{"title":"Ordinary","description":"\u003cp\u003eOrdinary differential equations, often abbreviated as ODEs, address equations involving functions of one independent variable and their derivatives. This field focuses on formulating, analyzing, and solving equations that model phenomena across mathematics, science, and engineering. Key topics include initial value problems, linear and nonlinear equations, and methods such as separation of variables and integrating factors.\u003c\/p\u003e\u003cp\u003eUnlike partial differential equations, which handle functions of multiple variables, ordinary differential equations concentrate on single-variable relationships. Readers interested in specialized subtopics—such as systems of ODEs, stability analysis, or numerical methods—can use subject-specific guides to deepen their study or connect their interest with broader themes in differential equations.\u003c\/p\u003e","products":[{"product_id":"nonlinear-interpolation-boundary-value-problems-9789814733472-new","title":"Nonlinear Interpolation and Boundary Value Problems","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis book is devoted to the study of boundary value problems for nonlinear ordinary differential equations and focuses on questions related to the study of nonlinear interpolation. In 1967, Andrzej Lasota and Zdzislaw Opial showed that, under suitable hypotheses, if solutions of a second-order nonlinear differential equation passing through two distinct points are unique, when they exist, then, in fact, a solution passing through two distinct points does exist. That result, coupled with the pioneering work of Philip Hartman on what was then called unrestricted \u003cem\u003en\u003c\/em\u003e-parameter families, has stimulated 50 years of development in the study of solutions of boundary value problems as nonlinear interpolation problems.\u003c\/p\u003e\u003cp\u003eThe purpose of this book is two-fold. First, the results that have been generated in the past 50 years are collected for the first time to produce a comprehensive and coherent treatment of what is now a well-defined area of study in the qualitative theory of ordinary differential equations. Second, methods and technical tools are sufficiently exposed so that the interested reader can contribute to the study of nonlinear interpolation.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543615897890,"sku":"9789814733472-new","price":111.38,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814733472.jpg?v=1776386652"},{"product_id":"ordinary-partial-differential-equations-beginner-9789814723992-new","title":"Ordinary and Partial Differential Equations for the Beginner","description":"\u003cp\u003eThis textbook is intended for college, undergraduate and graduate students, emphasizing mainly on ordinary differential equations. However, the theory of characteristics for first order partial differential equations and the classification of second order linear partial differential operators are also included. It contains the basic material starting from elementary solution methods for ordinary differential equations to advanced methods for first order partial differential equations.\u003c\/p\u003e\u003cp\u003eIn addition to the theoretical background, solution methods are strongly emphasized. Each section is completed with problems and exercises, and the solutions are also provided. There are special sections devoted to more applied tools such as implicit equations, Laplace transform, Fourier method, etc. As a novelty, a method for finding exponential polynomial solutions is presented which is based on the author's work in spectral synthesis. The presentation is self-contained, provided the reader has general undergraduate knowledge.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543619436834,"sku":"9789814723992-new","price":47.97,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814723992.jpg?v=1776386803"},{"product_id":"introduction-differential-equations-applications-9789813276659-new","title":"An Introduction to Differential Equations with Applications","description":"\u003cp\u003eThis book is for students in a first course in ordinary differential equations. The material is organized so that the presentations begin at a reasonably introductory level. Subsequent material is developed from this beginning. As such, readers with little experience can start at a lower level, while those with some experience can use the beginning material as a review, or skip this part to proceed to the next level.\u003c\/p\u003e\u003cp\u003eThe book contains methods of approximation to solutions of various types of differential equations with practical applications, which will serve as a guide to programming so that such differential equations can be solved numerically with the use of a computer. Students who intend to pursue a major in engineering, physical sciences, or mathematics will find this book useful.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543839244578,"sku":"9789813276659-new","price":175.82,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813276659.jpg?v=1776392695"},{"product_id":"ordin-diff-equa-bound-v2-9789813274020-new","title":"Ordin Diff Equa \u0026 Bound ..(V2)","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.\u003c\/p\u003e\u003cp\u003eA discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.\u003c\/p\u003e\u003cp\u003eThe important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543874896162,"sku":"9789813274020-new","price":103.06,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813274020.jpg?v=1776393304"},{"product_id":"lect-prob-sol-ordin-2nd-ed-9789813226135-new","title":"Lect, Prob \u0026 Sol Ordin (2nd Ed)","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis unique book on ordinary differential equations addresses practical issues of composing and solving differential equations by demonstrating the detailed solutions of more than 1,000 examples. The initial draft was used to teach more than 10,000 advanced undergraduate students in engineering, physics, economics, as well as applied mathematics. It is a good source for students to learn problem-solving skills and for educators to find problems for homework assignments and tests. The 2nd edition, with at least 100 more examples and five added subsections, has been restructured to flow more pedagogically.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543913660706,"sku":"9789813226135-new","price":61.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813226135.jpg?v=1776394452"},{"product_id":"lect-prob-sol-ordin-2nd-ed-9789813226128-new","title":"Lect, Prob \u0026 Sol Ordin (2nd Ed)","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis unique book on ordinary differential equations addresses practical issues of composing and solving differential equations by demonstrating the detailed solutions of more than 1,000 examples. The initial draft was used to teach more than 10,000 advanced undergraduate students in engineering, physics, economics, as well as applied mathematics. It is a good source for students to learn problem-solving skills and for educators to find problems for homework assignments and tests. 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It also includes classical and new methods and techniques to deal with the lack of compactness of the related operators.\u003c\/p\u003e\u003cp\u003eThe reader will find a selection of original and recent results in this field, conditions to obtain solutions with particular qualitative properties, such as homoclinic and heteroclinic solutions and its relation with the solutions of Lidstone problems on all the real line.\u003c\/p\u003e\u003cp\u003eEach chapter contains applications to real phenomena, to classical equations or problems, with a common denominator: they are defined on unbounded intervals and the existing results in the literature are scarce or proven only numerically in discrete cases.\u003c\/p\u003e\u003cp\u003eThe last part features some higher order functional problems, which generalize the classical two-point or multi-point boundary conditions, to more comprehensive data where an overall behavior of the unknown functions and their derivatives is involved.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543936434466,"sku":"9789813209909-new","price":103.05,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813209909.jpg?v=1776395111"},{"product_id":"basic-theo-fract-differ-2nd-ed-9789813148161-new","title":"Basic Theory of Fractional Differential Equations (Second Edition)","description":"\u003cp\u003e\u003cem\u003e\"The book is a good resource to familiarize oneself with current achievements in the theory of fractional differential equations of various types. It is well written, and every chapter is equipped with an interesting introduction.\"\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003eMathematical Reviews Clippings\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cem\u003e\"The last chapter of this book is devoted to fractional partial differential equations. It is very useful for readers who want to do theoretical work in this area.\"\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003eZentralblatt MATH\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis invaluable monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary and partial differential equations. It provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the technique of Picard operators, critical point theory and semigroup theory. Based on the research work carried out by the authors and other experts during the past seven years, the contents are very recent and comprehensive.\u003c\/p\u003e\u003cp\u003eIn this edition, two new topics have been added, that is, fractional impulsive differential equations, and fractional partial differential equations including fractional Navier-Stokes equations and fractional diffusion equations.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544000069922,"sku":"9789813148161-new","price":143.59,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813148161.jpg?v=1776395842"},{"product_id":"stieltjes-differential-calculus-applications-9789811294228-new","title":"Stieltjes Differential Calculus with Applications","description":"\u003cp\u003eThe Stieltjes derivative is a modification of the usual derivative through a nondecreasing and left-continuous map. This change in the definition allows us to study several differential problems under the same framework.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis monograph is the first published book that offers a comprehensive view of the fundamentals of Stieltjes calculus and its applications, making it approachable to newcomers and experts. It aims to provide an integrated approach to the foundations and recent developments in the area of the Stieltjes derivatives and the qualitative theory of the Stieltjes differential equations. Through 10 pedagogically organized chapters, the authors examine a wide scope of the concept of the Stieltjes derivative and its applications. Each chapter focuses on theory, and proofs, and contains sufficient examples to enrich the reader's understanding.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe Stieltjes derivative contains the Hilger delta derivative on time scales. Thus, offering a new unification and extension of continuous and discrete calculus. Further, a study of differential equations in the sense of the Stieltjes derivative allows the study of many classical problems in a unique framework. This theory has the advantage that ordinary differential equations, ordinary difference equations, quantum difference equations, impulsive differential equations, dynamic equations on time scales, and generalized differential equations can be treated as particular instances of the Stieltjes differential equations. Hence, this book serves as a basic reference for researchers to harness this powerful technique further to unlock new insights and embrace the intricacies of natural processes. Researchers and graduate students at various levels interested in learning about the Stieltjes differential calculus and related fields will find this text a valuable resource of both introductory and advanced material.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544100471074,"sku":"9789811294228-new","price":134.24,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811294228.jpg?v=1776398348"},{"product_id":"ordinary-differential-equations-dynamical-point-view-9789811282683-new","title":"Ordinary Differential Equations: A Dynamical Point of View","description":"\u003cp\u003eOrdinary differential equations is a standard course in the undergraduate mathematics curriculum that usually comes after the first university calculus and linear algebra courses taken by a mathematics major. Such courses may also typically be attended by undergraduates from other areas of physical and social sciences, and engineering. The content of such a course has remained fairly static over time, despite the expansion of the topic into other disciplines as a result of the dynamical systems point of view.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis core undergraduate course updated from the dynamical systems perspective can easily be covered in one semester, with room for projects or more advanced topics tailored to the interests of the students.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544117510434,"sku":"9789811282683-new","price":51.08,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811282683.jpg?v=1776398868"},{"product_id":"basic-theo-fract-differ-3rd-ed-9789811271687-new","title":"Basic Theo Fract Differ (3rd Ed)","description":"\u003cp\u003eThis accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, Picard operators technique, critical point theory and semigroups theory. This book is based on the research work done so far by the author and other experts, and contains comprehensive up-to-date materials on the topic.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eIn this third edition, four new topics have been added: Hilfer fractional evolution equations and infinite interval problems, oscillations and nonoscillations, fractional Hamiltonian systems, fractional Rayleigh-Stokes equations, and wave equations. The bibliography has also been updated and expanded.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis book is useful to researchers, graduate or PhD students dealing with fractional calculus and applied analysis, differential equations, and related areas of research.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544196350242,"sku":"9789811271687-new","price":165.42,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811271687.jpg?v=1776399846"},{"product_id":"analysis-diff-equation-2nd-ed-9789811268564-new","title":"Analysis \u0026 Diff Equation (2nd Ed)","description":"\u003cp\u003eThe book presents advanced methods of integral calculus and optimization, the classical theory of ordinary and partial differential equations and systems of dynamical equations. It provides explicit solutions of linear and nonlinear differential equations, and implicit solutions with discrete approximations.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe main changes of this second edition are: the addition of theoretical sections proving the existence and the unicity of the solutions for linear differential equations on real and complex spaces and for nonlinear differential equations defined by locally Lipschitz functions of the derivatives, as well as the approximations of nonlinear parabolic, elliptic, and hyperbolic equations with locally differentiable operators which allow to prove the existence of their solutions; furthermore, the behavior of the solutions of differential equations under small perturbations of the initial condition or of the differential operators is studied.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544200413474,"sku":"9789811268564-new","price":103.05,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811268564.jpg?v=1776400025"},{"product_id":"dissipative-lattice-dynamical-systems-9789811267758-new","title":"Dissipative Lattice Dynamical Systems","description":"\u003cp\u003eThere is an extensive literature in the form of papers (but no books) on lattice dynamical systems. 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Furthermore, the problems of a one-dimensional lattice vibration, the keyboard percussion vibration and the eigenvalue problems in quantum mechanics, such as the Aharonov-Bohm effect, are also investigated in detail.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544359960866,"sku":"9789811247453-new","price":103.06,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811247453.jpg?v=1776402071"},{"product_id":"casual-calculus-v2-9789811241987-new","title":"Casual Calculus (V2)","description":"\u003cp\u003eYes, this is another Calculus book. However, it fits in a niche between the two predominant types of such texts. It could be used as a textbook, albeit a streamlined one - it contains exposition on each topic, with an introduction, rationale, train of thought, and solved examples with accompanying suggested exercises. It could be used as a solution guide - because it contains full written solutions to each of the hundreds of exercises posed inside. But its best position is right in between these two extremes. It is best used as a companion to a traditional text or as a refresher - with its conversational tone, its \"get right to it\" content structure, and its inclusion of complete solutions to many problems, it is a friendly partner for students who are learning Calculus, either in class or via self-study.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eExercises are structured in three sets to force multiple encounters with each topic. Solved examples in the text are accompanied by \"You Try It\" problems, which are similar to the solved examples; the students use these to see if they're ready to move forward. Then at the end of the section, there are \"Practice Problems\" more problems similar to the \"You Try It\" problems, but given all at once. 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Fractional-order differential and integral operators provide an excellent instrument for the description of memory and hereditary properties of various materials and processes, which contributed significantly to the popularity of the subject and motivated many researchers and modelers to shift their focus from classical models to fractional order models. Some peculiarities of physical, chemical or other processes happening inside the domain cannot be formulated with the aid of classical boundary conditions. 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New concepts of attractors in nonautonomous dynamical system are thus required.\u003c\/p\u003e\u003cp\u003eIn addition, the definition of a dynamical system itself needs to be generalised to the nonautonomous context. Here two possibilities are considered: two-parameter semigroups or processes and the skew product flows. Their attractors are defined in terms of families of sets that are mapped onto each other under the dynamics rather than a single set as in autonomous systems. Two types of attraction are now possible: pullback attraction, which depends on the behaviour from the system in the distant past, and forward attraction, which depends on the behaviour of the system in the distant future. These are generally independent of each other.\u003c\/p\u003e\u003cp\u003eThe component subsets of pullback and forward attractors exist in actual time. The asymptotic behaviour in the future limit is characterised by omega-limit sets, in terms of which form what are called forward attracting sets. They are generally not invariant in the conventional sense, but are asymptotically invariant in general and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant.\u003c\/p\u003e\u003cp\u003eMuch of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a \"Thousand Expert\" Professorship at the Huazhong University of Science and Technology in Wuhan.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544417730850,"sku":"9789811228650-new","price":61.48,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811228650.jpg?v=1776403401"},{"product_id":"nonlinear-higher-order-differential-integral-coupled-sys-9789811225123-new","title":"Nonlinear Higher Order Differential \u0026 Integral Coupled Sys","description":"\u003cp\u003eBoundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo-Krasnosel'skiĭ fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Carath\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544437588258,"sku":"9789811225123-new","price":103.05,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811225123.jpg?v=1776403747"},{"product_id":"casual-calculus-v3-9789811224898-new","title":"Casual Calculus (V3)","description":"\u003cp\u003eYes, this is another Calculus book. 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Solved examples in the text are accompanied by \"You Try It\" problems, which are similar to the solved examples; the students use these to see if they're ready to move forward. Then at the end of the section, there are \"Practice Problems\" more problems similar to the \"You Try It\" problems, but given all at once. Finally, each section has Challenge Problems - these lean to being equally or a bit more difficult than the others, and they allow students to check on what they've mastered.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe goal is to keep the students engaged with the text, and so the writing style is very informal, with attempts at humor along the way. 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But its best position is right in between these two extremes. It is best used as a companion to a traditional text or as a refresher - with its conversational tone, its \"get right to it\" content structure, and its inclusion of complete solutions to many problems, it is a friendly partner for students who are learning Calculus, either in class or via self-study.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eExercises are structured in three sets to force multiple encounters with each topic. Solved examples in the text are accompanied by \"You Try It\" problems, which are similar to the solved examples; the students use these to see if they're ready to move forward. Then at the end of the section, there are \"Practice Problems\" more problems similar to the \"You Try It\" problems, but given all at once. Finally, each section has Challenge Problems - these lean to being equally or a bit more difficult than the others, and they allow students to check on what they've mastered.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe goal is to keep the students engaged with the text, and so the writing style is very informal, with attempts at humor along the way. The target audience is STEM students including those in engineering and meteorology programs.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544438472994,"sku":"9789811224881-new","price":83.33,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811224881.jpg?v=1776403750"},{"product_id":"boundary-value-problems-fractional-differen-equations-sys-9789811224454-new","title":"Boundary Value Problems Fractional Differen Equations \u0026 Sys","description":"\u003cp\u003eThis book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eIn each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544439161122,"sku":"9789811224454-new","price":134.24,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811224454.jpg?v=1776403774"},{"product_id":"casual-calculus-v3-9789811223952-new","title":"Casual Calculus (V3)","description":"\u003cp\u003eYes, this is another Calculus book. However, it fits in a niche between the two predominant types of such texts. It could be used as a textbook, albeit a streamlined one - it contains exposition on each topic, with an introduction, rationale, train of thought, and solved examples with accompanying suggested exercises. It could be used as a solution guide - because it contains full written solutions to each of the hundreds of exercises posed inside. But its best position is right in between these two extremes. It is best used as a companion to a traditional text or as a refresher - with its conversational tone, its \"get right to it\" content structure, and its inclusion of complete solutions to many problems, it is a friendly partner for students who are learning Calculus, either in class or via self-study.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eExercises are structured in three sets to force multiple encounters with each topic. Solved examples in the text are accompanied by \"You Try It\" problems, which are similar to the solved examples; the students use these to see if they're ready to move forward. Then at the end of the section, there are \"Practice Problems\" more problems similar to the \"You Try It\" problems, but given all at once. Finally, each section has Challenge Problems - these lean to being equally or a bit more difficult than the others, and they allow students to check on what they've mastered.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe goal is to keep the students engaged with the text, and so the writing style is very informal, with attempts at humor along the way. 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The continuability of solutions, their continuous dependence on initial conditions, and their continuous dependence with respect to parameters are presented in detail. This is followed by a discussion of the differentiability of solutions with respect to initial conditions and with respect to parameters. Comparison results and differential inequalities are included as well.\u003c\/p\u003e\u003cp\u003eLinear systems of differential equations are treated in detail as is appropriate for a study of ODEs at this level. Just the right amount of basic properties of matrices are introduced to facilitate the observation of matrix systems and especially those with constant coefficients. Floquet theory for linear periodic systems is presented and used to analyze nonhomogeneous linear systems.\u003c\/p\u003e\u003cp\u003eStability theory of first order and vector linear systems are considered. 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