Djurdjica Takači

Multimedia Approach in Teaching Mathematics--Example of Lesson about the Definite Integral Application for Determining an Area.

This article presents the importance of using multimedia in the math classes by an example of multimedia lesson about definite integral and the results of the research carried out among the students of the first years of faculty, divided into two groups of 25. One group had the traditional lecture about the definite integral, while the other one had the multimedia method. The main information source in multimedia lectures was the software created in Macromedia Flash, with definitions, theorems, examples, tasks as well as in traditional lectures but with emphasized visualization possibilities, animations, illustrations, etc. Both groups were tested after the lectures. Students from the multimedia group showed better theoretical, practical and visual knowledge. Besides that, survey carried out at the end of this research clearly showed that students from multimedia group were highly interested in this way of learning.

On the operational solutions of fuzzy fractional differential equations

Fuzzy fractional differential equations with fuzzy coefficients are analyzed in the frame of Mikusiński operators. Systems of fuzzy operational algebraic equations are obtained, in view of the definition of fuzzy derivatives. Their exact and approximate solutions are constructed and their characters are analyzed, considering them as the corresponding solutions of the given problem. The described procedure of the construction of solutions is illustrated on an example and the obtained approximate solutions of the considered problems are visualized by using the GeoGebra software package.

On the Continuity of Functions.

In this paper, results of a questionnaire about continuity of functions are analysed. The tested students attend Novi Sad grammar school. The aim of this test was to check the students theoretical and visual knowledge of continuous functions at the end of their high school education. The questions were given with and without the graphs of functions. The main conclusion is that the graph of a function has a significant influence on the students opinion about continuity. Looking at the graphs of functions mostly led to correct answers, but sometimes it causes problems, if it has a break. The idea came from a 1981 paper by Tall and Vinner, where the “concept image” of a continuous functions was examined.

Partial Differential Equations through Examples and Exercises

Preface. List of Symbols. 1. Introduction. 2. First Order PDEs. 3. Classification of the Second Order PDEs. 4. Hyperbolic Equations. 5. Elliptic Equations. 6. Parabolic Equations. 7. Numerical Methods. 8. Lebesgues Integral, Fourier Transform. 9. Generalized Derivative and Sobolev Spaces. 10. Some Elements from Functional Analysis. 11. Functional Analysis Methods in PDEs. 12. Distributions in the Theory of PDEs. Bibliography. Index.

The g-operational calculus

Using the g-calculus, introduced earlier by E. Pap, the g-operator field Fg is introduced analogously to the classical field of Mikusinski operators F. The obtained results enable the solving of a certain nonlinear PDE of the Burgers type in a wider framework of the generalized functions, which is a generalization of the earlier obtained result.

Elementary analysis through examples and exercises

Preface. 1. Real numbers. 2. Functions. 3. Sequences. 4. Limits of functions. 5. Continuity. 6. Derivatives. 7. Graphs of functions. Bibliography. Index.

Using Computers and Context in the Modeling-Based Teaching of Logarithms

This article proposes various uses of computers in the modeling-based teaching of mathematics. Modeling activities require computer-based learning approaches and challenge teachers and students with new technologies. The authors analyze the joint use of Internet resources, the educational software GeoGebra, and real-life situations for introducing problems involving logarithms. The strategy of preparing for a modeling-based lesson was presented to a group of Serbian high school teachers and their comments regarding this presentation are included in the article.

On matrices with operator entries

In this paper we consider certain matrix equations in the field of Mikusiński operators, and construct a method for obtaining an approximate solution which allows working with numerical constants instead of operators. The theory of diagonally dominant matrices is applied for the analysis, existence and character of the obtained solutions. We introduce a method for determining approximate solutions of a discrete analogue for operational differential equations and give conditions for their existence. The error of the approximation is estimated.

Operational and approximate solutions of a fractional integro-differential equation

We dedicate this paper to the 100th anniversary of the birth of Professor Jan Mikusinski. A time-fractional integro-differential equation is analyzed in the frames of the Mikusinski calculus. We present a method for obtaining the exact and the approximate operational solution. A numerical example and some plots are provided as illustration.

On the solution of a mathematical model of a viscoelastic bar

A hyperbolic type equation with certain initial and boundary conditions, appropriate for application of the Mikusinski calculus, is considered. Similar problems appeared as mathematical models of the shock between a solid body and a viscoelastic bar.