Course title
V01900023
Advanced Studies in Mathematical Sciences B

 ISHIWATA Tetsuya
Course description
Advanced Studies in Mathematical Sciences A,B,C and D are intensive courses. We invite professors from other universities and they give topics in applied mathematics or mathematical sciences. The topics depend on each professor.

This class will be taught in English by Professor Slawomir Michalik(Cardinal Stefan Wyszynski University, Poland), who will be staying at SIT in 2025.

This is an introductory course in complex analysis. The course is devoted to complex numbers, complex functions, complex integration as well as Taylor and Laurent series.
Purpose of class
The aim is to learn topics that are not provided by professors in our department. To increase knowledge is essential for engineers in mathematical sciences.

The purpose of this class in 2025 are as follows:
The main purpose of the course is to present the basics of complex analysis and to understand the difference between the real and complex case
Goals and objectives
  1. The students are able to present complex numbers in various form
  2. The students are able to investigate various properties of functions of a complex variable
  3. The students are able to apply the Cauchy integral theorem
  4. The students are able to expand functions in Taylor and Laurent series, and to determine their radius of convergence
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Exam Total.
1. 20% 20%
2. 40% 40%
3. 20% 20%
4. 20% 20%
Total. 100% -
Language
English
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Complex numbers and complex plane Review of basics topics in complex analysis 1330minutes
2. Functions of a complex variables and their properties N/A 0minutes
3. Basic examples of complex functions N/A 0minutes
4. Holomorphic functions and the Cauchy-Riemann equations N/A 0minutes
5. Complex integration, the Cauchy integral theorem and its applications N/A 0minutes
6. Taylor and Laurent series N/A 0minutes
7. Exam and review N/A 0minutes
8. N/A N/A 0minutes
9. N/A N/A 0minutes
10. N/A N/A 0minutes
11. N/A N/A 0minutes
12. N/A N/A 0minutes
13. N/A N/A 0minutes
14. N/A N/A 0minutes
Total. - - 1330minutes
Evaluation method and criteria
The exam is worth 100points, and a passing grade is 60points or more. The exam questions are at the same level as examples used in class
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
References: Steven G. Krantz, Handbook of Complex Variables, Birkhauser 1999
Prerequisites
Differential and Integral Calculus 1, Differential and Integral Calculus 2, Linear Algebra 1, Vector Analysis
Office hours and How to contact professors for questions
  • After class, take questions
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
N/A
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A 該当しない
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
Last modified : Thu Feb 20 04:07:21 JST 2025