Syllabus-MA1434-Complex Analysis and Transforms
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This document provides a course syllabus for Complex Analysis and Transforms, a 7.5 ECTS credit course offered at Blekinge Institute of Technology. The syllabus outlines the course objectives, content, structure, and assessment. Students will learn complex analysis, residue calculus, and transforms including Fourier, Laplace, and z-transforms. They will apply these concepts to solve ordinary differential equations, Volterra integral equations, and difference equations. Assessment consists of a written examination, and the course aims to provide students with skills in mathematical problem solving and communication.
![Blekinge Institute of Technology
Department of Mathematics and Natural Science
COURSE SYLLABUS
Komplex analys och transformer
Complex Analysis and Transforms
7,5 ECTS credit points (7,5 högskolepoäng)
Course code: MA1434
Educational level: Basic level
Course level: G1F
Field of education: Natural sciences
Subject group: Mathematics
Subject area: Mathematics
Version: 2
Applies from: 2013-07-01
Approved: 2013-04-30
Replaces course syllabus approved: 2008-10-24
1 Course title and credit points
The course is titled Complex Analysis and
Transforms/Komplex analys och transformer and
awards 7,5 ECTS credits. One credit point
(högskolepoäng) corresponds to one credit point in
the European Credit Transfer System (ECTS).
2 Decision and approval
This course is established by Department of
Mathematics and Science 2013-04-30. The course
syllabus was revised by School of Engineering and
applies from 2013-07-01.
Dnr: BTH 4.1.1-0326-2013.
Replaces MA1305.
3 Objectives
The course yields knowledge in analytic functions
and residue calculus in order to teach the Fourier,
Laplace and z-transforms. These constitute the
background of applications to telecommunications,
signal processes and other technical fields.
4 Content
• Complex functions, analytic functions, the
Cauchy-Riemann equations, integration along open
and close curves
• The Taylor and Laurent series, poles and residues,
the Cauchy theorems
• Calculations of the values of real integrals over the
intervals using resudues
• The Laplace, Fourier and z-transforms
• Solution of ordinary differential equations, the
Volterra integral equations and difference equations
5 Aims and learning outcomes
On completion of the course the student will be able
to:
•learn the basis of complex analysis and residue
calculus.
•evaluate the values of generalized integrals of the
Laplace and Fourier type by means of residue
page 1
calculus.
•learn the Laplace, Fourier and z-transforms.
•use the transforms and the residue calculus to
solutions of ordinary differential equations and
difference equations.
•analyze and synthesize hypotheses to determine
correct methods of solutions.
6 Generic skills
The following generic skills are trained in the
course:
• Skills in searching of the mathematical apparatus
that has been learnt to select solution models fitted
to the posed questions
• Skills in working in interdisciplinary teams
• Skills in expressing problems in English
7 Learning and teaching
The teaching comprises lectures and exercises.
The teaching language is English.
8 Assessment and grading
Examination of the course
-------------------------------------------------
Code Module Credit Grade
-------------------------------------------------
1310 Written examination[1] 7.5 ECTS A-F
-------------------------------------------------
1 The final grade is the same as the examination
mark.
The course will be graded A Excellent, B Very good,
C Good, D Satisfactory, E Sufficient, FX Insufficient,
supplementation required, F Fail.If grade Fx are
given, the student may after consultation with the
course coordinator / examiner get an opportunity to
within 6 weeks complement to grade E for the
specific course element.
9 Course evaluation
The course coordinator is responsible for
systematically gathering feedback from the students
in course evaluations and making sure that the](https://image.slidesharecdn.com/e4f274af-bf96-4ab9-8240-3024a8703b83-160911224916/85/Syllabus-MA1434-Complex-Analysis-and-Transforms-1-320.jpg)
Syllabus-MA1434-Complex Analysis and Transforms
- 1. Blekinge Institute of Technology Department of Mathematics and Natural Science COURSE SYLLABUS Komplex analys och transformer Complex Analysis and Transforms 7,5 ECTS credit points (7,5 högskolepoäng) Course code: MA1434 Educational level: Basic level Course level: G1F Field of education: Natural sciences Subject group: Mathematics Subject area: Mathematics Version: 2 Applies from: 2013-07-01 Approved: 2013-04-30 Replaces course syllabus approved: 2008-10-24 1 Course title and credit points The course is titled Complex Analysis and Transforms/Komplex analys och transformer and awards 7,5 ECTS credits. One credit point (högskolepoäng) corresponds to one credit point in the European Credit Transfer System (ECTS). 2 Decision and approval This course is established by Department of Mathematics and Science 2013-04-30. The course syllabus was revised by School of Engineering and applies from 2013-07-01. Dnr: BTH 4.1.1-0326-2013. Replaces MA1305. 3 Objectives The course yields knowledge in analytic functions and residue calculus in order to teach the Fourier, Laplace and z-transforms. These constitute the background of applications to telecommunications, signal processes and other technical fields. 4 Content • Complex functions, analytic functions, the Cauchy-Riemann equations, integration along open and close curves • The Taylor and Laurent series, poles and residues, the Cauchy theorems • Calculations of the values of real integrals over the intervals using resudues • The Laplace, Fourier and z-transforms • Solution of ordinary differential equations, the Volterra integral equations and difference equations 5 Aims and learning outcomes On completion of the course the student will be able to: •learn the basis of complex analysis and residue calculus. •evaluate the values of generalized integrals of the Laplace and Fourier type by means of residue page 1 calculus. •learn the Laplace, Fourier and z-transforms. •use the transforms and the residue calculus to solutions of ordinary differential equations and difference equations. •analyze and synthesize hypotheses to determine correct methods of solutions. 6 Generic skills The following generic skills are trained in the course: • Skills in searching of the mathematical apparatus that has been learnt to select solution models fitted to the posed questions • Skills in working in interdisciplinary teams • Skills in expressing problems in English 7 Learning and teaching The teaching comprises lectures and exercises. The teaching language is English. 8 Assessment and grading Examination of the course ------------------------------------------------- Code Module Credit Grade ------------------------------------------------- 1310 Written examination[1] 7.5 ECTS A-F ------------------------------------------------- 1 The final grade is the same as the examination mark. The course will be graded A Excellent, B Very good, C Good, D Satisfactory, E Sufficient, FX Insufficient, supplementation required, F Fail.If grade Fx are given, the student may after consultation with the course coordinator / examiner get an opportunity to within 6 weeks complement to grade E for the specific course element. 9 Course evaluation The course coordinator is responsible for systematically gathering feedback from the students in course evaluations and making sure that the
- 2. results of these feed back into the development of the course. 10 Prerequisites 15 credits in MA1102 Calculus and 7,5 credits in MA1109 Mathematics, second course. 11 Field of education and subject area The course is part of the field of education and is included in the subject area Mathematics. 12 Restrictions regarding degree The course cannot form part of a degree with another course, the content of which completely or partly corresponds with the contents of this course. 13 Additional information The course is included in programmes at Blekinge Institute of Technology and is also available as a separate course. 14 Course literature and other teaching material The lecturer’s own material (the home page of the course). s page 2