COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Analytical Mechanics
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
PHYS 309
Fall/Spring
2
2
3
5
Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
First Cycle
Mode of Delivery face to face
Teaching Methods and Techniques of the Course Problem Solving
Q&A
Lecture / Presentation
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives The main objective of this course is to introduce classical mechanics in a mathematically advanced perspective using the so called Lagrange and Hamilton pictures so that it can also be related to quantum mechanics.
Learning Outcomes The students who succeeded in this course;
  • write down Lagrange equations for any mechanical system.
  • determine the effects of conservation laws and constraints to the Lagrange equations.
  • solve Lagrange equations directly analytically or numerically.
  • obtain Hamiltonian equations by using Legendre transformation.
  • apply Hamiltonian-Jacobi theory to mechnaics problems.
Course Description A new perspective for classical mechanics, which is easier to connect to quantum mechanics, will be introduced using new mathematical techniques,such as Lagrange and Hamilton approaches.

 



Course Category

Core Courses
Major Area Courses
X
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Fundementals, newtonian mechanics Jakob Schwichtenberg, No-nonsense classical mechanics,(2018) Chapter 2,3 İSBN 1096195380.
2 Lagrange mechanics Jakob Schwichtenberg, No-nonsense classical mechanics,(2018) Chapter 4 İSBN 1096195380Wolfgang Nolting, Theoretical Physics 2: Analytical Mechanics (Springer, 2016). Chapter 1.1-2. ISBN: 9783319401287
3 Hamilton principal Jakob Schwichtenberg, No-nonsense classical mechanics,(2018) Chapter 5 İSBN 1096195380Wolfgang Nolting, Theoretical Physics 2: Analytical Mechanics (Springer, 2016). Chapter 1.3. ISBN: 9783319401287
4 Point transformations, Generalized coordinates Jakob Schwichtenberg, No-nonsense classical mechanics,(2018) Chapter 7.2 İSBN 1096195380
5 Canonical transformations. Jakob Schwichtenberg, No-nonsense classical mechanics,(2018) Chapter 7.3 İSBN 1096195380. Wolfgang Nolting, Theoretical Physics 2: Analytical Mechanics (Springer, 2016). Chapter 2.2-5. ISBN: 9783319401287
6 Harmonic oscillator problem Jakob Schwichtenberg, No-nonsense classical mechanics,(2018) Chapter 8 İSBN 1096195380.
7 Pendulum problem Jakob Schwichtenberg, No-nonsense classical mechanics,(2018) Chapter 9 İSBN 1096195380.
8 Midterm exam 1
9 Noether Theorem Jakob Schwichtenberg, No-nonsense classical mechanics,(2018) Chapter 10 İSBN 1096195380.
10 Hamilton-Jacobi Mechanics 1 Jakob Schwichtenberg, No-nonsense classical mechanics,(2018) Chapter 11.1-2 İSBN 1096195380. Wolfgang Nolting, Theoretical Physics 2: Analytical Mechanics (Springer, 2016). Chapter 3.1-5. ISBN: 9783319401287
11 Hamilton-Jacobi Mechanics 2 Jakob Schwichtenberg, No-nonsense classical mechanics,(2018) Chapter 11-3 İSBN 1096195380. Wolfgang Nolting, Theoretical Physics 2: Analytical Mechanics (Springer, 2016). Chapter 3.1-5. ISBN: 9783319401287
12 Solution methods Wolfgang Nolting, Theoretical Physics 2: Analytical Mechanics (Springer, 2016). Chapter 3.2-5. ISBN: 9783319401287
13 The origins of classical mechanics. Jakob Schwichtenberg, No-nonsense classical mechanics,(2018) Chapter 12 İSBN 1096195380
14 Connection to quantum mechanics. Wolfgang Nolting, Theoretical Physics 2: Analytical Mechanics (Springer, 2016). Chapter 3.6. ISBN: 9783319401287
15 Semester review
16 Final Exam
Course Notes/Textbooks

Wolfgang Nolting, Theoretical Physics 2: Analytical Mechanics (Springer, 2016). ISBN: 9783319401287

Suggested Readings/Materials

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
1
10
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
1
25
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
25
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
3
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
2
32
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
2
Study Hours Out of Class
14
3
42
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
3
6
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
8
Final Exams
1
18
    Total
150

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To be able master and use fundamental phenomenological and applied physical laws and applications,

X
2

To be able to identify the problems, analyze them and produce solutions based on scientific method,

X
3

To be able to collect necessary knowledge, able to model and self-improve in almost any area where physics is applicable and able to criticize and reestablish his/her developed models and solutions,

X
4

To be able to communicate his/her theoretical and technical knowledge both in detail to the experts and in a simple and understandable manner to the non-experts comfortably,

5

To be familiar with software used in area of physics extensively and able to actively use at least one of the advanced level programs in European Computer Usage License,

6

To be able to develop and apply projects in accordance with sensitivities of society and behave according to societies, scientific and ethical values in every stage of the project that he/she is part in,

7

To be able to evaluate every all stages effectively bestowed with universal knowledge and consciousness and has the necessary consciousness in the subject of quality governance,

8

To be able to master abstract ideas, to be able to connect with concreate events and carry out solutions, devising experiments and collecting data, to be able to analyze and comment the results,

9

To be able to refresh his/her gained knowledge and capabilities lifelong, have the consciousness to learn in his/her whole life,

10

To be able to conduct a study both solo and in a group, to be effective actively in every all stages of independent study, join in decision making stage, able to plan and conduct using time effectively.

11

To be able to collect data in the areas of Physics and communicate with colleagues in a foreign language ("European Language Portfolio Global Scale", Level B1).

12

To be able to speak a second foreign at a medium level of fluency efficiently

13

To be able to relate the knowledge accumulated throughout the human history to their field of expertise.

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