Ders Planı

Lesson Information

Course Credit	4.0
Course ECTS Credit	5.0
Teaching Language of Instruction	Türkçe
Level of Course	Bachelor's Degree, TYYÇ: Level 6, EQF-LLL: Level 6, QF-EHEA: First Cycle
Type of Course	Compulsory
Mode of Delivery	Face-to-face
Does the course require compulsory or optional work experience?	Z
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Instructor (s)
Course Assistant

Purpose and Content

The aim of the course	It is discussed Rn ,space and its properties,function of several variables and its properties, sequences defined on the space Rn,convergent of infinite sequences,Cauchy's criter,funtions of several variables, limits and continuity, the general chain rule, implicit functions, the directional derivative, maxima and minima of functions of several variables in the course.
Course Content	This course covers,Rn ,space and its properties,function of several variables and its properties, sequences defined on the space Rn,convergent of infinite sequences,Cauchy's criter,limit and continuity, partial derivatives, partial derivatives of higher order, derivative in a given direction, gradient, total differential, approximations with total differential, the chain rule ,derivative of implicit functions ,maximum and minimum concept for the function of several variables, extreme values of functions defined on restricted domains, applications of differential calculus to solid geometry, rules for differentiating vectors (vector functions), the tangent line and the normal plane to a curve, the tangent plane and the normal to a surface, Taylor’s and Maclaurin’s formulas ,regional transformations,Jacobian,the functional dependence.

The aim of the course

It is discussed Rn ,space and its properties,function of several variables and its properties, sequences defined on the space Rn,convergent of infinite sequences,Cauchy's criter,funtions of several variables, limits and continuity, the general chain rule, implicit functions, the directional derivative, maxima and minima of functions of several variables in the course.

Course Content

This course covers,Rn ,space and its properties,function of several variables and its properties, sequences defined on the space Rn,convergent of infinite sequences,Cauchy's criter,limit and continuity, partial derivatives, partial derivatives of higher order, derivative in a given direction, gradient, total differential, approximations with total differential, the chain rule ,derivative of implicit functions ,maximum and minimum concept for the function of several variables, extreme values of functions defined on restricted domains, applications of differential calculus to solid geometry, rules for differentiating vectors (vector functions), the tangent line and the normal plane to a curve, the tangent plane and the normal to a surface, Taylor’s and Maclaurin’s formulas ,regional transformations,Jacobian,the functional dependence.

Learning Outcomes

Ability to have adequate knowledge in mathematics, physics, chemistry, and also textile engineering and technology subjects, and to apply the theoretical and practical engineering studies.
Ability to design administrative and work-flow organization, production planning, capacity balancing. Recognizing machines, facility, system and devices in related areas. Ability to identify complex machine, material, personal problems, and to present solution in textile production problems. Ability to discuss and comment about all kinds of textile problems.
Ability to take precautions for keeping production machines and facilities at full capacity in the production. Ability to design system, facility and operations of business, to keep active machines and devices, or to produce goods to meet the specific requirements under the compelling constraints and circumstances; by this purpose, ability to apply such modern design methods.
Ability to choose, use and develop the modern techniques, devices and information technologies that required in textile engineering applications.
Ability to investigate sample production, to comment the disruptions, to take remedy precautions, and becoming habits. Ability to be conscious of the usage and validity functions for textile products, and accordingly, to design and manufacture. Ability to utilize modern information Technologies.
Ability to conduct both individual and team work, and to communicate effectively
Ability to pay attention about not only what you told, but also what you are saying regarding to communicate with lower and upper level staff. Ability to be conscious of investigating the error, not the guilt, regarding to the problems. Ability to make reporting, presenting, cooperating with industrial establishments and being competent on Technical English with related to their own field.
Ability to be conscious of lifelong learning, to learn and apply the possibilities of reaching new information, to develop strategies and techniques for effective learning, to encourage critical thinking, creativity and objective thinking, to self-renew by following up-to-date information.
Sense of responsibility in general and professional ethics. Ability to know standards in general engineering, especially in textile, and act accordingly.
Ability to think and act innovative, entrepreneurial and forward thinking in production and application of textile engineering projects and renovations of enterprises.
Ability to conduct textile applications, both in product-based and production processes, from the view of principles regarding to be conscious and aware of harmless in human health and life, social, economic and environmental safety. Awareness of the legal consequences of various activities and solutions.
Ability to work effectively in interdisciplinary and multi-disciplinary teams and individual works.
Have the confidence to take responsibility
Sense of professional and ethical responsibility.
Awareness of the necessity of lifelong learning; ability to reach information, follow the latest developments in science and technology; ability to ensure self-renewal perpetually.
Ability to communicate efficiently both in oral and written ways in Turkish; knowledge of at least one foreign language.
Fullfill the national health enviremental and security rules and policies during the textile applications and productions
Be aware of the use and validity function of textile materials and fulfill the design and functions of production accordingly.

Weekly Course Subjects

1	Rn space and its properties.
2	Functions of several variables and properties.
3	Sequences defined on the space Rn,convergent of infinite sequences,Cauchy's criter.
4	Limit of functions of several variables and basic properties.
5	Continuity of functions of several variables ,uniform continuity and properties.
6	Partial derivatives and applications.
7	Directional derivatives, the concept of gradient, Differentiability.
8	Fundamental theorems of differential calculus.
9	Tangent plane, the chain rule and implicit function theorem, the derivative of the inverse function.Midterm Exam.
10	Maximum and minimum concepts for the function of several variables.
11	Extreme values for a function of several variables defined on restricted domains.
12	Langrage multipliers method.
13	Taylor’s and Maclaurin’s formulas.
14	Regional transformations, Jacobian, the functional dependence.

Resources

1-Mustafa Bayraktar,Analiz,Nobel Yayınları,2010
2-Mustafa Balcı, Matematik Analiz II, Balcı Yayınları,2009
3. George B. Thomas, Jr., Calculus, Perason & Addison (Çeviri: Recep Korkmaz), Beta, 2009
4.Maddox, I. J., Mathematical Analysis, British Library Catalouing in Publicatiın, 1977
5.Silverman, Richard A., Calculus with Analytic Geometryi Prentice - Hall, 1985
6. Murray R. Spiegel, Advanced Calculus, Schaum's Outline Series, McGraw-Hill Book Company, USA, 1963

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CLASS 4

Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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