Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
2EEE585ASYMPTOTIC TEC.3+0+03619.06.2026

 
Course Details
Language of Instruction English
Level of Course Unit Master's Degree
Department / Program ELECTRICAL AND ELECTRONICS ENGINEERING
Type of Program Formal Education
Type of Course Unit Elective
Course Delivery Method Face To Face
Objectives of the Course The objective of this course is to provide graduate students with a comprehensive introduction to asymptotic analysis methods and to enable their effective application in differential equations, integral transforms, and applied mathematics problems. Students will be able to define asymptotic sequences, expansions, and series; apply integral asymptotics techniques such as Laplace's method, the method of stationary phase, and the method of steepest descents; solve differential equations with large parameters using the WKB method; and gain analytical competency in asymptotic approximation for engineering problems.
Course Content Definitions of asymptotic sequences, expansions and series. Laplace's method for integrals; Watson's Lemma. Method of stationary phase and method of steepest descents. Transform integrals and their asymptotic evaluation. Singularities and asymptotic methods of differential equations. Differential equations with a large parameter (WKB method).
Course Methods and Techniques The course is primarily lecture-based, complemented by question-and-answer sessions and discussion techniques based on mathematical proofs and derivations. Topics are reinforced through example applications drawn from engineering and physics problems. Problem-solving exercises and in-class discussions are employed to develop students' analytical thinking and mathematical modelling competencies.
Prerequisites and co-requisities None
Course Coordinator Prof.Dr. AHMET METE VURAL https://eee.gantep.edu.tr/pages.php?url=akademik-personel-2 mvural@gantep.edu.tr
Name of Lecturers None
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Bender, C.M., Orszag, S.A. (1999). Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory. Springer.
Ablowitz, M.J., Fokas, A.S. (2003). Complex Variables: Introduction and Applications, 2nd Ed. Cambridge University Press.
Course Notes Weekly slide presentations and solved example problems prepared by the course instructor will be shared via the Learning Management System (LMS). In addition, selected academic papers and technical notes related to the topics will be provided as supplementary material.
Assignments dersin hocası tarafından ödevler verilebilmektedir.
Exams sınavlar klasik formatında yapılmaktadır.

Course Category
Mathematics and Basic Sciences %100
Engineering %10
Engineering Design %0
Social Sciences %0
Education %0
Science %0
Health %0
Field %10

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Mid-terms 2 % 60
Final examination 1 % 40
Total
3
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly lecture hours 14 3 42
Reading Activities 14 3 42
Internet browsing, library work 7 2 14
Midterm and midterm exam preparation 2 20 40
Final exam and preparation for the final exam 1 30 30
Total Work Load   Number of ECTS Credits 6 168

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
5 Identifies singularities of differential equations and applies asymptotic methods to them.
6 Applies the WKB method to the solution of differential equations with a large parameter
Bilgi 
1 Explains the fundamental concepts and definitions of asymptotic sequences, expansions, and series.
Beceri 
2 Applies Laplace's method and Watson's Lemma to the asymptotic evaluation of integrals.
3 Applies the method of stationary phase and the method of steepest descents to appropriate integral problems.
4 Evaluates transform integrals and performs their asymptotic assessment.

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Introduction to Asymptotic Analysis definitions of asymptotic sequences, expansions and series, and fundamental concepts Reading the relevant topic from the course materials course materials
2 Properties of asymptotic expansions Poincaré definition, asymptotic equivalence, sum and product rules Reading the relevant topic from the course materials course materials
3 Laplace`s Method for Integrals: fundamental theory and applications Reading the relevant topic from the course materials course materials
4 Watson`s Lemma and asymptotics of Laplace transforms Reading the relevant topic from the course materials course materials
5 Method of Stationary Phase: oscillatory integrals and applications Reading the relevant topic from the course materials course materials
6 Method of Steepest Descents: saddle point analysis and asymptotics in the complex plane Reading the relevant topic from the course materials course materials
7 Transform Integrals and their asymptotic evaluation: Fourier and Laplace transforms Reading the relevant topic from the course materials course materials
8 Singular Points in Differential Equations: regular and irregular singular points Reading the relevant topic from the course materials course materials
9 Asymptotic expansions at singular points Frobenius method and its generalizations Reading the relevant topic from the course materials course materials
10 Differential Equations with a Large Parameter: WKB method – fundamental theory Reading the relevant topic from the course materials course materials
11 Differential Equations with a Large Parameter: WKB method – fundamental theory Reading the relevant topic from the course materials course materials
12 WKB method – connection formulas and the Stokes phenomenon Reading the relevant topic from the course materials course materials
13 Applications of the WKB method to quantum mechanics and wave propagation problems Reading the relevant topic from the course materials course materials
14 Applications of asymptotic methods to engineering problems course review Reading the relevant topic from the course materials course materials

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4
All 4 5 2
C5 4 4 2
C6 4 5 2
In1 3 5 2
Sk2 4 5 2
Sk3 5 5 2
Sk4 4 5 2

  bbb

  
  https://obs.gantep.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=147961&lang=en