| INDUSTRIAL PRODUCTS DESIGN | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT4053 | Differentiable Manifolds | Fall | 3 | 0 | 3 | 6 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
| Language of instruction: | English |
| Type of course: | Non-Departmental Elective |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | |
| Recommended Optional Program Components: | None |
| Course Objectives: | The differentiable manifolds course aims to give the fundamental knowledge for the studies of graduate students who intends to study at geometry. |
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The students who have succeeded in this course; upon succeeding this course 1)be able to test a differentiable structure given on a set 2)be able to give examples of Differentiable structures on a set 3) be able to check differentiablity of a function 4) be able to solve problems involving the derived map of a transformation between two manifolds 5) be able to use the properties of induced topology on a manifold, 6) be able to coordinatize Grassmann manifolds and can evaluate their dimensions, 7) be able to understand the existence problems by using the unity of partition 8)be able to explain the derived function of a function by using the Leibniz rule, 9) be able to explain submanifolds as images under Immersions 10) be able to coordinatize quotient manifolds and calculate their dimensions, 11) be able to construct Klein bottle and Mobius strip as an example of a quotient manifold |
| Differentiable (diff.able) functions, Atlas, diff.able structures on a set, Examples of diff.able structures, diff.able manifolds, diff.able functions, The induced topology on a manifold, diff.able varieties, Grassmann manifolds, Manifold structure on a topological space, properties of the induced topology, Topological restrictions on a manifold, Partitions of unity, Partial differentiation, tangent vectors, The invers function Theorem, Leibniz's rule. İmmersions, submanifolds, regular submanifolds, some topological properties of submanifolds. Submersions, The fibres of submersions, Quotient manifolds, Transformation groups, Examples of quotient manifolds. |
| Week | Subject | Related Preparation |
| 1) | Preliminaires | |
| 2) | Some classical theory of differentiable functions | |
| 3) | Atlas, differentiable structures on a set | |
| 4) | Examples of differentiable structures on a set | |
| 5) | Differentiable manifolds | |
| 6) | Differentiable functions | |
| 7) | The induced topology on a manifold | |
| 8) | Differentiable varieties, Grassmann manifolds | |
| 9) | Topological restrictions on a manifold, Partitions of unity | |
| 10) | Manifold structure on a topological space, properties of the induced topology | |
| 11) | Partial differentiation, tangent vectors, derived linear functions, The invers function Theorem, Leibniz's rule. | |
| 12) | İmmersions, submanifolds, regular submanifolds, some topological properties of submanifolds. | |
| 13) | Submersions, The fibres of submersions, Quotient manifolds | |
| 14) | Transformation groups, Examples of quotient manifolds. |
| Course Notes / Textbooks: | Differentiable Manifolds an Introduction ,F Brickell, R. S. Clark. |
| References: | . |
| Semester Requirements | Number of Activities | Level of Contribution |
| Midterms | 2 | % 45 |
| Final | 1 | % 55 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 45 | |
| PERCENTAGE OF FINAL WORK | % 55 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 7 | 2 | 14 |
| Midterms | 2 | 20 | 40 |
| Final | 1 | 30 | 30 |
| Total Workload | 126 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Having the theoretical and practical knowledge proficiency in the discipline of industrial product design | |
| 2) | Applying professional knowledge to the fields of product, service and experience design development | |
| 3) | Understanding, using, interpreting and evaluating the design concepts, knowledge and language | |
| 4) | Knowing the research methods in the discipline of industrial product design, collecting information with these methods, interpreting and applying the collected knowledge | |
| 5) | Identifying the problems of industrial product design, evaluating the conditions and requirements of problems, producing proposals of solutions to them | |
| 6) | Developing the solutions with the consideration of social, cultural, environmental, economic and humanistic values; being sensitive to personal differences and ability levels | |
| 7) | Having the ability of communicating the knowledge about design concepts and solutions through written, oral and visual methods | |
| 8) | To identify and apply the relation among material, form giving, detailing, maintenance and manufacturing methods of design solutions | |
| 9) | Using the computer aided information and communication technologies for the expression of industrial product design solutions and applications | |
| 10) | Having the knowledge and methods in disciplines like management, engineering, psychology, ergonomics, visual communication which support the solutions of industrial product design; having the ability of searching, acquiring and using the knowledge that belong these disciplines when necessary. | |
| 11) | Using a foreign language to command the jargon of industrial product design and communicate with the colleagues from different cultures | |
| 12) | Following and evaluating the new topics and trends that industrial product design needs to integrate according to technological and scientific developments |