Course Details

Return to Classes
Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
4MATH208ADVANCED MATHEMATICS3+2+05515.05.2026

 
Course Details
Language of Instruction English
Level of Course Unit Bachelor's Degree
Department / Program ELECTRICAL-ELECTRONICS ENGINEERING
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course Analyzing the need for applications of advanced vector calculus and complex analysis methods to global challenges in natural and engineering sciences.
Understanding the features of applications of advanced vector calculus and complex analysis methods to engineering problems;
Evaluating how to apply the studied advanced vector calculus methods to real-life engineering problems.
Evaluating how to apply the studied complex analysis methods to real-life engineering problems.
Course Content Advanced Vector Differential Calculus: Vector and Scalar Functions and Their Fields. Vector Derivatives. Curves. Arc Length. Curvature. Torsion. Gradient of a Scalar Field and Directional Derivative. Divergence of a Vector Field. Curl of a Vector Field.
Complex Differential Calculus: Complex Numbers and Their Geometric Representation. Polar Form of Complex Numbers. Powers and Roots. Complex Derivative. Analytic Function. Cauchy-Riemann Equations. Laplace’s Equation. Exponential Function. Trigonometric and Hyperbolic Functions. Euler’s Formula. Complex Logarithm. General Power. Principal Value.
Complex Integral Calculus: Line Integral in the Complex Plane. Cauchy’s Integral Theorem. Cauchy’s Integral Formula. Derivatives of Analytic Functions.
Complex Series and Residue Integration: Complex Laurent Series. Singularities and Zeros. Infinity. Residue Integration Method. Residue Integration of Real Integrals.
Conformal Mapping: Geometry of Analytic Functions: Conformal Mapping. Linear Fractional Transformations (Möbius Transformations). Special Linear Fractional Transformations. Conformal Mapping by Other Functions.
Complex Analysis and Potential Theory: Electrostatic Fields. Use of Conformal Mapping. Modeling. Heat Problems. Fluid Flow. Poisson’s Integral Formula for Potentials. General Properties of Harmonic Functions.
Course Review: Modeling Engineering Problems with Advanced Vector and Complex Calculus.
Course Methods and Techniques
Prerequisites and co-requisities ( MATH153 or MATH154 or MATH162 )
Course Coordinator Associate Prof. Sergey Borisenok
Name of Lecturers Associate Prof.Dr. SERGEY BORISENOK
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Advanced Mathematics for Engineers and Scientists, Paul Du Chateau


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
Yarıl yılSonu Sınavı/Dönem Projesinin Başarı Notuna Katkısı 1 % 30
Quiz/Küçük Sınav 6 % 20
Proje/Çizim 1 % 20
Final examination 1 % 30
Total
9
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
F2F Dersi 13 3 39
Grup Projesi 1 20 20
Sunum 1 5 5
Kişisel Çalışma 1 40 40
Final Sınavı 1 20 20
Total Work Load   Number of ECTS Credits 5 124

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Build conceptual understanding of essential mathematical methods related to advanced vector calculus and complex analysis.
2 Solve analytically and numerically basic types of advanced vector calculus and complex analysis problems.
3 Relate mathematical methods of advanced vector calculus to aspects of basic engineering problems deduced from real life.
4 Relate mathematical methods of complex analysis to aspects of basic engineering problems deduced from real life.
5 er solutions to real-life engineering problems by applying relevant advanced vector and complex calculus computation and analysis techniques.

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Advanced Vector Differential Calculus: Vector and Scalar Functions and Their Fields. Vector Derivatives. Curves. Arc Length. Curvature. Torsion. Gradient of a Scalar Field and Directional Derivative. Divergence of a Vector Field. Curl of a Vector Field.
2 Advanced Vector Differential Calculus: Vector and Scalar Functions and Their Fields. Vector Derivatives. Curves. Arc Length. Curvature. Torsion. Gradient of a Scalar Field and Directional Derivative. Divergence of a Vector Field. Curl of a Vector Field.
3 Complex Differential Calculus: Complex Numbers and Their Geometric Representation. Polar Form of Complex Numbers. Powers and Roots. Complex Derivative. Analytic Function. Cauchy-Riemann Equations. Laplace’s Equation. Exponential Function. Trigonometric and Hyperbolic Functions. Euler’s Formula. Complex Logarithm. General Power. Principal Value.
4 Complex Differential Calculus: Complex Numbers and Their Geometric Representation. Polar Form of Complex Numbers. Powers and Roots. Complex Derivative. Analytic Function. Cauchy-Riemann Equations. Laplace’s Equation. Exponential Function. Trigonometric and Hyperbolic Functions. Euler’s Formula. Complex Logarithm. General Power. Principal Value.
5 Complex Integral Calculus: Line Integral in the Complex Plane. Cauchy’s Integral Theorem. Cauchy’s Integral Formula. Derivatives of Analytic Functions.
6 Complex Integral Calculus: Line Integral in the Complex Plane. Cauchy’s Integral Theorem. Cauchy’s Integral Formula. Derivatives of Analytic Functions.
7 Complex Series and Residue Integration: Complex Laurent Series. Singularities and Zeros. Infinity. Residue Integration Method. Residue Integration of Real Integrals.
8 Complex Series and Residue Integration: Complex Laurent Series. Singularities and Zeros. Infinity. Residue Integration Method. Residue Integration of Real Integrals.
9 Conformal Mapping: Geometry of Analytic Functions: Conformal Mapping. Linear Fractional Transformations (Möbius Transformations). Special Linear Fractional Transformations. Conformal Mapping by Other Functions
10 Conformal Mapping: Geometry of Analytic Functions: Conformal Mapping. Linear Fractional Transformations (Möbius Transformations). Special Linear Fractional Transformations. Conformal Mapping by Other Functions
11 Complex Analysis and Potential Theory: Electrostatic Fields. Use of Conformal Mapping. Modeling. Heat Problems. Fluid Flow. Poisson’s Integral Formula for Potentials. General Properties of Harmonic Functions.
12 Complex Analysis and Potential Theory: Electrostatic Fields. Use of Conformal Mapping. Modeling. Heat Problems. Fluid Flow. Poisson’s Integral Formula for Potentials. General Properties of Harmonic Functions.
13 Course Review: Modeling Engineering Problems with Advanced Vector and Complex Calculus.
14 Course Review: Modeling Engineering Problems with Advanced Vector and Complex Calculus.

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12
C1 1 4 1 2 1 1 1 1 1 1 1 1
C2 1 4 1 2 2 1 1 2 1 2 1 1
C3 1 4 1 2 2 1 1 2 1 2 1 1
C4 3 5 2 3 3 1 1 4 1 3 5 1
C5 3 5 2 5 5 3 2 5 2 3 5 1

  Contribution: 1: Very Slight 2:Slight 3:Moderate 4:Significant 5:Very Significant

  
  https://sis.agu.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=78988&lang=en
Return to Classes