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# Real and Complex Calculus

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

Introduction to function theory in one complex and several real variables, including convergence/divergence of series, both real and complex.

### 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 for 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.

### Contents

Functions of several variables, complex numbers and functions, analytic functions; series, Taylor series, Fourier series.

None.

### Recommended previous knowledge

MAT100 Mathematical Methods 1
MAT100 1 Mathematical Methods 1

### Exam

Weight Duration Marks Aid
Written exam1/14 hoursA - FBasic calculator.
Compilation of mathematical formulae (Rottmann).

### Course teacher(s)

Course teacher
Course coordinator
Alexander Rashkovskii

### Method of work

6 hours lectures and exercises per week

### Overlapping courses

Course Reduction (SP)
Mathematical Methods 2b (MAT220_1) 1
Mathematical Methods 2 (ÅMA260_1) 5
Mathematical methods 2b (ÅMA270_1) 1
Mathematical methods 2c (ÅMA330_1) 5
Mathematics 5 - Complex analysis (ÅMA310_2) 5
Mathematical Methods 2 (MAT200_1) 5
Mathematics 5 - Complex analysis (ÅMA310_1) 6

### Open to

Mathematics - One Year Foundation Programme at the Faculty of Science and Technology.

Bachelor studies at the Faculty of Science and Technology.

Master studies at the Faculty of Science and Technology.

### Course assessment

Use evaluation forms and/or conversation for students' evaluation of the course and teaching, according to current guidelines

### Literature

Text book: Adams & Essex: Calculus. (Pearson).
Erwin Kreyszig, Advanced Engineering Mathematics. Last edition.
Detailed description of syllabus will be given at the semester start.

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

Sist oppdatert: 13.11.2019