11 results on '"Mathematics"'
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2. The Big Book of Real Analysis : From Numbers to Measures
- Author
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Syafiq Johar and Syafiq Johar
- Subjects
- Mathematics, Mathematical analysis, Sequences (Mathematics), Differential equations, Measure theory, Functions of real variables
- Abstract
This book provides an introduction to real analysis, a fundamental topic that is an essential requirement in the study of mathematics. It deals with the concepts of infinity and limits, which are the cornerstones in the development of calculus. Beginning with some basic proof techniques and the notions of sets and functions, the book rigorously constructs the real numbers and their related structures from the natural numbers. During this construction, the readers will encounter the notions of infinity, limits, real sequences, and real series. These concepts are then formalised and focused on as stand-alone objects. Finally, they are expanded to limits, sequences, and series of more general objects such as real-valued functions. Once the fundamental tools of the trade have been established, the readers are led into the classical study of calculus (continuity, differentiation, and Riemann integration) from first principles. The book concludes with an introduction to the studyof measures and how one can construct the Lebesgue integral as an extension of the Riemann integral. This textbook is aimed at undergraduate students in mathematics. As its title suggests, it covers a large amount of material, which can be taught in around three semesters. Many remarks and examples help to motivate and provide intuition for the abstract theoretical concepts discussed. In addition, more than 600 exercises are included in the book, some of which will lead the readers to more advanced topics and could be suitable for independent study projects. Since the book is fully self-contained, it is also ideal for self-study.
- Published
- 2024
3. PROJECT-BASED LEARNING (ABP) IN THE TEACHING OF MATHEMATICS IN THE CONTEXT OF COMPUTER PROGRAMMING.
- Author
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Inca Balseca, Cristian Luis, Inca Balseca, Evelyn Geovanna, Morocho Orellana, Julio Cesar, Morocho Caiza, Andrés Fernando, Coronel Maji, Franklin Marcelo, and Silva Godoy, Lizeth Fernanda
- Subjects
ACHIEVEMENT motivation ,COMPUTER programming ,PROJECT method in teaching ,ACADEMIC motivation ,DIFFERENTIAL equations ,MATHEMATICS - Abstract
Mathematics is one of the areas of knowledge where there are greater difficulties for its learning, due to its complexity, and the little usefulness that is perceived of them in real life, which is why pedagogical alternatives have been developed ( ABP). The usefulness of this tool in learning mathematics, which is sought by solving real problems through the use of mathematics. In this sense, the use of the PBL was evaluated in a group of 60 students of the Software career of the Polytechnic High School of Chimborazo (ESPOCH), 30 before the use of APB and 30 after its use comparing the changes in the academic performance of the students after the implementation of the PBL, as well as the perception of the students in relation to the interest, value, motivation and utilities of mathematics by solving problems using differential equations, The results found show that the students had a greater achievement when understanding and solving the equations adequately using derivation rules and analyzing and adequately interpret the information, which was related to a greater interest (50.85%), assessment (57.36%), satisfaction 57.62 (%) and utility 66.07%, despite the fact that the use of the PBL achieved a significant increase in grades, even the students state that they make a great effort to carry out projects in the area of mathematics, which was expressed by more than half of the students approached, the findings found lead to the conclusion that the use of this learning tool translates into a significant improvement in the acquisition of mathematical skills since a greater understanding and importance of the use of the itself, increases the interest and motivation of students for their study. [ABSTRACT FROM AUTHOR]
- Published
- 2023
4. New Trends in the Applications of Differential Equations in Sciences : NTADES 2022, Sozopol, Bulgaria, June 14–17
- Author
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Angela Slavova and Angela Slavova
- Subjects
- Differential equations, Mathematical analysis, Mathematical physics, Mathematics
- Abstract
This book convenes peer-reviewed, selected papers presented at the Ninth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Sozopol, Bulgaria, June 17–20, 2022. The works are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis.In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them for solving real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations.The NTADES 2022 conference was organized in cooperation with the Society of Industrial and Applied Mathematics (SIAM), the major international organization for Industrial and Applied Mathematics and for the promotion of interdisciplinary collaboration between applied mathematics and science, engineering, finance, and neuroscience.
- Published
- 2023
5. Calculus III : Practice Problems, Methods, and Solutions
- Author
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Mehdi Rahmani-Andebili and Mehdi Rahmani-Andebili
- Subjects
- Engineering mathematics, Mathematics, Mathematical analysis, Mathematical optimization, Calculus of variations, Differential equations
- Abstract
This study guide is designed for students taking a Calculus III course. The textbook includes examples, questions, and practice problems that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. The material covered in the book includes linear algebra and analytical geometry; lines, surfaces, and vector functions in three-dimensional coordinate systems; multiple-variable functions; multiple integrals and their applications; line integrals and their applications. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve students'problem-solving skills and foster a solid understanding of calculus, which will benefit them in all of their calculus-based courses.
- Published
- 2023
6. Analysis, Applications, and Computations : Proceedings of the 13th ISAAC Congress, Ghent, Belgium, 2021
- Author
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Uwe Kähler, Michael Reissig, Irene Sabadini, Jasson Vindas, Uwe Kähler, Michael Reissig, Irene Sabadini, and Jasson Vindas
- Subjects
- Mathematical analysis, Differential equations, Mathematics
- Abstract
This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium.The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.
- Published
- 2023
7. Advanced Topics in Fractional Differential Equations : A Fixed Point Approach
- Author
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Mouffak Benchohra, Erdal Karapinar, Jamal Eddine Lazreg, Abdelkrim Salim, Mouffak Benchohra, Erdal Karapinar, Jamal Eddine Lazreg, and Abdelkrim Salim
- Subjects
- Differential equations, Mathematics, Mathematical analysis, Integral equations, Difference equations, Functional equations, Functional analysis
- Abstract
This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers'understanding of the concepts presented. Includes illustrations in order to support readers understanding of the presented concepts · Approaches the topic of fractional differential equations while employing fixed point theorems as tools · Presents novel results, which build upon previous literature and many years of research by the authors
- Published
- 2023
8. Boundary Value Problems : Advanced Fractional Dynamic Equations on Time Scales
- Author
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Svetlin Georgiev and Svetlin Georgiev
- Subjects
- Mathematics, Mathematical analysis, Differential equations, Dynamical systems, Special functions
- Abstract
This book explores boundary value problems for fractional dynamic equations on arbitrary time scales, including Caputo fractional dynamic equations, impulsive Caputo fractional dynamic equations, and impulsive Riemann-Liouville fractional dynamic equations. The author provides an introduction to each fractional dynamic equation before delving into the problems. The book also covers initial value problems, boundary value problems, initial boundary value problems for each type of equation. The author provides integral representations of the solutions and proves the existence and uniqueness of the solutions.
- Published
- 2023
9. Boundary Value Problems : Essential Fractional Dynamic Equations on Time Scales
- Author
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Svetlin Georgiev and Svetlin Georgiev
- Subjects
- Mathematics, Mathematical analysis, Differential equations, Dynamical systems, Dynamics, Nonlinear theories, Special functions
- Abstract
This book explores boundary value problems for Riemann-Liouville fractional dynamic equations on arbitrary time scales as well as the shifting problem on the whole time scale. The author includes an introductory overview of fractional dynamic calculus on time scales. The book also introduces the Laplace transform on arbitrary time scales, including the bilateral Laplace transform, the Laplace transform of power series, and a deduction of an inverse formula. The author then discusses the generalized convolutions of functions on arbitrary time scales and the shifting problem for existence of solutions. The book moves on to cover boundary value problems and initial boundary value problems for some classes Riemann-Liouville fractional dynamic equations.
- Published
- 2023
10. Fractional Differential Equations : New Advancements for Generalized Fractional Derivatives
- Author
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Mouffak Benchohra, Erdal Karapınar, Jamal Eddine Lazreg, Abdelkrim Salim, Mouffak Benchohra, Erdal Karapınar, Jamal Eddine Lazreg, and Abdelkrim Salim
- Subjects
- Differential equations, Mathematics, Mathematical analysis, Integral equations, Difference equations, Functional equations, Functional analysis
- Abstract
This book covers problems involving a variety of fractional differential equations, as well as some involving the generalized Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations based on the most recent research in the area. The book discusses the classic and novel fixed point theorems related to the measure of noncompactness in Banach spaces and explains how to utilize them as tools. The authors build each chapter upon the previous one, helping readers to develop their understanding of the topic. The book includes illustrated results, analysis, and suggestions for further study.
- Published
- 2023
11. Analytical Methods for Solving Nonlinear Partial Differential Equations
- Author
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Daniel Arrigo and Daniel Arrigo
- Subjects
- Differential equations, Mathematics, Mathematical analysis
- Abstract
This textbook provides an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, readers are introduced to techniques to obtain exact solutions of NLPDEs. The chapters include the following topics: Nonlinear PDEs are Everywhere; Differential Substitutions; Point and Contact Transformations; First Integrals; and Functional Separability. Readers are guided through these chapters and are provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. This Second Edition includes a new method of generating contact transformations and focuses on a solution method (parametric Legendre transformations) to solve a particular class of two nonlinear PDEs.
- Published
- 2022
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