Цей посібник містить умови близько 400 олімпіадних задач зі шкільного курсу математики та їх розв’язання. Відібрано найоригінальніші задачі з обласних та Всеукраїнських олімпіад, які проводилися останніми роками. Матеріал систематизовано, подано у логічній послідовності. Чіткий виклад полегшує сприймання, а розв’язання дають можливість здійснити самоконтроль. Адресовано учням, абітурієнтам, вчителям, викладачам.

An introduction to the mathematical theory of multistage decision processes, this text takes a "functional equation" approach to the discovery of optimum policies. The text examines existence and uniqueness theorems, the optimal inventory equation, bottleneck problems in multistage production processes, a new formalism in the calculus of variation, multistage games, and more

Nowadays, not only tackling the phenomena of physics, but also many issues in technology, engineering and production, oftentimes require complicated mathematical processing. Recently, a CEO of an industrial plant revealed that, through application of a boundary value problem of elastic stress, he was able to save 30 percent in material. It seems that close cooperation of sci- ence with technology and production is more relevant today than ever. Many processes of production and technology can be simulated through differential equations. Knowledge of these mathematical procedures and their applica- tions is therefore not only essential in theory for the student, but also vital for the practitioner, the engineer, physicist or technologist.

This important book gives an interconnected presentation of some basic ideas, concepts, results of the theory of generalized functions (first of all, in the framework of the theory of distributions) and equations of mathematical physics. A part of the material is given according to the scheme: definition - theorem - proof. This scheme is convenient for presenting results in clear and concentrated form. However, it seems reasonable to give a student the possibility not only to study a priori given definitions and proofs of theorems, but also to discover them while considering the problems involved. A series of sections serve this purpose. Moreover, a part of the material is given as exercises and problems.

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Vol. 1 : A - N. - Р. 1 - 1147

Striking a careful balance between mathematical rigor and engineering-oriented applications, this textbook aims to maximize the readers' understanding of both the mathematical and engineering aspects of control theory. The bedrock elements of classical control theory are comprehensively covered: the Routh–Hurwitz theorem and applications, Nyquist diagrams, Bode plots, root locus plots, the design of controllers (phase-lag, phase-lead, lag-lead, and PID), and three further advanced topics: non-linear control, modern control and discrete-time control. A Mathematical Introduction to Control Theory will be an invaluable book for junior and senior level university students in engineering, particularly electrical engineering. Students with a good knowledge of algebra and complex variables will also find many interesting applications in this volume.

In this course, we will study some mathematical models and problems associated with basic problems in computer vision and digital image processing. The mathematical models are set up with various mathematical theories, ranging from Bayesian inference approach, Markov random fields, variational calculus, scale space theory, partial differential equations, to stochastic differential equations.

Robert J. Lang, one of the worlds foremost origami artists and scientists, presents the never-before-described mathematical and geometric principles that allow anyone to design original origami, something once restricted to an elite few. From the theoretical underpinnings to detailed step-by-step folding sequences, this book takes a modern look at the centuries-old art of origami.

Engineers around the world depend on MATLAB for its power, usability, and outstanding graphics capabilities. Yet too often, engineering students are either left on their own to acquire the background they need to use MATLAB, or they must learn the program concurrently within an advanced course. Both of these options delay students from solving realistic design problems, especially when they do not have a text focused on applications relevant to their field and written at the appropriate level of mathematics.Ideal for use as a short-course textbook and for self-study Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB fills that gap. Accessible after just one semester of calculus, it introduces the many practical analytical and numerical tools that are essential to success both in future studies and in professional life. Sharply focused on the needs of the electrical and computer engineering communities, the text provides a wealth of relevant exercises and design problems. Changes in MATLAB's version 6.0 are included in a special addendum.The lack of skills in fundamental quantitative tools can seriously impede progress in one's engineering studies or career. By working through this text, either in a lecture/lab environment or by themselves, readers will not only begin mastering MATLAB, but they will also hone their analytical and computational skills to a level that will help them to enjoy and succeed in subsequent electrical and computer engineering pursuits.

This book is mostly based on a series of notes for a primer course in electrical and computer engineering that I taught at the City College of New York School of Engineering. Each week, the class met for an hour of lecture and a three-hour computer laboratory session where students were divided into small groups of 12 to 15 students each. The students met in an informal learning community setting, a computer laboratory, where each student had the exclusive use of a PC. The small size of the groups permitted a great deal of individualized instruction, which was a key ingredient to cater successfully to the needs of students with heterogeneous high school backgrounds.

Vol. 1 : Ab - Cy. - 214 p.

Matlab is a commercial "Matrix Laboratory" package which operates as an interactive programming environment. It is a mainstay of the Mathematics Department software lineup and is also available for PC's and Macintoshes and may be found on the CIRCA VAXes. Matlab is well adapted to numerical experiments since the underlying algorithms for Matlab's builtin functions and supplied m-files are based on the standard libraries LINPACK and EISPACK. Matlab program and script files always have filenames ending with ".m"; the programming language is exceptionally straightforward since almost every data object is assumed to be an array. Graphical output is available to supplement numerical results.

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У теории групп три исторических корня: теория алгебраических уравнений, теория чисел и геометрия. Математики, стоящие у истоков теории групп, — это Леонард Эйлер, Карл Фридрих Гаусс, Жозеф Луи Лагранж, Нильс Хенрик Абель и Эварист Галуа. Галуа был первым математиком, связавшим теорию групп с другой ветвью абстрактной алгебры — теорией полей, разработав теорию, ныне называемую теорией Галуа.