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Ordinary Differential Equations (Dover Books on Mathematics)
by Edward L. InceThe theory of ordinary differential equations in real and complex domains is here clearly explained and analyzed. Not only classical theory, but also the main developments of modern times are covered. Exhaustive sections on the existence and nature of solutions, continuous transformation groups, the algebraic theory of linear differential systems, and the solution of differential equations by contour integration are as valuable to the pure mathematician as the fine treatment of the equations of Legendre, Bessel, and Mathieu, the conditions for the oscillatory character of solutions of a differential equation, and the relation between a linear differential system and an integral equation are to the engineer and the physicist.Partial contents: real domain (elementary methods of integration, the existence and nature of solutions, continuous transformation-groups, linear differential equations-the general theory, with constant coefficients, solutions, algebraic theory, Sturmian theory, and later developments); complex domain (existence theorems, equations of first order, non-linear equations of higher order, solutions, systems, classifications of linear equations, oscillation theorems).
Ordinary Differential Equations: Basics and Beyond
by David G. Schaeffer John W. CainThis book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text. Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom).
Ordinary Differential Equations
by Bernd J. SchroersOrdinary Differential Equations introduces key concepts and techniques in the field and shows how they are used in current mathematical research and modelling. It deals specifically with initial value problems, which play a fundamental role in a wide range of scientific disciplines, including mathematics, physics, computer science, statistics and biology. This practical book is ideal for students and beginning researchers working in any of these fields who need to understand the area of ordinary differential equations in a short time.<P> Advisory: Bookshare has learned that this book offers only partial accessibility. We have kept it in the collection because it is useful for some of our members. To explore further access options with us, please contact us through the Book Quality link on the right sidebar. Benetech is actively working on projects to improve accessibility issues such as these.
Ordinary Differential Equations: Mathematical Tools For Physicists
by Raza Tahir-KheliThis textbook describes rules and procedures for the use of Differential Operators (DO) in Ordinary Differential Equations (ODE). The book provides a detailed theoretical and numerical description of ODE. It presents a large variety of ODE and the chosen groups are used to solve a host of physical problems. Solving these problems is of interest primarily to students of science, such as physics, engineering, biology and chemistry. <P><P> Scientists are greatly assisted by using the DO obeying several simple algebraic rules. The book describes these rules and, to help the reader, the vocabulary and the definitions used throughout the text are provided. A thorough description of the relatively straightforward methodology for solving ODE is given. <P><P>The book provides solutions to a large number of associated problems. ODE that are integrable, or those that have one of the two variables missing in any explicit form are also treated with solved problems. The physics and applicable mathematics are explained and many associated problems are analyzed and solved in detail. Numerical solutions are analyzed and the level of exactness obtained under various approximations is discussed in detail.
Ordinary Differential Equations and Dynamical Systems
by Thomas C. SiderisThis book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.
Ordinary Differential Equations and Mechanical Systems
by Jan AwrejcewiczThis book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization. Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition. The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.
Ordinary Differential Equations and Stability Theory: An Introduction (Dover Books on Mathematics)
by David A. SanchezThis brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations.The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.
Ordinary Differential Equations for Engineers: Problems with MATLAB Solutions
by Ali Ümit KeskinThis monograph presents teaching material in the field of differential equations while addressing applications and topics in electrical and biomedical engineering primarily. The book contains problems with varying levels of difficulty, including Matlab simulations. The target audience comprises advanced undergraduate and graduate students as well as lecturers, but the book may also be beneficial for practicing engineers alike.
Ordinary Differential Equations with Applications (Texts in Applied Mathematics #34)
by Carmen ChiconeThis book, developed during 20 years of the author teaching differential equations courses at his home university, is designed to serve as a text for a graduate level course focused on the central theory of the subject with attention paid to applications and connections to other advanced topics in mathematics. Core theory includes local existence and uniqueness, the phase plane, Poincaré-Bendixson theory, Lyapunov and linearized stability, linear systems, Floquet theory, the Grobman–Hartman theorem, persistence of rest points and periodic orbits, the stable and center manifold theorems, and bifurcation theory. This edition includes expanded treatment of deterministic chaos, perturbation theory for periodic solutions, boundary value problems, optimization, and a wide range of their applications. In addition, it contains a formulation and new proof of a theorem on instability of rest points in the presence of an eigenvalue with positive real part, and new proofs of differential inequalities and Lyapunov’s center theorem. New sections present discussions of global bifurcation, the Crandall–Rabinowitz theorem, and Alekseev’s formula. Of particular note is a new chapter on basic control theory, a discussion of optimal control, and a proof of a useful special case of the maximum principle. A key feature of earlier editions, a wide selection of original exercises, is respected in this edition with the inclusion of a wealth of new exercises. Reviews of the first edition:“As an applied mathematics text on linear and nonlinear equations, the book by Chicone is written with stimulating enthusiasm. It will certainly appeal to many students and researchers.”—F. Verhulst, SIAM Review “The author writes lucidly and in an engaging conversational style. His book is wide-ranging in its subject matter, thorough in its presentation, and written at a generally high level of generality, detail, and rigor.”—D. S. Shafer, Mathematical Reviews
Orienteering Problems: Models and Algorithms for Vehicle Routing Problems with Profits (EURO Advanced Tutorials on Operational Research)
by Pieter Vansteenwegen Aldy GunawanThis tutorial introduces readers to several variants of routing problems with profits. In these routing problems each node has a certain profit, and not all nodes need to be visited. Since the orienteering problem (OP) is by far the most frequently studied problem in this category of routing problems, the book mainly focuses on the OP. In turn, other problems are presented as variants of the OP, focusing on the similarities and differences. The goal of the OP is to determine a subset of nodes to visit and in which order, so that the total collected profit is maximized and a given time budget is not exceeded.The book provides a comprehensive review of variants of the OP, such as the team OP, the team OP with time windows, the profitable tour problem, and the prize-collecting travelling salesperson problem. In addition, it presents mathematical models and techniques for solving these OP variants and discusses their complexity. Several simple examples and benchmark instances, together with their best-known results, are also included. Finally, the book reviews the latest applications of these problems in the fields of logistics, tourism and others.
Origametry: Mathematical Methods in Paper Folding
by Thomas C. HullOrigami, the art of paper folding, has a rich mathematical theory. Early investigations go back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of the mathematics of folding. Besides its use in describing origami and designing new models, it is also finding real-world applications from building nano-scale robots to deploying large solar arrays in space. Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It brings together historical results, modern developments, and future directions into a cohesive whole. Over 180 figures illustrate the constructions described while numerous 'diversions' provide jumping-off points for readers to deepen their understanding. This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design. Educators, students, and enthusiasts will also find much to enjoy in this fascinating account of the mathematics of folding.
Origami Dots: Folding paper to explore geometry
by Andy ParkinsonAll the challenges in this entertaining puzzle book are the same. Fold the corner of the paper to a given dot and find the folded area. A small move of the target dot can drastically change the logic needed to find the solution to the challenge. The problems become increasingly complex as the book progresses, with possible solutions involving Pythagoras' and similar triangles as well as trigonometry and algebra. However, insights learnt from earlier challenges can help with those that follow. If at any point the challenge becomes too great, the answers can always be found by measurement with a ruler and directly calculating the area. The book encourages curiosity, a "find out what you can" approach that creates interesting and varied solution strategies. The aim is that deep thinking and geometrical reasoning can come out of exploring and discussing the paper folds. The challenges are for all ages (10 years and over). Thus, for teachers the book provides a rich source of challenges that have a similar appearance, yet hide an obvious method and require students to choose how to approach the problem. Comparing solution methods when checking the answers is also useful as the solutions highlight some fascinating facts linked with these simple folds.
Origami Tessellations: Awe-Inspiring Geometric Designs
by Eric GjerdeEric Gjerde demonstrates 25 of his favorite tessellations and turns them into projects for newcomers as well as experienced origamists. With step-by-step instructions, illustrated crease patterns, and how-to photos, you'll learn to create these wonderful designs yourself. Eric's first book covers the fundamentals of origami tessellations, provides history, and describes simple beginning techniques with detailed illustrations and photographs. An extensive gallery showcases tessellations folded by the world's leading origami fine artists---inspiring you to experiment, innovate, and eventually create your own unique designs.
The Original Area Mazes: 100 Addictive Puzzles to Solve with Simple Math—and Clever Logic! (Original Area Mazes)
by Alex Bellos Naoki Inaba Ryoichi MurakamiThe rules are simple . . . The math is easy . . .The puzzles get harder and harder! Once you match wits with area mazes, you’ll be hooked! Your quest is to navigate a network of rectangles to find a missing value.Just Remember:Area = length × widthUse spatial reasoning to find helpful relationshipsWhole numbers are all you need. You can always get the answer without using fractions! Originally invented for gifted students, area mazes (menseki meiro), have taken all of Japan by storm. Are you a sudoku fanatic? Do you play brain games to stay sharp? Did you love geometry . . . or would you like to finally show it who’s boss? Feed your brain some area mazes—they could be just what you’re craving!
The Original Area Mazes, Volume 2: 100 More Addictive Puzzles to Solve with Simple Math—and Clever Logic! (Original Area Mazes)
by Naoki Inaba Ryoichi MurakamiThe rules are simple . . . The math is easy . . . The puzzles get harder and harder! Hooked on area mazes? YOU’RE IN LUCK! Volume Two delivers 100 more puzzles. Your quest is to navigate a network of rectangles to find a missing value. Just remember: Area = length × widthUse spatial reasoning to find helpful relationshipsWhole numbers are all you need. You can always get the answer without using fractions! Originally invented for gifted students, area mazes have taken all of Japan by storm. Are you a sudoku fanatic? Do you play brain games to stay sharp? Did you love geometry . . . or would you like to finally show it who’s boss? Try area mazes—they could be just what you’re craving!
The Origins and Evolution of Family Planning Programs in Developing Countries
by Judith R. SeltzerThis book analyzes the origins and rationale of family planning programs and how they have evolved based on experience in different country settings.
Origins and Varieties of Logicism: On the Logico-Philosophical Foundations of Mathematics (Routledge Studies in the Philosophy of Mathematics and Physics)
by Francesca Boccuni Andrea SereniThis book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism.The essays, written by prominent scholars, are divided into three thematic sections. Part I focuses on major authors like Frege, Dedekind, and Russell, providing a historical and theoretical exploration of such figures in the philosophical and mathematical milieu in which logicist views were first expounded. Part II sheds new light on the interconnections between these founding figures and a number of influential other traditions, represented by authors like Hilbert, Husserl, and Peano, as well as on the reconsideration of logicism by Carnap and the logical empiricists. Finally, Part III assesses the legacy of such authors and of logicist themes for contemporary philosophy of mathematics, offering new perspectives on highly debated topics—neo-logicism and its extension to accounts of ordinal numbers and set-theory, the comparison between neo-Fregean and neo-Dedekindian varieties of logicism, and the relation between logicist foundational issues and empirical research on numerical cognition—which define the prospects of logicism in the years to come.This book offers a comprehensive account of the development of logicism and its contemporary relevance for the logico-philosophical foundations of mathematics. It will be of interest to graduate students and researchers working in philosophy of mathematics, philosophy of logic, and the history of analytic philosophy.
The Origins of Cauchy's Rigorous Calculus (Dover Books on Mathematics)
by Judith V. GrabinerThis text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his peers. These intellectuals transformed the uses of calculus from problem-solving methods into a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. Beginning with a survey of the characteristic 19th-century view of analysis, the book proceeds to an examination of the 18th-century concept of calculus and focuses on the innovative methods of Cauchy and his contemporaries in refining existing methods into the basis of rigorous calculus. 1981 edition.
The Origins of Mathematical Knowledge in Childhood (Studies in Mathematical Thinking and Learning Series)
by Catherine SophianThis book examines the origins and development of children's mathematical knowledge. It contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the concept of number builds upon more basic concepts of equality, inequality, and less-than and greater-than relations, which derive from comparisons between unenumerated quantities such as lengths. The concept of number combines these basic comparative concepts with the concept of a unit of measure, which allows one quantity to be described as a multiple of another. Sophian examines these alternative accounts of children's developing mathematical knowledge in the light of research: on children's counting; on their reasoning about continuous quantities such as length and area; on the development of the concept of unit; on additive and multiplicative reasoning; and on knowledge about fractions. In the closing chapters, Sophian draws out the developmental and the educational implications of the research and theory presented. Developmentally, the comparison-of-quantities position undermines the idea that numerical knowledge develops through domain-specific learning mechanisms in that it links numerical development both to physical knowledge about objects, which is the starting point for the concept of unit, and to the acquisition of linguistic number terms. Instructionally, the comparison-of-quantities perspective diverges from the counting-first perspective in that it underscores the continuity between whole-number arithmetic and fraction learning that stems from the importance of the concept of unit for both. Building on this idea, Sophian advances three instructional recommendations: First, instruction about numbers should always be grounded in thinking about quantities and how numbers represent the relations between them; second, instruction in the early years should always be guided by a long-term perspective in which current objectives are shaped by an understanding of their role in the overall course of mathematics learning; and third, instruction should be directly toward promoting the acquisition of the most general mathematical knowledge possible. The Origins of Mathematical Knowledge in Childhood is intended for researchers, professionals, and graduate students in developmental psychology, educational psychology, and mathematics education, and as a supplementary text for advanced undergraduate courses in cognitive development, educational psychology, and mathematics education.
Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek, and Arabic Roots
by Anthony Lo BelloThe most comprehensive math root dictionary ever published.Outstanding Academic Title, ChoiceDo you ever wonder about the origins of mathematical terms such as ergodic, biholomorphic, and strophoid? Here Anthony Lo Bello explains the roots of these and better-known words like asymmetric, gradient, and average. He provides Greek, Latin, and Arabic text in its original form to enhance each explanation. This sophisticated, one-of-a-kind reference for mathematicians and word lovers is based on decades of the author's painstaking research and work.Origins of Mathematical Words supplies definitions for words such as conchoid (a shell-shaped curve derived from the Greek noun for "mussel") and zenith (Arabic for "way overhead"), as well as approximation (from the Latin proximus, meaning "nearest"). These and hundreds of other terms wait to be discovered within the pages of this mathematical and etymological treasure chest.
ORIGO Stepping Stones 2.0, Comprehensive Mathematics [Grade 2], Student Book A
by James Burnett Calvin Irons Peter StowasserNIMAC-sourced textbook
ORIGO Stepping Stones 2.0, Comprehensive Mathematics [Grade 2], Student Book B
by James Burnett Calvin Irons Peter StowasserNIMAC-sourced textbook
ORIGO Stepping Stones 2.0, Comprehensive Mathematics [Grade 5], Student Book A
by James Burnett Calvin Irons Peter StowasserNIMAC-sourced textbook
ORIGO Stepping Stones 2.0, Comprehensive Mathematics [Grade 5], Student Book B
by James Burnett Calvin Irons Peter Stowasser Allan TurtonNIMAC-sourced textbook
ORIGO Stepping Stones, Core Mathematics [Grade 2], Practice Book
by James Burnett Calvin Irons Peter StowasserNIMAC-sourced textbook