Course Name Code Semester T+U Hours Credit ECTS
Analytic Methods II MEK 602 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Doç.Dr. ERGÜN NART
Course Lecturers
Course Assistants
Course Category
Course Objective The main aim is to teach students the theory of Advanced Analytical Methods and have them solve various examples from Mechanical engineering
Course Content It contains analytical solution methods in engineering mathematics. It starts with variational calculus, continue with complex functions, and finishes with Hilbert transformations.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 Students know the main idea of variational calculus Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
2 They apply variational calculus in mechanical problems Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
3 Student know definitions, introduction, multivalued functions of complex variables Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
4 They take derivatives of complex variable functions and test Cauchy-Riemann conditions Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
5 Students find Laurent series for functions Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
6 They calculate infinite integrals Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
7 Students know partial differential equations and the solution techniques, and apply boundary conditions Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
8 They know integral transformations Problem Solving, Lecture, Question-Answer, Discussion, Drilland Practice, Testing, Homework,
9 Students apply Laplace transformation to engineering problems Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
10 They apply Mellin transformation to engineering problems Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
11 Students apply Henkel transformation to engineering problems Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
12 They apply Hilbert transformation to engineering problems Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Variational Calculus
2 Complex Variables : Definitions, introduction, multivalued functions
3 Derivatives, Analytic Functions, Cauchy-Riemann Conditions
4 Laurent series, Residues, simple and multiple poles, examples : contour integrals, evaluation of some real definite integrals
5 Infinite integrals, examples : Fourier integrals, branch cuts
6 Partial Differential Equations ( unbounded domain )
7 Characteristic equation, example : the wave equations, continuous eigenvalues : Fourier series to Fourier integrals
8 Integral Transforms
9 Initial Value Problems Laplace Transform
10 Midterm exam
11 Boundary Value Problems in Polar Coord. Mellin Transforms
12 Integral Equations
13 Boundary Value Problems in cylindrical coord. Hankel Transform
14 Hibert Transforms
Resources
Course Notes F.B. Hildebrand, Advanced Calculus for Applications 2nd Edition, Prentice-Hall, Inc.<br>F.B. Hildebrand, Methods of Applied Mathematics, Dover Publications, Inc.
Course Resources C.R. Wylie, L.C. Barrett, Advanced Engineering Mathematics, McGraw-Hill Book Company
Order Program Outcomes Level of Contribution
1 2 3 4 5
1 Ability to access wide and deep information with scientific researches in the field of Engineering, evaluate, interpret and implement the knowledge gained in his/her field of study
2 Develop new strategic approach and produce solutions by taking responsibility in unexpected and complicated situations in mechatronic engineering
3 Aware of social, scientific and ethical values guarding adequacy at all professional activities and at the stage of data collection, interpretation, and announcement
4 Develop and use data processing and communication technologies together with the machine, electronic and computer software-hardware knowledge required by the field of mechatronic engineering expertise
5 Ability to complete and implement &quot;limited or incomplete data&quot; by using the scientific methods.
6 Ability to consolidate engineering problems, develop proper method(s) to solve and apply the innovative solutions to them
7 Ability to develop new and original ideas and method(s), to develop new innovative solutions at design of system, component or process
8 Ability to design and apply analytical, modeling and experimental based research, analyze and interpret the faced complex issues during the design and apply process
9 Gain high level ability to define the required information and data
10 Aware of new and developing application of profession and ability to analyze and study on those applications
11 Ability to interpret engineering applications social and environmental dimensions and it´s compliance with the social environment
12 At least be capable of oral and written communication in a foreign language
13 Ability to work in multi-disciplinary teams and to take responsibility to define approaches for complex situations
14 Systematic and clear verbal or written transfer of the process and results of studies at national and international environments
15 Gain comprehensive information on modern techniques, methods and their borders which are being applied to engineering
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 45
1. Kısa Sınav 15
1. Ödev 2
1. Proje / Tasarım 10
2. Kısa Sınav 15
2. Ödev 2
3. Ödev 2
4. Ödev 2
5. Ödev 2
6. Ödev 2
7. Ödev 3
Total 100
1. Yıl İçinin Başarıya 40
1. Final 60
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 4 4
Quiz 2 5 10
Assignment 7 5 35
Project / Design 1 5 5
Final examination 1 10 10
Total Workload 160
Total Workload / 25 (Hours) 6.4
dersAKTSKredisi 6