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Course Code: 
MATH 454
Course Type: 
Area Elective
P: 
3
Lab: 
0
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
7
Course Language: 
English
Course Objectives: 
To understand the problems of Physics and Engineering better and find their solutions
Course Content: 

Euler-Lagrange equations and generalizations.Hamiltonian functions. Invariant integrals. Noether theorem.  Second variation and Jacobi fields.  Constraint variational problems. Isoperimetric problems. Non-holonomic systems. 

Course Methodology: 
1: Lecture, 2: Problem Solving, 3:Question-answer, 4: Homework
Course Evaluation Methods: 
A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes

Program Learning Outcomes

Teaching Methods

Assessment Methods

1) Knows variations and their properties

3,4,5,7,8,9

1,2

A

2) Derives Euler equation

3,4,5,7,8,9

1,2

A

3) Can perform generalizations

3,4,5,7,8,9

1,2

A

4) Investigates moving boundary value problems

3,4,5,7,8,9

1,2

A

5) Knows the direct method and Ritz method

3,4,5,7,8,9

1,2

A

6) Can investigate the multiple independent variables case

3,4,5,7,8,9

1,2

A

Course Flow

Week

Topics

Study Materials

1

Minima and maxima of differentiable functions

 

2

Variations and its properties

 

3

Euler equation

 

4

Some generalizations

 

5

Parametric representations of variation problems

 

6

Variation problems with moving boundaries

 

7

Variation problems with moving boundaries (continued)

 

8

Sufficiency for an extremum

 

9

Problems with constrained extrema

 

10

Problems with constrained extrema (continued)

 

11

Direct methods

 

12

Ritz’s method

 

13

Generalizations to more than one independent variables

 

14

Generalizations to more than one independent variables

 

Recommended Sources

Textbook

L. E. Elsgolc; Calculus of Variations

Additional Resources

F. B. Hildebrand; Methods of Applied Mathematics

Material Sharing

Documents

 

Assignments

 

Exams

 

Assessment

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

2

100

Quizzes

-

 

Assignments

-

 

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

40

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

60

Total

 

100

 

COURSE CATEGORY

Expertise/Field Courses

 

Course’s Contribution to Program

No

Program Learning Outcomes

Contribution

1

2

3

4

5

1

The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)

     

X

 

2

Acquiring fundamental knowledge on fundamental research fields in mathematics

   

X

   

3

Ability form and interpret the relations between research topics in mathematics

       

X

4

Ability to define, formulate and solve mathematical problems

       

X

5

Consciousness of professional ethics and responsibilty

   

X

   

6

Ability to communicate actively

   

X

   

7

Ability of self-development in fields of interest

       

X

8

Ability to learn, choose and use necessary information technologies

   

X

   

9

Lifelong education

   

X

   

ECTS

Activities

Quantity

Duration
(Hour)

Total
Workload
(Hour)

Course Duration (14x Total course hours)

14

3

42

Hours for off-the-classroom study (Pre-study, practice)

14

5

70

Mid-terms (Including self study)

2

15

30

Quizzes

0

0

0

Assignments

0

0

0

Final examination (Including self study)

1

30

30

Total Work Load

   

172

Total Work Load / 25 (h)

   

6.88

ECTS Credit of the Course

   

7