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Item Open Access Solution of differential equations with vertical asymptotes(Suleyman Demirel University, 2011) Uxikbayev K.B.This article investigates the kernel of the inverse operator associated with the third-order differential operator defined by Ly = −y'' + q(x)y under periodic-type boundary conditions. Using Kolmogorov widths and s-number theory, we establish estimates for the operator’s properties and demonstrate that the inverse operator is a kernel operator when q(x) is continuous and satisfies q(x) ≥ 1. Several supporting lemmas are proven, including inequalities for the operator and relationships between s-numbers and Kolmogorov widths. The results provide a theoretical framework for understanding the behavior of higher-order differential operators in Hilbert and Banach spaces.Item Open Access A comparison between the traditional lecture method and concept mapping method on teaching boolean algebra(Suleyman Demirel University, 2011) Cemil TosikIn education implemented throughout the history of humanity, all kinds of information and social values intended to be transferred to the young generation are realized by teachers. The higher quality of teaching, the more achievement of student is. To achieve the goal of teaching and learning, the teacher must adopt effective teaching and learning methods in education. The teacher has many options to choose from different methods designed specifically for teaching and learning. The purpose of this research presented here is to investigate the effects of using concept maps on student achievement at teaching 'Binary System and Boolean Algebra'. Nowadays the information easy to reach but to keep in mind and to reach new findings and synthesis are quite difficult. In educational process for effective learning, the teaching materials for the learning purpose should be comprehensible and appropriate for the students. Furthermore, the learners are expected to construct the concepts and relations of the learning materials so as to achieve the desired learning objectives. Concept mapping is a method using graphs for representing knowledge in a structure according to different levels of abstraction and inclusion. The method has been widely applied in many disciplines and various educational levels. This learning environment is intended to guide the learners toward general understandings of the subject they have to learn.Item Open Access Functional Equations: Review of Solution Methods and Applications in Real and Complex Analysis(Suleyman Demirel University, 2011) Muammer GulThis article provides an overview of functional equations, one of the oldest and most fundamental topics in mathematical analysis. It discusses classical types of equations, including Cauchy’s additive and multiplicative equations, and highlights their historical development through the works of D’Alembert, Poisson, Cauchy, and Lobachevsky. Several well-known equations, such as those related to the parallelogram law, hyperbolic functions, and non-Euclidean geometry, are illustrated as examples of how functional equations arise naturally in mathematics. The paper also explores the existence of discontinuous solutions, the role of continuity and boundedness assumptions, and how these conditions restrict solutions to linear or exponential forms. Finally, it emphasizes that many functional equations characterize broad classes of functions—such as periodic or symmetric functions—and outlines general strategies for solving them.Item Open Access Ağaç Yaşken Eğilir(Suleyman Demirel University, 2011) Esra CIGThis article explores effective strategies for teaching young learners a foreign language, focusing particularly on how children naturally acquire their first language and how these processes can inform early foreign language instruction. Drawing on personal observations, developmental linguistics, and characteristics of young learners, the author emphasizes the importance of early and rich language exposure. The article discusses children’s innate abilities such as interpreting meaning through gestures, intonation, and context, as well as their creativity and imagination, which make them highly receptive to language learning. It highlights the role of multiple intelligences and the need to adapt teaching methods to diverse learner profiles. The author also shares practical techniques used outside the classroom to increase children’s exposure to English and enhance motivation through natural communication.Item Open Access Early help, Better education!(Suleyman Demirel University, 2011) Yechshanov G.This paper examines the problem of school underachievement with particular attention to early foreign language instruction in preschool and primary school age. The study highlights that despite the recognized advantages of early systematic foreign language learning, many children experience learning difficulties that lead to poor academic performance and school maladjustment. The causes of underachievement are analyzed from psychological, pedagogical, biological, and social perspectives. Special emphasis is placed on factors such as insufficient school readiness, health problems, speech and sensory impairments, unfavorable social conditions, and weaknesses in teaching methods. The paper reviews classical and modern theories of school failure and stresses the importance of early diagnosis and timely pedagogical support. It is argued that effective assistance to underachieving students requires a комплекс approach involving teachers, psychologists, and medical specialists to prevent long-term learning difficulties and ensure successful education.Item Open Access The internet as a tool for the development of intercultural communicative competence in english language education(Suleyman Demirel University, 2011) Yusuf YaylacıThis article explores the use of the Internet as a tool for developing intercultural communicative competence in English language education. It examines the evolution of computer-assisted language learning (CALL) from behavioristic to communicative and integrative approaches, highlighting the increasing role of multimedia and Internet technologies in fostering learner autonomy, authentic communication, and intercultural awareness. The paper discusses the context of English language teaching (ELT) in Kazakhstan, including Internet accessibility, computer literacy, and state educational policies that support English as a medium for intercultural communication. Practical strategies for integrating the Internet into task-based instruction are provided, emphasizing the potential for online collaborative projects, blogs, social networks, and intercultural interaction to enhance learners’ cognitive, behavioral, and affective development in intercultural competence.Item Open Access About Existence of Solution of Third-Order Derivative of −y'' + q(x)y = f Type Equations(Suleyman Demirel University, 2011) Omer CakirIn this paper, we investigate the existence of solutions for third-order differential equations of the form −y'' + q(x)y = f within a Hilbert space of square-integrable functions on the interval from −π to π. The study focuses on the differential operator defined by −y'' + q(x)y under periodic-type conditions, where the function and its first two derivatives satisfy y(i)(−π) = y(i)(π) for i = 0, 1, 2. Several preliminary lemmas are established, including integral identities and inequalities related to the scalar product involving the operator. Using these lemmas, it is shown that the kernel of the operator is trivial, and a bounded inverse operator exists. Consequently, the boundary value problem has a unique solution for any square-integrable function f, provided that the coefficient function q(x) is continuous. These results contribute to the theoretical understanding of higher-order differential operators in Hilbert spaces.Item Open Access The effect of mind mapping instruction on the attitudes toward geometry(Suleyman Demirel University, 2011) H. Aliyev; Erdal AyanThis article examines the impact of mind mapping instruction on 8th-grade students’ attitudes toward geometry. Grounded in constructivist learning principles, the study explores how mind mapping, as a visual and associative note-taking technique, supports students’ comprehension, creativity, and recall of geometric concepts. The research was conducted with 52 students divided into experimental and control groups over an 8-week period. While the control group received traditional instruction, the experimental group was taught mind mapping techniques and used them consistently during lessons on angles and triangles. Attitudes toward geometry were measured using the Attitudes Toward Mathematics Inventory (ATMI). Results indicate that mind mapping instruction contributed positively to students’ enjoyment, confidence, and motivation toward geometry, while reducing anxiety related to the subject.Item Open Access The advantages of using smartboards to teach geometry lesson of 10. grade students(Suleyman Demirel University, 2011) Ahmet ÇakırThe aim of this assay is to analyse the results of using smartboard in geometry lessons of 10. grade students. By looking at the results of experiment I will explain the advantages and disadvantages of using smartboards. To investigate the advantages of using smartboards in geometry lessons I made an 8 week experiment in Almaty Kazakh Turkish High School for Girls. In the experiment there were two homogenous groups of students. In one of the classes, which was my experimental group. I used smartboard and teach Vectors unit, in the second group, that was control group, there were no smartboard, by using only blackboard I explained the Vectors. Both of the groups wrote a pre-test at the beginning of the unit. At the end of experiment both of the groups wrote a post-test. Also I used sample t-test to determine whether there was a significant difference between the means. In the experiment there were 40 students that were similar in age, knowledge, performance and ability. As a result of the experiment there were a significiant difference between the means of exams of the groups. Experimental group made a better average from the post-test and other small exams. After 1 month I made a permanence test and check the results. The results show that the students in experimental group remember the topics more than the students in control group. That shows the advantage of using smartboard.Item Open Access Numerical method for solving the equation of navier-stokes(Suleyman Demirel University, 2011) Kuttykozhaeva Sh. N.This article presents a numerical method for solving the Navier-Stokes equations based on a variant of the fictitious domain method with continuation of the leading coefficient. A key feature of the method is that the boundary of the auxiliary domain is defined using the tangential components of velocity and pressure. This allows the construction of an efficient iterative method for numerical calculations. It is shown that the rate of convergence of the iterative method is independent of variations in a small parameter. The proposed approach provides a reliable and effective tool for the numerical solution of linear stationary Navier-Stokes equations.