       
Programme 
Graduate School of Natural and Applied Sciences Manufacturing Engineering 
Course Information 
Course Unit Code  Course Unit Title   Credit Pratic  Credit Lab/A  Credit Total  Credit Ects  Semester 
01IMM5142  Analytical Methods in Engineering  3.00  0.00  0.00  3.00  6.00  1 
Course Information 
Language of Instruction  Turkish 
Type of Course Unit  Elective 
Course Coordinator  Associate Professor Dr. M.Reşit USAL 
Course Instructors  3Mustafa Reşit Usal 
Course Assistants  
Course Aims  The aim of this course is to learn vector and tensor analysis in details. 
Course Goals  1) To give information about analytical methods in engineering 2) To teach applications of vector and tensor analysis in engineering 3) To teach concepts of tensor analysis in curvilinear coordinates 
Learning Outcomes of The Course Unit  1) To recognize analytical methods which can be used extensively in engineering 2) To learn using index notation 3) To achieve implementation of differential operators to scalar, vectorial and tansorial functions 4) To achieve implementation of integral theorems for vector analysis to a region containing discontinuity surfaces 5) To understand of invariant concept 6) Concept of integrity basis for vectors and second degree tensors 7)To achieve systematically formulation of physical laws by using curvilinear coordinates and tensor calculus 
Course Contents  To achieve basic vector and tensor operation by using Einstein summation convention. To define interconnections for reciprocal base vectors by using Euclidean metric tensor. To learn differentiation and integral theorems for vector functions. To recognize invariant parameters in according to fundamental rules of matrix algebra. Using the tensor analysis in the curvilinear coordinates. Concept of covariant and contravariant partial derivative. To express basic differential opeartors in orthogonal curvilinear coordinates. The RiemannChristoffel tensor as a measure of the curvature of the space. 
Prerequisities and Corequisities Courses  
Recommended Optional Programme Components  
Mode Of Delivery  
Level of Course Unit  
Assessment Methods and Criteria  ECTS / Table Of Workload (Number of ECTS credits allocated) 
Studies During Halfterm  Number  CoEfficient  Activity  Number  Duration  Total 
Visa  1  40  Course Duration (Excluding Exam Week)  14  3  42 
Quiz  1  10  Time Of Studying Out Of Class  14  5  70 
Homework  7  40  Homeworks  7  5  35 
Attendance  1  10  Presentation  0  0  0 
Application  0  0  Project  0  0  0 
Lab  0  0  Lab Study  0  0  0 
Project  0  0  Field Study  0  0  0 
Workshop  0  0  Visas  1  10  10 
Seminary  0  0  Finals  1  20  20 
Field study  0  0  Workload Hour (30)  30 
TOTAL  100  Total Work Charge / Hour  177 
The ratio of the term to success  40  Course's ECTS Credit  6 
The ratio of final to success  60  
TOTAL  100  
Recommended or Required Reading 
Textbook  
Additional Resources  Arfken, George B., Weber,Hans J. "Mathematical Methods for Physicists", Academic Pres, 2000.
Eringen, A. Cemal, "Mechanics of Continua", Krieger Pub Co; 2nd edition.1980.
Kay, David C., "Schaum's outline of Theory and Problems of Tensor Calculus" , McGrawHill New York .1988.
Spiegel, Murray R., "Vektörel Analiz ve Tensör Analizine Giriş". Birsen kitabevi yayınları, 1959.İstanbul.
Önem, Coşkun., "Mühendislik ve Fizikte Matematik Metodlar". Birsen Yayınevi, 1999. İstanbul.

Material Sharing 
Documents  
Assignments  
Exams  
Additional Material  
Planned Learning Activities and Teaching Methods 
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary) 
Work Placements 
As with any other educational component, credits for work placements are only awarded when the learning outcomes have been achieved and assessed. If a work placement is part of organised mobility (such as Farabi and Erasmus), the Learning Agreement for the placement should indicate the number of credits to be awarded if the expected learning outcomes are achieved. 
Program Learning Outcomes 
No  Course's Contribution to Program  Contribution 
1  An able to use informations of mathematicall, science, engineeringin solving the manufacturing engineering problems  5 