| Week |
Subject |
Related Preparation |
| 1) |
Defining kinematics, geometric properties of vectors and sliding vectors |
|
| 2) |
Vector and analytic expressions of sliding vector, comoment, geometric interpretation and results. Vector coordinates of a line, detailed studies on it and related results. Introduction to tensors. |
|
| 3) |
Composition of tensors, moments, equivalence class, moment with respect to an axis, analytic expressions, invariant and axis. Special tensors and examing them. Warignon theorem, related theorems and results. |
|
| 4) |
Operations on tensors, which leave them equivalent to themselves, reduction and examining of tensors. Algebraic structure of tensors. Comoment, automoment, invariant of a system, related theorems and results. |
|
| 5) |
Line to zero moment, polar plane, conjugate lines, Plucker coordinates related theorems and problems. Vector production tensors; theorem and problems |
|
| 6) |
Definition of kinematics. Kinematics in plane. Constructing plane motion of one-parameter, translation and rotation. Derivation equations of motion and interpretations. Relative velocity. |
|
| 7) |
Angular velocity, absolute and drift velocity. Composition of velocities and interpretation. Pole of instantaneous rotation orbits of poles. The relation of plane motion with the locus of pole points. |
|
| 8) |
Rolling of pole curves without sliding. Inverse motion, examples of motion. Moving coordinate system and norming them. Pffafian forms. |
|
| 9) |
Constructing motion in moving planes. Expressions of relative, drift and absolute velocity and composition of velocities. Expressing pole points with Pffafian forms. Chain of plane moving with respect to each other. Pole of rotation, line of pole. |
|
| 10) |
Canonic relative system. Differential forms and interpretation of them. Orbit curve and its curvature. Center of curvature. Euler- Savary formula. |
|
| 11) |
Point correspondence in plane motion. Examples and applications of Euler-Savary formula. Introduction to sphere kinematics. Motions around a fixed pointy sphere motions. Showing motion on sphere. Introduction to sphere motions of one- parameter. |
|
| 12) |
Velocities in sphere motion of one parameter (absolute, relative and drift velocities), Pffafian vector. Composition of motions, related theorems and results. |
|
| 13) |
Reducing sphere motion, Correspondence of Euler- Savary formulas of orbit curves in sphere motion. Space kinematics (introduction to kinematics in space) |
|
| 14) |
Canonic relative system. Pol curves and rolling of them without sliding. Theorems and results about moving spheres of same center and moving with respect to each other. |
|
| |
Program Outcomes |
Level of Contribution |
| 1) |
To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics |
5 |
| 2) |
To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods, |
4 |
| 3) |
To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials, |
4 |
| 4) |
To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, |
4 |
| 5) |
To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way, |
4 |
| 6) |
To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,
|
3 |
| 7) |
To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement, |
|
| 8) |
To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, |
|
| 9) |
By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere, |
3 |
| 10) |
To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning, |
|
| 11) |
To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school, |
3 |
| 12) |
To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. |
4 |
BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
