Course Name Code Semester T+U Hours Credit ECTS
Analytical Methods I MEK 503 0 3 + 0 3 6
 Precondition Courses Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Compulsory Course Coordinator Doç.Dr. ERGÜN NART Course Lecturers Course Assistants Course Category Available Basic Education in the Field 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 The solution methods in mathematical modeling of continuous and discrete systems in engineering are given. The solution of Bessel differential equation and Sturm-Liouville problems in continuous systems are lectured.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 Students can classify physical systems and problems Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
2 They know generalized mathematical models Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
3 Students turn discrete systems into discrete eigenvalue problems and solve Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
4 They solve differential equation and differential equation systems Lecture, Question-Answer, Discussion, Drilland Practice, Testing, Homework,
5 Students select suitable series and solve differential equations Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
6 They know how to solve Laplace and Bessel differential equations
7 Students know Gamma function and its properties
8 They turn continuous systems into eigenvalue problems
9 Student recognize Sturm-Liouville problem for second order systems and test whether the system is self-adjoint
10 They make eigenvalues and eigenfunction orthogonalzed
11 Students know Nonself-adjoint boundary conditions
12 They know approximate solution techniques for nonself-adjoint eigenvalue problems
Week Course Topics Preliminary Preparation
1 Classification of physical systems and problems
2 Generalized mathematical models
3 Discrete eigenvalue problems, properties of eigenvalues & eigenvectors, zero and repeated eigenvalues, iterative methods
4 Linear System of ODEs, characteristic eq. , variation of parameters, non-homog. eqs., nonlinear eqs. examples
5 Method of Frobenius, Fuchs theorem: series expansion around singular points
6 Laplaces eq. in cylindrical coordinates: Solution of Bessels eq., properties of Gamma function, Bessel function of 1st and 2nd kind, modified Bessel functions, applications
7 Eigenvalue problems for continuous systems, eigenvalues, eigenfunctions & the solution of initial-boundary problems
8 Sturm-Liouville problem for second order systems, general self-adjoint systems, self-adjoint B.C.
9 Properties of eigenvalues and eigenfunction, orthogonalization of eigenfunctions
10 Midterm exam
11 Applications : nonsymetric vibration of circular membrane
12 Non-selfadjoint boundary conditions: self-adjoint systems in generalized sense, orthogonality condition, example: vibrating elastic bar with a concentrated mass
13 Sturm-Liouville problem for 4th order systems
14 Approximate solution of self-adjoint and nonself-adjoint eigenvalue problems, weighted residual techniques.
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 X
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. X
6 Ability to consolidate engineering problems, develop proper method(s) to solve and apply the innovative solutions to them X
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 X
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 40
2. Kısa Sınav 15
3. Kısa Sınav 15
4. Ödev 30
Total 100
1. Yıl İçinin Başarıya 40
1. Final 60
Total 100