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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Purpose and Content

The aim of the course	his course introduces concept of definite integral to functions of several variables and functions of a single real variable that have vector values. They are used to represent and calculate quantities specified in terms of densities in regions of the plane or spaces of higher dimensions. Such integrals are discussed in this course.
Course Content	Students will acquire sequences and series of functions ,double sequences and series ,convergence ,point and uniform convergence ,power series,convergents of infinite power seriesTaylor series of several variables of function, double Riemann integrals and basic properties, calculating double integrals, change of variables in a double integral( polar coordinates) applications of double integrals(geometric and physicale applications), triple integrals and basic properties, change of variables in a triple integral (spherical and slynderical coordinates) , applications of triple integrals(geometric and physicale applications), ,impropre double integrals, line integrals and basic properties,basic theorems of line integrals,applications of line integrals ,Green’s Theorem ,surface integrals and basic propertiers, basic theorems of surfaces integral,applications of surface integrals,the divergence theorem,and Stokes’ Theorem.

The aim of the course

his course introduces concept of definite integral to functions of several variables and functions of a single real variable that have vector values. They are used to represent and calculate quantities specified in terms of densities in regions of the plane or spaces of higher dimensions. Such integrals are discussed in this course.

Course Content

Students will acquire sequences and series of functions ,double sequences and series ,convergence ,point and uniform convergence ,power series,convergents of infinite power seriesTaylor series of several variables of function, double Riemann integrals and basic properties, calculating double integrals, change of variables in a double integral( polar coordinates) applications of double integrals(geometric and physicale applications), triple integrals and basic properties, change of variables in a triple integral (spherical and slynderical coordinates) , applications of triple integrals(geometric and physicale applications), ,impropre double integrals, line integrals and basic properties,basic theorems of line integrals,applications of line integrals ,Green’s Theorem ,surface integrals and basic propertiers, basic theorems of surfaces integral,applications of surface integrals,the divergence theorem,and Stokes’ Theorem.

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	Sequences and series of functions.
2	Double sequences and series ,concept of convergence ,point and uniform convergence,power series.
3	Convergents of infinite power series,Taylor series of funtions of several variables.
4	Double Riemann integrals and basic properties, calculating double integrals.
5	Change of variables in a double integrals and applications of double integrals(geometric and physicale applications).
6	Triple integrals and basic properties,calculating triple integrals.
7	Change of variables in a triple integrals (spherical and slynderical coordinates).
8	Applications of triple integrals(geometric and physicale applications).
9	Impropre double integrals,line integrals and basic properties Line integrals, line integrals of scaler and vector field.Midterm Exam.
10	Fundamental theorems of line integrals and applications.
11	Applications of line integrals(Green’s theorem etc.).
12	Surface integrals and basic properties.
13	Surface integrals on the oriented surfaces, fundamental theorems of surface integrals.
14	Applications of surface integrals (divergence and Stokes’ theorems etc.) Green’s Theorem and Stokes’ Theorem.

Resources

1-1-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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Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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