Complex Analysis
Description: The discipline contains the theory of functions of a complex variable and a number of applications of this theory (to electrostatics, hydrodynamics, etc.), as well as elements of operational calculus and its applications to the integration of ordinary linear differential equations with constant coefficients and some other types of equations
Amount of credits: 5
Course Workload:
| Types of classes | hours |
|---|---|
| Lectures | 15 |
| Practical works | 30 |
| Laboratory works | |
| SAWTG (Student Autonomous Work under Teacher Guidance) | 30 |
| SAW (Student autonomous work) | 75 |
| Form of final control | Exam |
| Final assessment method | Тest |
Component: Component by selection
Cycle: Base disciplines
Goal
- The purpose of teaching the discipline "Complex Analysis" is to present the basic concepts of the theory of the function of a complex variable and methods of operational calculus, as well as to introduce the mathematical apparatus of the theory of function, which are the basic component for mastering disciplines using mathematical models in the field of engineering and technology, the formation of students' theoretical knowledge and practical skills in the application of mathematical methods in the formulation and solution of applied problems.
Objective
- The student must acquire knowledge of the basic concepts of the discipline, understanding and ability to prove the theory and derivations of the basic formulas, learn the methods of operational calculus, skills in solving practical problems using the mathematical apparatus of the theory of the function of a complex variable.
Learning outcome: knowledge and understanding
- Knows formulas and properties, symbols of the basic concepts of complex analysis, the theory of operational calculus, as well as methods for solving applied problems of technological processes using methods of operational calculus.
Learning outcome: applying knowledge and understanding
- The knowledge gained in the study of the discipline "Integrated Analysis" is successfully applied in solving applied problems, in compiling mathematical models of various problems and in comparative data analysis.
Learning outcome: formation of judgments
- Knows formulas and properties, symbols of the basic concepts of complex analysis, the theory of operational calculus, as well as methods for solving applied problems of technological processes using methods of operational calculus.
Learning outcome: communicative abilities
- Able to solve problems in the field of technology in a team by mathematical methods, to correctly defend his point of view, to propose new solutions. Able to carry out a systematic collection of scientific and technical information, analysis of domestic and foreign experience in mathematics for research.
Learning outcome: learning skills or learning abilities
- Able to correctly present knowledge in mathematical form using elements of the theory of complex analysis, operational calculus.
Teaching methods
Information and communication technology;
Technology for the development of critical thinking;
Integrated learning technology;
Technologies of level differentiation;
Traditional technologies (lectures, practical classes)
Assessment of the student's knowledge
Teacher oversees various tasks related to ongoing assessment and determines students' current performance twice during each academic period. Ratings 1 and 2 are formulated based on the outcomes of this ongoing assessment. The student's learning achievements are assessed using a 100-point scale, and the final grades P1 and P2 are calculated as the average of their ongoing performance evaluations. The teacher evaluates the student's work throughout the academic period in alignment with the assignment submission schedule for the discipline. The assessment system may incorporate a mix of written and oral, group and individual formats.
| Period | Type of task | Total |
|---|---|---|
| 1 rating | individual homework 1 | 0-100 |
| Independent work 1 | ||
| individual homework 2 | ||
| Test 1 | ||
| 2 rating | individual homework 3 | 0-100 |
| Independent work 2 | ||
| individual homework 4 | ||
| Test 2 | ||
| Total control | Exam | 0-100 |
The evaluating policy of learning outcomes by work type
| Type of task | 90-100 | 70-89 | 50-69 | 0-49 |
|---|---|---|---|---|
| Excellent | Good | Satisfactory | Unsatisfactory |
Evaluation form
The student's final grade in the course is calculated on a 100 point grading scale, it includes:
- 40% of the examination result;
- 60% of current control result.
The final grade is calculated by the formula:
| FG = 0,6 | MT1+MT2 | +0,4E |
| 2 |
Where Midterm 1, Midterm 2are digital equivalents of the grades of Midterm 1 and 2;
E is a digital equivalent of the exam grade.
Final alphabetical grade and its equivalent in points:
The letter grading system for students' academic achievements, corresponding to the numerical equivalent on a four-point scale:
| Alphabetical grade | Numerical value | Points (%) | Traditional grade |
|---|---|---|---|
| A | 4.0 | 95-100 | Excellent |
| A- | 3.67 | 90-94 | |
| B+ | 3.33 | 85-89 | Good |
| B | 3.0 | 80-84 | |
| B- | 2.67 | 75-79 | |
| C+ | 2.33 | 70-74 | |
| C | 2.0 | 65-69 | Satisfactory |
| C- | 1.67 | 60-64 | |
| D+ | 1.33 | 55-59 | |
| D | 1.0 | 50-54 | |
| FX | 0.5 | 25-49 | Unsatisfactory |
| F | 0 | 0-24 |
Topics of lectures
- Complex numbers and operations on them
- Functions of a complex variable
- Basic elementary functions of a complex variable
- Differentiation of functions of a complex variable
- Integration of functions of a complex variable
- Series in the complex domain
- Function nulls
- Function residues
- Application of residues to the calculation of definite integrals
- Operational calculus
- Properties of the Laplace transform
- Inverse Laplace transform
- Operational method for solving linear differential equations and their systems
Key reading
- Краснов М.Л. и др. Функции комплексного переменного. Операционное исчисление. Теория устойчивости. – М.: Наука, 2013.
- Бейсебай П.Б. Комплекс айнымалы функциялар теориясы және операциялық есептеулер ШҚМТУ: 2011.
- Айдос Е.Ж., Боровский Ю.В. Теория функций комплексного переменного и операционное исчисление. - Алматы: КазНТУ, 2013г.
- Мухамедова Р.О., Тыныбекова С.Д. Специальные разделы математики. - У-Ка.: ВКГТУ, 2011 г.
- Белослюдова В.В., Дронсейка И.П. Специальные разделы математики. Электронное учебное пособие. – Усть-Каменогорск: ВКГТУ, 2011.
Further reading
- Жантасов Т.Ғ. Комплекс аргументті функциялар теориясы және операциялық есептеулер. ШҚМТУ: 2001.
- Чудесенко В.Ф. Сборник задач по специальным курсам высшей математики (типовые расчеты). - М.: «Высшая школа», 2013г.
- Эйдерман В.Я. Основы теории функций комплексного переменного и операционного исчисления. – М.: Физматлит, 2002.
