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