MMU603 - ANALYTICAL METHODS IN ENGINEERING

Course Name Code Semester Theory
(hours/week)		 Application
(hours/week)		 Credit ECTS
ANALYTICAL METHODS IN ENGINEERING MMU603 2nd Semester 3 0 3 8
PrequisitesNone
Course languageTurkish
Course typeMust 
Mode of DeliveryFace-to-Face 
Learning and teaching strategiesLecture
Discussion
Other: description, individual work,exercises  
Instructor (s)Öğr. Gör. Dr. Volkan ParlaktaÅŸ 
Course objectiveThe objective of this course is to give the students the knowledge and skills required to model physical phenomena and solve engineering problems using ordinary and partial differential equations. 
Learning outcomes
  1. Use the concepts and methods of standard ODE analysis including linearity, linear independence, homogeneity, constant coefficient and equidimensional equations, system of equations, operator notation and variation of parameters.
  2. Develop series solutions for linear second order ODE?s, using regular and singular point expansions.
  3. Identify and solve Bessel equations using Bessel functions.
  4. Develop Fourier series and Fourier integral representations of given suitable functions.
  5. Develop operational skills to use Fourier, Fourier sine and Fourier cosine transforms.
  6. Identify and solve Sturm-Liouville problems.
  7. Identify and solve parabolic PDE?s.
  8. Identify and solve hyperbolic PDE?s. / Identify and solve elliptic PDE?s.
Course ContentReview of ordinary differential equations: Series solutions; special functions (Bessel, Fourier).
/ Boundary and initial value problems (Sturm-Liouville).
/ Fourier transforms.
/ Fourier integrals. Introduction to integral equations.
/ Partial differential equations; separation of variables.
 
ReferencesS.L. Ross, Differential Equations.
M. D. Greenberg, Advanced Engineering Mathematics, Second Ed., Prentice Hall.
 

Course outline weekly

WeeksTopics
Week 1Ordinary differential equations
Week 2Homogeneous differential equations with constant coefficients
Week 3Systems of linear differential equations
Week 4Series solutions of linear differential equations
Week 5The method of Frobenious
Week 6Bessel equation and Bessel function
Week 7Midterm
Week 8Fourier series
Week 9Fourier integral
Week 10Fourier transformations
Week 11Sturm-Liouville problems
Week 12Midterm
Week 13Partial differential equations
Week 14Separation of variables
Week 15
Week 16Final Exam

Assesment methods

Course activitiesNumberPercentage
Attendance15
Laboratory00
Application00
Field activities00
Specific practical training00
Assignments515
Presentation00
Project00
Seminar00
Midterms240
Final exam140
Total100
Percentage of semester activities contributing grade succes760
Percentage of final exam contributing grade succes140
Total100

WORKLOAD AND ECTS CALCULATION

Activities Number Duration (hour) Total Work Load
Course Duration (x14) 14 3 42
Laboratory 0 0 0
Application000
Specific practical training000
Field activities000
Study Hours Out of Class (Preliminary work, reinforcement, ect)12448
Presentation / Seminar Preparation000
Project000
Homework assignment51890
Midterms (Study duration)22040
Final Exam (Study duration) 12020
Total Workload3465240

Matrix Of The Course Learning Outcomes Versus Program Outcomes

D.9. Key Learning OutcomesContrubition level*
12345
1. Has the theoretical and practical knowledge to improve and deepen the information in the different fields of the mechanical eng ineering at the level of expertize based on the undergraduate engineering outcomes.    X
2. Realizes the interaction between the interdiciplines in which the mechanical engineering applications take place.  X  
3. Uses the theoretical and practical knowledge at the levels of expertize in which he/she gains from his/her field in solving engineering problems.    X
4. Has the ability to be able to interpret and develop new information via combining his/her knowledge in which he/she becomes expert with the knowledge that comes from different diciplines.   X 
5. Has the abilitiy to be able to solve the problems in engineering applications using research methods.    X
6. Be able to perform an advanced level work in his/her field independently.    X
7. Takes the responsibility and develops new strategical approaches for solving encountered and unforeseen complicated problems in engineering applications     X
8. Be able to lead when the problems encountered are in the fields of the mechanical engineering in which he/she specialized     X
9. Evaluates the information and skills which he/she gains at the level of expertize in the specifics of mechanical engineering and adjusts his/her learnings as and when needed. X   
10. Systematically transfers the current progress in engineering field and his/her own studies to the groups in his/her field and to the groups out of his/her fields in written, oral and visual presentations supported by quantitative and qualitative data .      
11. Establishes oral and written communication skills by using one foreign language at least at the level of B1 European Language Portfolia.     
12. Uses the information and communication technologies at the advanced level with the computer softwares as required by the area of specialization and work.  X   
13. Develops strategy, policy and application plans to the problems at which engineering solutions are needed and evaluates the results within the quality processes framework. X   
14. Uses the information which he/she absorbs from his/her field, the problem solving and practical skills in interdiciplinary studies. X   

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest