SDU Education Information System
   Home   |  Login Türkçe  | English   
 
   
 
 


 
Course Information
Course Unit Title : Analytical Methods in Engineering
Course Unit Code : 01IMM5142
Type of Course Unit : Optional
Level of Course Unit : Second Cycle
Year of Study : Preb
Semester : 255.Semester
Number of ECTS Credits Allocated : 6,00
Name of Lecturer(s) : ---
Course Assistants :
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
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
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 Riemann-Christoffel tensor as a measure of the curvature of the space.
Languages of Instruction : Turkish
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
Course Aims : The aim of this course is to learn vector and tensor analysis in details.
WorkPlacement   Not Available
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" , McGraw-Hill 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)
ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.
Activity :
Number Duration Total  
Course Duration (Excluding Exam Week) :
14 3 42  
Time Of Studying Out Of Class :
14 5 70  
Homeworks :
7 5 35  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 10 10  
Finals :
1 20 20  
Workload Hour (30) :
30  
Total Work Charge / Hour :
177  
Course's ECTS Credit :
6      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
1 40
Quiz :
1 10
Homework :
7 40
Attendance :
1 10
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
100
The ratio of the term to success :
40
The ratio of final to success :
60
TOTAL :
100
Weekly Detailed Course Content
Week Topics  
1 Base vectors, cartesian coordinates, summation convention,range, Kronecker delta and permutation symbols.
  Study Materials: To review vector knowledge in the undergraduate lessons
2 Scalar and vecctor product, scalar triple producti vector triple product, reciprocal base vectors.
  Study Materials: To review vector knowledge in the undergraduate lessons
3 Covariant and contravariant components of a vector and Euclidean metric tensor.
  Study Materials: To review integral knowledge in the undergraduate lessons
4 Vector functions, differentiation, Green-Gauss ande Stokes integral theorems
  Study Materials: To review matrix knowledge in the undergraduate lessons
5 Fundamental concepts for matrix algebra, matrix polynomials and Cayley-Hamilton theorem
  Study Materials: Fundamental books for Linear Algebra
6 Theory of invariants and integrity basis
  Study Materials: Research and reading
7 Introduction to the curvilinear coordinates
  Study Materials: Research and reading
8 Vectors and tensors in curvilinear coordinates
  Study Materials: Research and reading
9 Physical components of vectors and tensors
  Study Materials: Research and reading
10 Tensor calculus, Covariant and contravariant partial derivatives
  Study Materials: Research and reading
11 Divergance, Curl and laplacian operators in curvilinear coordinates
  Study Materials: Research and reading
12 Differential operators in cylindrical and spherical coordinates
  Study Materials: Research and reading
13 Green-Gauss and Stokes theorems in curvilinear coordinates
  Study Materials: Research and reading
14 Riemann_Christoffel curvature tensor and Bianchi identities
  Study Materials: Research and reading
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0
 
0