snider, Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, Third Edition, Pearson, 2003.
(The former is a reprint of the latter with some insignificant omissions.)

This is the study programme for 2019/2020. It is subject to change.

Sist oppdatert: 13.11.2019