Ders Planı

Lesson Information

Course Credit	4.0
Course ECTS Credit	7.0
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
Course Coordinator
Instructor (s)
Course Assistant

Purpose and Content

The aim of the course	Provide an ability to gain a knowledge and formation about the advanced calculus with class training and to provide an ability to use the concepts of integration in the applications , apply the knowledge of mathematics on solving engineering problemsand evaluate the integrals by using integral techniques.Give the basic concepts of analytic geometry and give a broad knowledge and basic understanding of sequences and series. Investigate the limit, continuity and integral of vector-valued functions in application.
Course Content	Concept of area, estimating with finite sums, sigma notation and limits of finite sums, definite integral, The Fundamental Theorems of Calculus and Integral,integration by parts,substitution rule, indefinite integrals, numerical integration , hyperbolic and inverse hyperbolic functions, techniques of integration, area, lengths of plane curves, volumes of a solid of revolution, areas of surfaces of revolution, moments and centers of mass, moments of inertia, Pappus theorems, areas and lengths in polar coordinates. improper integrals, sequences, infinite series, tests of convergence for arithmetic,geometric,harmonic, alternating series ,absolutly convergent, conditionaly convergent,derivation and interal of power series,convergence of power series, Taylor and Maclaurin Series, Fourier Series,vectors, dot Product, cross product, lines and planes in space, cylinders and quadric surfaces, vector-valued functions, limits and continuity and integrals of vector-valued functions.

The aim of the course

Provide an ability to gain a knowledge and formation about the advanced calculus with class training and to provide an ability to use the concepts of integration in the applications , apply the knowledge of mathematics on solving engineering problemsand evaluate the integrals by using integral techniques.Give the basic concepts of analytic geometry and give a broad knowledge and basic understanding of sequences and series. Investigate the limit, continuity and integral of vector-valued functions in application.

Course Content

Concept of area, estimating with finite sums, sigma notation and limits of finite sums, definite integral, The Fundamental Theorems of Calculus and Integral,integration by parts,substitution rule, indefinite integrals, numerical integration , hyperbolic and inverse hyperbolic functions, techniques of integration, area, lengths of plane curves, volumes of a solid of revolution, areas of surfaces of revolution, moments and centers of mass, moments of inertia, Pappus theorems, areas and lengths in polar coordinates. improper integrals, sequences, infinite series, tests of convergence for arithmetic,geometric,harmonic, alternating series ,absolutly convergent, conditionaly convergent,derivation and interal of power series,convergence of power series, Taylor and Maclaurin Series, Fourier Series,vectors, dot Product, cross product, lines and planes in space, cylinders and quadric surfaces, vector-valued functions, limits and continuity and integrals of vector-valued functions.

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	Concept of area, estimating with finite sums, sigma notation and limits of finite sums, definite integral, The Fundamental Theorems of Calculus.
2	Evaluation of Limit using the definite integral,indefinite integral and its properties.
3	Integration by parts,substitution rule, integral formulas.
4	Numerical integration metods , hyperbolic and inverse hyperbolic fnctions.
5	Derivatives and integrals of hyperbolic and inverse hyperbolic fnctions.
6	Techniques of integration.
7	Techniques of integration.
8	Area, lengths of plane curves,volums of a solid of revolution, areas of surfaces of revolution.
9	Moments and centers of mass, moments of inertia,Pappus theorems. Areas and lengths in polar coordinates,improper integrals. Midterm Exam.
10	Sequences, infinite series, tests of convergence for arithmetic, geometric,harmonic, alternating series.
11	Absolute convergent,conditional convergent, convergence of power series.
12	Derivation and integral of power series, Taylor and Maclaurin Series, Fourier Series.
13	Vectors, dot product, cross product, lines and planes in space, cylinders and quadric surfaces.
14	Vector-valued functions, limits and continuity and integrals of vector-valued functions.

Resources

1- Mustafa Balcı,Genel Matematik I,Balcı Yayınları,Ankara,2008.
2-G.B Thomas, M.D.Weir, J.Hass and F.R.Giordano,Thomas’ Calculus, 11th Edition, Addison-Wesley, 2005.
3-Mustafa Bayraktar, Analize Giriş II(2.Baskı) , Grafiker Yayınları,Ankara,2007.
4- Speigel, M. R., Çeviri Editörü: H. H. Hacısalioğlu, İleri Matematik, 6. Baskı, McGraw-HILL, Schaum’s Outline Series, NY., Ankara Üniversitesi,1997.
5- Ahmet Dernek, Genel Mat ematik, 3. Baskı, Nobel Yayın Dağıtım Tic. Ltd. Şti. Ankara,2009.

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Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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