Ders Planı

Lesson Information

Course Credit	5.0
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)	Prof. Dr. ÇİĞDEM GENCER BALBİANİ
Course Assistant	Prof. Dr. İSMAİL TOK

Purpose and Content

The aim of the course	This course aims to upskill students on the concepts of integration the applications of integration To give the evaluation of integrals by using integral techniques,a broad knowledge and basic understanding of sequences and series. To give an ability to apply knowledge of mathematics on engineering problems.
Course Content	This course covers antiderivatives,indefinite integral, methods of the indefinite integrals,integration by change of variable, integration by parts,a plane region of area,definite integral,fundamental theorem of Calculus,fundamental theorem of Integral Calculus,Properties of the Riemann integral and related theorems,evaluation of some limits by integration,numerical integration,integration of techniques, geometric and physical applications of Riemann integral ,improper integrals and properties,sequences , infinite series,arithmetic,geometric,harmonic series and properties,convergence tests for series of positive terms,alternating series,absolutly and conditional convergent ,power series,derivatives of term to term,integration, series of McLaurin and Taylor and integrals of vector functions.

The aim of the course

This course aims to upskill students on the concepts of integration the applications of integration To give the evaluation of integrals by using integral techniques,a broad knowledge and basic understanding of sequences and series. To give an ability to apply knowledge of mathematics on engineering problems.

Course Content

This course covers antiderivatives,indefinite integral, methods of the indefinite integrals,integration by change of variable, integration by parts,a plane region of area,definite integral,fundamental theorem of Calculus,fundamental theorem of Integral Calculus,Properties of the Riemann integral and related theorems,evaluation of some limits by integration,numerical integration,integration of techniques, geometric and physical applications of Riemann integral ,improper integrals and properties,sequences , infinite series,arithmetic,geometric,harmonic series and properties,convergence tests for series of positive terms,alternating series,absolutly and conditional convergent ,power series,derivatives of term to term,integration, series of McLaurin and Taylor and integrals of vector functions.

Learning Outcomes

Have advanced theoretical and practical knowledge in mathematics and computer science.
Gain an in-depth knowledge on Computer Science including computer programming, word processing, database functions, accessing the internet and softwares.
Possess the knowledge of advanced research methods in mathematics-computer field.
Possess theoretical and practical knowledge in mathematics, computation and computer science.
Define computer programming, word processing, data functions, internete access and software programs.
Describe advanced research methods in the field of Mathematics-Computer Science.
Evaluate and interpret data using the knowledge and skills gained in the fields of mathematics and computer science.
Identify, define and analyze problems in the fields of mathematics and computer science; develop solutions based on research and evidence.
Identify, define and model mathematics, computation and computer science problems; select and apply appropriate analysis and modeling methods for this purpose.
Design and apply interactive experimental environments to get the definitions and first solutions of the problems of computer science and computer science and evaluate these environments.
Having the discipline of mathematics, understand the operating logic of the computer and gain the ability to think based on account.
Perform all phases of life cycle in computer based systems.
Work effectively as an individual and as a team member to solve problems in the areas of mathematics and computer science.
Have the ability to act independently, use initiative and creativity.
Work effectively either individually or in multidisciplinary teams.
Evaluate advanced knowledge and skills in the field with a critical approach.
Follow current developments about the awareness of the necessity of continuous professional development and information and communication technologies.
Have the consciousness of the necessity of lifelong learning and continuously develop professional knowledge and skills.
Use the time effectively in the process of getting the conclusion with analytical thinking ability.
Have at least one foreign language knowledge and the ability to communicate effectively in Turkish, verbally and in writing.
Be aware of the effects of information applications on individual, institutional, social and universal dimensions and have the awareness about entrepreneurship, innovation.
Have the awareness of professional and ethical responsibility and legal consequences of information applications
Use the knowledge about the field for the benefit to society.

Weekly Course Subjects

1	Indefinite integrals and properties.
2	Methods of integrals, integration by change of variables,integration by parts .
3	Area of a plane region,definite integrals and properties Mean Value Theorem for integral, Fundamental theorems of Calculus and integral calculus.
4	Properties of the Riemann integral,evalution of some limits by definite integral.
5	Methods of numerical integrations.
6	Hyperbolic and inverse hyporbolic funtions,derivatives,integrals.
7	Techniques of integration.
8	Techniques of integration.
9	Geometric and physical applications of the Riemann integral.Midterm Exam.
10	Improper integrals.
11	Sequences and properties,covergence.
12	Infinites series and properties,arithmetic,geometric and harmonic series,convergence test for series of positive terms.
13	Alternating series and properties,convergence,absolut convergent and conditional converegent.Power series and properties,derivatives of term to term ,integration, series of McLaurin and Taylor.
14	Integral of vector valued functions and its properties.

Resources

1.Mustafa Bayraktar, Analize Giriş I(2.Baskı) , Grafiker Yayınları,Ankara,2007.
2.Mustafa Balcı,Analiz I,Balcı Yayınları,Ankara,2008

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Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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