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| consider the initial value problem: Ordinary Differential Equations Kenneth B. Howell, 2019-12-06 The Second Edition of Ordinary Differential Equations: An Introduction to the Fundamentals builds on the successful First Edition. It is unique in its approach to motivation, precision, explanation and method. Its layered approach offers the instructor opportunity for greater flexibility in coverage and depth. Students will appreciate the author’s approach and engaging style. Reasoning behind concepts and computations motivates readers. New topics are introduced in an easily accessible manner before being further developed later. The author emphasizes a basic understanding of the principles as well as modeling, computation procedures and the use of technology. The students will further appreciate the guides for carrying out the lengthier computational procedures with illustrative examples integrated into the discussion. Features of the Second Edition: Emphasizes motivation, a basic understanding of the mathematics, modeling and use of technology A layered approach that allows for a flexible presentation based on instructor's preferences and students’ abilities An instructor’s guide suggesting how the text can be applied to different courses New chapters on more advanced numerical methods and systems (including the Runge-Kutta method and the numerical solution of second- and higher-order equations) Many additional exercises, including two chapters of review exercises for first- and higher-order differential equations An extensive on-line solution manual About the author: Kenneth B. Howell earned bachelor’s degrees in both mathematics and physics from Rose-Hulman Institute of Technology, and master’s and doctoral degrees in mathematics from Indiana University. For more than thirty years, he was a professor in the Department of Mathematical Sciences of the University of Alabama in Huntsville. Dr. Howell published numerous research articles in applied and theoretical mathematics in prestigious journals, served as a consulting research scientist for various companies and federal agencies in the space and defense industries, and received awards from the College and University for outstanding teaching. He is also the author of Principles of Fourier Analysis, Second Edition (Chapman & Hall/CRC, 2016). |
| consider the initial value problem: CK-12 Calculus CK-12 Foundation, 2010-08-15 CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration. |
| consider the initial value problem: Differential Equations and Boundary Value Problems Charles Henry Edwards, David E. Penney, David Calvis, 2015 Written from the perspective of the applied mathematician, the latest edition of this bestselling book focuses on the theory and practical applications of Differential Equations to engineering and the sciences. Emphasis is placed on the methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace the development of the discipline and identify outstanding individual contributions. This book builds the foundation for anyone who needs to learn differential equations and then progress to more advanced studies. |
| consider the initial value problem: Numerical Solution of Initial-value Problems in Differential-algebraic Equations K. E. Brenan, S. L. Campbell, L. R. Petzold, 1996-01-01 Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. This classic edition, originally published in 1989, is the only general DAE book available. It not only develops guidelines for choosing different numerical methods, it is the first book to discuss DAE codes, including the popular DASSL code. An extensive discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAE's. New to this edition is a chapter that brings the discussion of DAE software up to date. The objective of this monograph is to advance and consolidate the existing research results for the numerical solution of DAE's. The authors present results on the analysis of numerical methods, and also show how these results are relevant for the solution of problems from applications. They develop guidelines for problem formulation and effective use of the available mathematical software and provide extensive references for further study. |
| consider the initial value problem: Dennis G. Zill, Warren S. Wright, 2009-12-21 Now with a full-color design, the new Fourth Edition of Zill's Advanced Engineering Mathematics provides an in-depth overview of the many mathematical topics necessary for students planning a career in engineering or the sciences. A key strength of this text is Zill's emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Fourth Edition is comprehensive, yet flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. Numerous new projects contributed by esteemed mathematicians have been added. New modern applications and engaging projects makes Zill's classic text a must-have text and resource for Engineering Math students! |
| consider the initial value problem: Handbook of Differential Equations Daniel Zwillinger, Vladimir Dobrushkin, 2021-12-30 Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers. The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations, as well as numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations. Included for nearly every method are: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition. |
| consider the initial value problem: Elementary Differential Equations and Boundary Value Problems William E. Boyce, Richard C. DiPrima, Douglas B. Meade, 2017-05-10 Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. |
| consider the initial value problem: Hans Lewy Selecta Hans Lewy, 2002 The work of Hans Lewy (1904--1988) has had a profound influence in the direction of applied mathematics and partial differential equations, in particular, from the late 1920s. Two of the particulars are well known. The Courant--Friedrichs--Lewy condition (1928), or CFL condition, was devised to obtain existence and approximation results. This condition, relating the time and spatial discretizations for finite difference schemes, is now universally employed in the simulation of solutions of equations describing propagation phenomena. Lewy's example of a linear equation with no solution (1957), with its attendant consequence that most equations have no solution, was not merely an unexpected fact, but changed the viewpoint of the entire field. Lewy made pivotal contributions in many other areas, for example, the regularity theory of elliptic equations and systems, the Monge--Ampère Equation, the Minkowski Problem, the asymptotic analysis of boundary value problems, and several complex variables. He was among the first to study variational inequalities. In much of his work, his underlying philosophy was that simple tools of function theory could help one understand the essential concepts embedded in an issue, although at a cost in generality. This approach was extremely successful. In this two-volume work, most all of Lewy's papers are presented, in chronological order. They are preceded by several short essays about Lewy himself, prepared by Helen Lewy, Constance Reid, and David Kinderlehrer, and commentaries on his work by Erhard Heinz, Peter Lax, Jean Leray, Richard MacCamy, François Treves, and Louis Nirenberg. Additionally, there are Lewy's own remarks on the occasion of his honorary degree from the University of Bonn. |
| consider the initial value problem: Calculus Howard Anton, Irl C. Bivens, Stephen Davis, 2016-06-08 This text is an unbound, three hole punched version. Access to WileyPLUS sold separately. Calculus, 11th Edition Binder Ready Version strives to increase student comprehension and conceptual understanding through a balance between rigor and clarity of explanations; sound mathematics; and excellent exercises, applications, and examples. Anton pedagogically approaches Calculus through the Rule of Four, presenting concepts from the verbal, algebraic, visual, and numerical points of view. |
| consider the initial value problem: Applied Partial Differential Equations: An Introduction Alan Jeffrey, 2003 This book is written to meet the needs of undergraduates in applied mathematics, physics and engineering studying partial differential equations. It is a more modern, comprehensive treatment intended for students who need more than the purely numerical solutions provided by programs like the MATLAB PDE Toolbox, and those obtained by the method of separation of variables, which is usually the only theoretical approach found in the majority of elementary textbooks. This will fill a need in the market for a more modern text for future working engineers, and one that students can read and understand much more easily than those currently on the market. * Includes new and important materials necessary to meet current demands made by diverse applications * Very detailed solutions to odd numbered problems to help students * Instructor's Manual Available |
| consider the initial value problem: Elementary Differential Equations Charles Roberts, 2018-12-13 Elementary Differential Equations, Second Edition is written with the knowledge that there has been a dramatic change in the past century in how solutions to differential equations are calculated. However, the way the topic has been taught in introductory courses has barely changed to reflect these advances, which leaves students at a disadvantage. This second edition has been created to address these changes and help instructors facilitate new teaching methods and the latest tools, which includes computers. The text is designed to help instructors who want to use computers in their classrooms. It accomplishes this by emphasizing and integrating computers in teaching elementary or ordinary differential equations. Many examples and exercises included in the text require the use of computer software to solve problems. It should be noted that since instructors use their own preferred software, this book has been written to be independent of any specific software package. Features: Focuses on numerical methods and computing to generate solutions Features extensive coverage of nonlinear differential equations and nonlinear systems Includes software programs to solve problems in the text which are located on the author's website Contains a wider variety of non-mathematical models than any competing textbook This second edition is a valuable, up-to-date tool for instructors teaching courses about differential equations. It serves as an excellent introductory textbook for undergraduate students majoring in applied mathematics, computer science, various engineering disciplines and other sciences. They also will find that the textbook will aide them greatly in their professional careers because of its instructions on how to use computers to solve equations. |
| consider the initial value problem: An Introduction to Nonlinear Boundary Value Problems Lakshmikantham, 1974-05-31 A book on an advanced level that exposes the reader to the fascinating field of differential equations and provides a ready access to an up-to-date state of this art is of immense value. This book presents a variety of techniques that are employed in the theory of nonlinear boundary value problems. For example, the following are discussed: - methods that involve differential inequalities; - shooting and angular function techniques; - functional analytic approaches; - topological methods. |
| consider the initial value problem: Numerical Partial Differential Equations: Finite Difference Methods J.W. Thomas, 2013-12-01 What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible. |
| consider the initial value problem: A First Course in Applied Mathematics Jorge Rebaza, 2021-04-27 Explore real-world applications of selected mathematical theory, concepts, and methods Exploring related methods that can be utilized in various fields of practice from science and engineering to business, A First Course in Applied Mathematics details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems. Written at a level that is accessible to readers from a wide range of scientific and engineering fields, the book masterfully blends standard topics with modern areas of application and provides the needed foundation for transitioning to more advanced subjects. The author utilizes MATLAB® to showcase the presented theory and illustrate interesting real-world applications to Google's web page ranking algorithm, image compression, cryptography, chaos, and waste management systems. Additional topics covered include: Linear algebra Ranking web pages Matrix factorizations Least squares Image compression Ordinary differential equations Dynamical systems Mathematical models Throughout the book, theoretical and applications-oriented problems and exercises allow readers to test their comprehension of the presented material. An accompanying website features related MATLAB® code and additional resources. A First Course in Applied Mathematics is an ideal book for mathematics, computer science, and engineering courses at the upper-undergraduate level. The book also serves as a valuable reference for practitioners working with mathematical modeling, computational methods, and the applications of mathematics in their everyday work. |
| consider the initial value problem: Functional Differential Operators and Equations U.G. Kurbatov, 1999-04-30 This book deals with linear functional differential equations and operator theory methods for their investigation. The main topics are: the equivalence of the input-output stability of the equation Lx = &mathsf; and the invertibility of the operator L in the class of casual operators; the equivalence of input-output and exponential stability; the equivalence of the dichotomy of solutions for the homogeneous equation Lx = 0 and the invertibility of the operator L; the properties of Green's function; the independence of the stability of an equation from the norm on the space of solutions; shift invariant functional differential equations in Banach space; the possibility of the reduction of an equation of neutral type to an equation of retarded type; special full subalgebras of integral and difference operators, and operators with unbounded memory; and the analogue of Fredholm's alternative for operators with almost periodic coefficients where one-sided invertibility implies two-sided invertibility. Audience: This monograph will be of interest to students and researchers working in functional differential equations and operator theory and is recommended for graduate level courses. |
| consider the initial value problem: Ordinary Differential Equations Hartmut Logemann, Eugene P. Ryan, 2014-07-08 The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook literature. The following topics are particularly emphasised: • existence, uniqueness and continuation of solutions, • continuous dependence on initial data, • flows, • qualitative behaviour of solutions, • limit sets, • stability theory, • invariance principles, • introductory control theory, • feedback and stabilization. The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability. Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science. |
| consider the initial value problem: Introduction to Partial Differential Equations with Applications E. C. Zachmanoglou, Dale W. Thoe, 2012-04-20 This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers. |
| consider the initial value problem: Differential Equations for Engineers Wei-Chau Xie, 2010-04-26 Xie presents a systematic introduction to ordinary differential equations for engineering students and practitioners. Mathematical concepts and various techniques are presented in a clear, logical, and concise manner. Various visual features are used to highlight focus areas. Complete illustrative diagrams are used to facilitate mathematical modeling of application problems. Readers are motivated by a focus on the relevance of differential equations through their applications in various engineering disciplines. Studies of various types of differential equations are determined by engineering applications. Theory and techniques for solving differential equations are then applied to solve practical engineering problems. A step-by-step analysis is presented to model the engineering problems using differential equations from physical principles and to solve the differential equations using the easiest possible method. This book is suitable for undergraduate students in engineering. |
| consider the initial value problem: Partial Differential Equations of Applied Mathematics Erich Zauderer, 2011-10-24 This new edition features the latest tools for modeling, characterizing, and solving partial differential equations The Third Edition of this classic text offers a comprehensive guide to modeling, characterizing, and solving partial differential equations (PDEs). The author provides all the theory and tools necessary to solve problems via exact, approximate, and numerical methods. The Third Edition retains all the hallmarks of its previous editions, including an emphasis on practical applications, clear writing style and logical organization, and extensive use of real-world examples. Among the new and revised material, the book features: * A new section at the end of each original chapter, exhibiting the use of specially constructed Maple procedures that solve PDEs via many of the methods presented in the chapters. The results can be evaluated numerically or displayed graphically. * Two new chapters that present finite difference and finite element methods for the solution of PDEs. Newly constructed Maple procedures are provided and used to carry out each of these methods. All the numerical results can be displayed graphically. * A related FTP site that includes all the Maple code used in the text. * New exercises in each chapter, and answers to many of the exercises are provided via the FTP site. A supplementary Instructor's Solutions Manual is available. The book begins with a demonstration of how the three basic types of equations-parabolic, hyperbolic, and elliptic-can be derived from random walk models. It then covers an exceptionally broad range of topics, including questions of stability, analysis of singularities, transform methods, Green's functions, and perturbation and asymptotic treatments. Approximation methods for simplifying complicated problems and solutions are described, and linear and nonlinear problems not easily solved by standard methods are examined in depth. Examples from the fields of engineering and physical sciences are used liberally throughout the text to help illustrate how theory and techniques are applied to actual problems. With its extensive use of examples and exercises, this text is recommended for advanced undergraduates and graduate students in engineering, science, and applied mathematics, as well as professionals in any of these fields. It is possible to use the text, as in the past, without use of the new Maple material. |
| consider the initial value problem: Data Assimilation for the Geosciences Steven J. Fletcher, 2022-11-16 Data Assimilation for the Geosciences: From Theory to Application, Second Edition brings together all of the mathematical and statistical background knowledge needed to formulate data assimilation systems into one place. It includes practical exercises enabling readers to apply theory in both a theoretical formulation as well as teach them how to code the theory with toy problems to verify their understanding. It also demonstrates how data assimilation systems are implemented in larger scale fluid dynamical problems related to land surface, the atmosphere, ocean and other geophysical situations. The second edition of Data Assimilation for the Geosciences has been revised with up to date research that is going on in data assimilation, as well as how to apply the techniques. The new edition features an introduction of how machine learning and artificial intelligence are interfacing and aiding data assimilation. In addition to appealing to students and researchers across the geosciences, this now also appeals to new students and scientists in the field of data assimilation as it will now have even more information on the techniques, research, and applications, consolidated into one source. - Includes practical exercises and solutions enabling readers to apply theory in both a theoretical formulation as well as enabling them to code theory - Provides the mathematical and statistical background knowledge needed to formulate data assimilation systems into one place - New to this edition: covers new topics such as Observing System Experiments (OSE) and Observing System Simulation Experiments; and expanded approaches for machine learning and artificial intelligence |
| consider the initial value problem: Calculus for the Life Sciences Frederick R. Adler, Miroslav Lovric, |
| consider the initial value problem: Hyperbolicity In Delay Equations Luis Barreira, Claudia Valls, 2021-03-12 This book provides a comprehensive introduction to the study of hyperbolicity in both linear and nonlinear delay equations. This includes a self-contained discussion of the foundations, main results and essential techniques, with emphasis on important parts of the theory that apply to a large class of delay equations. The central theme is always hyperbolicity and only topics that are directly related to it are included. Among these are robustness, admissibility, invariant manifolds, and spectra, which play important roles in life sciences, engineering and control theory, especially in delayed feedback mechanisms.The book is dedicated to researchers as well as graduate students specializing in differential equations and dynamical systems who wish to have an extensive and in-depth view of the hyperbolicity theory of delay equations. It can also be used as a basis for graduate courses on the stability and hyperbolicity of delay equations. |
| consider the initial value problem: Introduction to Abstract Analysis W. Light, 1990-07-01 Abstract analysis, and particularly the language of normed linear spaces, now lies at the heart of a major portion of modern mathematics. Unfortunately, it is also a subject which students seem to find quite challenging and difficult. This book presumes that the student has had a first course in mathematical analysis or advanced calculus, but it does not presume the student has achieved mastery of such a course. Accordingly, a gentle introduction to the basic notions of convergence of sequences, continuity of functions, open and closed set, compactness, completeness and separability is given. The pace in the early chapters does not presume in any way that the readers have at their fingertips the techniques provided by an introductory course. Instead, considerable care is taken to introduce and use the basic methods of proof in a slow and explicit fashion. As the chapters progress, the pace does quicken and later chapters on differentiation, linear mappings, integration and the implicit function theorem delve quite deeply into interesting mathematical areas. There are many exercises and many examples of applications of the theory to diverse areas of mathematics. Some of these applications take considerable space and time to develop, and make interesting reading in their own right. The treatment of the subject is deliberately not a comprehensive one. The aim is to convince the undergraduate reader that analysis is a stimulating, useful, powerful and comprehensible tool in modern mathematics. This book will whet the readers' appetite, not overwhelm them with material. |
| consider the initial value problem: Applied Linear Analysis for Chemical Engineers Vemuri Balakotaiah, Ram R. Ratnakar, 2022-12-31 This textbook gives a unified treatment of the solution of various linear equations that arise in science and engineering with examples. It is based on a course taught by the first author for over thirty years. Some unique features include: Use of symbolic software for illustrating and enhancing the impact of physical parameter changes on solutions. Multi-scale analysis of engineering problems with physical interpretation of time and length scales in terms of eigenvalues and eigenvectors/eigenfunctions. Discussion of compartment models for various finite dimensional problems. Evaluation and illustration of functions of matrices (and use of symbolic manipulation) to solve multi-component diffusion-convection-reaction problems. Illustration of the techniques and interpretation of solutions to several classical engineering problems. Emphasis on the connection between discrete (matrix algebra) and continuum. Physical interpretation of adjoint operator and adjoint systems. Use of complex analysis and algebra in the solution of practical engineering problems. |
| consider the initial value problem: A First Course in Differential Equations J. David Logan, 2006-05-20 Therearemanyexcellenttextsonelementarydi?erentialequationsdesignedfor the standard sophomore course. However, in spite of the fact that most courses are one semester in length, the texts have evolved into calculus-like pres- tations that include a large collection of methods and applications, packaged with student manuals, and Web-based notes, projects, and supplements. All of this comes in several hundred pages of text with busy formats. Most students do not have the time or desire to read voluminous texts and explore internet supplements. The format of this di?erential equations book is di?erent; it is a one-semester, brief treatment of the basic ideas, models, and solution methods. Itslimitedcoverageplacesitsomewherebetweenanoutlineandadetailedte- book. I have tried to write concisely, to the point, and in plain language. Many worked examples and exercises are included. A student who works through this primer will have the tools to go to the next level in applying di?erential eq- tions to problems in engineering, science, and applied mathematics. It can give some instructors, who want more concise coverage, an alternative to existing texts. |
| consider the initial value problem: Differential Equations with Boundary Value Problems James R. Brannan, 2010-11-08 Unlike other books in the market, this second edition presents differential equations consistent with the way scientists and engineers use modern methods in their work. Technology is used freely, with more emphasis on modeling, graphical representation, qualitative concepts, and geometric intuition than on theoretical issues. It also refers to larger-scale computations that computer algebra systems and DE solvers make possible. And more exercises and examples involving working with data and devising the model provide scientists and engineers with the tools needed to model complex real-world situations. |
| consider the initial value problem: Chaotic Oscillators: Theory And Applications Tomasz Kapitaniak, 1992-11-30 This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection. |
| consider the initial value problem: Non-Stationary Electromagnetics Alexander Nerukh, Trevor Benson, 2018-10-26 This book is devoted to the investigations of non-stationary electromagnetic processes. The investigations are undertaken analytically mainly using the Volterra integral equations approach. The book contains a systematic statement of this approach for the investigations of electrodynamics phenomena in the time domain and new results and applications in microwave techniques and photonics. Particular consideration is given to electromagnetic transients in time-varying media and their potential applications. The approach is formulated and electromagnetic phenomena are investigated in detail for a hollow metal waveguide, which contains moving dielectric or plasma-bounded medium, and dielectric waveguides with time-varying medium inside a core. |
| consider the initial value problem: Numerical Mathematics Jeffrey S. Ovall , 2024-10-24 This textbook introduces key numerical algorithms used for problems arising in three core areas of scientific computing: calculus, differential equations, and linear algebra. Theoretical results supporting the derivation and error analysis of algorithms are given rigorous justification in the text and exercises, and a wide variety of detailed computational examples further enhance the understanding of key concepts. Numerical Mathematics includes topics not typically discussed in similar texts at this level, such as a Fourier-based analysis of the trapezoid rule, finite volume methods for the 2D Poisson problem, the Nyström method for approximating the solution of integral equations, and the relatively new FEAST method for targeting clusters of eigenvalues and their eigenvectors. An early emphasis is given to recognizing or deducing orders of convergence in practice, which is essential for assessing algorithm performance and debugging computational software. Numerical experiments complement many of the theorems concerning convergence, illustrating typical behavior of the associated algorithms when the assumptions of the theorems are satisfied and when they are not. This book is intended for advanced undergraduate and beginning graduate students in mathematics seeking a solid foundation in the theory and practice of scientific computing. Students and researchers in other disciplines who want a fuller understanding of the principles underlying these algorithms will also find it useful. The text is divided into three parts, corresponding to numerical methods for problems in calculus, differential equations, and linear algebra. Each part can be used for a one-term course (quarter or semester), making the book suitable for a two- or three-term sequence in numerical analysis or for largely independent courses on any of the three main topics. |
| consider the initial value problem: Advanced Engineering Mathematics Dennis G. Zill, Warren S. Wright, 2014 Modern and comprehensive, the new Fifth Edition of Zill's Advanced Engineering Mathematics, Fifth Edition provides an in depth overview of the many mathematical topics required for students planning a career in engineering or the sciences. A key strength of this best-selling text is Zill's emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Fifth Edition is a full compendium of topics that are most often covered in the Engineering Mathematics course or courses, and is extremely flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. The new edition offers a reorganized project section to add clarity to course material and new content has been added throughout, including new discussions on: Autonomous Des and Direction Fields; Translation Property, Bessel Functions, LU-Factorization, Da Vinci's apparatus for determining speed and more. New and Key Features of the Fifth Edition: - Available with WebAssign with full integrated eBook - Two new chapters, Probability and Statistics, are available online - Updated example throughout - Projects, formerly found at the beginning of the text, are now included within the appropriate chapters. - New and updated content throughout including new discussions on: Autonomous Des and Direction Fields; Translation Property, Bessel Functions, LU-Factorization, Da Vinci's apparatus for determing speed and more. - The Student Companion Website, included with every new copy, includes a wealth of study aids, learning tools, projects, and essays to enhance student learning Instructor materials include: complete instructor solutions manual, PowerPoint Image Bank, and Test Bank. |
| consider the initial value problem: Differential Equations: Techniques, Theory, and Applications Barbara D. MacCluer, Paul S. Bourdon, Thomas L. Kriete, 2019-10-02 Differential Equations: Techniques, Theory, and Applications is designed for a modern first course in differential equations either one or two semesters in length. The organization of the book interweaves the three components in the subtitle, with each building on and supporting the others. Techniques include not just computational methods for producing solutions to differential equations, but also qualitative methods for extracting conceptual information about differential equations and the systems modeled by them. Theory is developed as a means of organizing, understanding, and codifying general principles. Applications show the usefulness of the subject as a whole and heighten interest in both solution techniques and theory. Formal proofs are included in cases where they enhance core understanding; otherwise, they are replaced by informal justifications containing key ideas of a proof in a more conversational format. Applications are drawn from a wide variety of fields: those in physical science and engineering are prominent, of course, but models from biology, medicine, ecology, economics, and sports are also featured. The 1,400+ exercises are especially compelling. They range from routine calculations to large-scale projects. The more difficult problems, both theoretical and applied, are typically presented in manageable steps. The hundreds of meticulously detailed modeling problems were deliberately designed along pedagogical principles found especially effective in the MAA study Characteristics of Successful Calculus Programs, namely, that asking students to work problems that require them to grapple with concepts (or even proofs) and do modeling activities is key to successful student experiences and retention in STEM programs. The exposition itself is exceptionally readable, rigorous yet conversational. Students will find it inviting and approachable. The text supports many different styles of pedagogy from traditional lecture to a flipped classroom model. The availability of a computer algebra system is not assumed, but there are many opportunities to incorporate the use of one. |
| consider the initial value problem: Introduction to Partial Differential Equations Aslak Tveito, Ragnar Winther, 2008-01-21 Combining both the classical theory and numerical techniques for partial differential equations, this thoroughly modern approach shows the significance of computations in PDEs and illustrates the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between these techniques. The authors present the material at an easy pace and exercises ranging from the straightforward to the challenging have been included. In addition there are some projects suggested, either to refresh the students memory of results needed in this course, or to extend the theories developed in the text. Suitable for undergraduate and graduate students in mathematics and engineering. |
| consider the initial value problem: Algebra and Analysis for Engineers and Scientists Anthony N. Michel, Charles J. Herget, 2007-09-04 This book allows students in engineering or science to become familiar with a great deal of pertinent mathematics in a rapid and efficient manner without sacrificing rigor. It gives readers a unified overview of applicable mathematics. |
| consider the initial value problem: Advanced Engineering Mathematics - Book Alone Dennis G. Zill, Warren S. Wright, 2012-10-01 Modern and comprehensive, the new Fifth Edition of Zill's Advanced Engineering Mathematics, Fifth Edition provides an in depth overview of the many mathematical topics required for students planning a career in engineering or the sciences. A key strength of this best-selling text is Zill's emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Fifth Edition is a full compendium of topics that are most often covered in the Engineering Mathematics course or courses, and is extremely flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. The new edition offers a reorganized project section to add clarity to course material and new content has been added throughout, including new discussions on: Autonomous Des and Direction Fields; Translation Property, Bessel Functions, LU-Factorization, Da Vinci's apparatus for determining speed and more. New and Key Features of the Fifth Edition: - Available with WebAssign with full integrated eBook - Two new chapters, Probability and Statistics, are available online - Updated example throughout - Projects, formerly found at the beginning of the text, are now included within the appropriate chapters. - New and updated content throughout including new discussions on: Autonomous Des and Direction Fields; Translation Property, Bessel Functions, LU-Factorization, Da Vinci's apparatus for determing speed and more. - The Student Companion Website, included with every new copy, includes a wealth of study aids, learning tools, projects, and essays to enhance student learning Instructor materials include: complete instructor solutions manual, PowerPoint Image Bank, and Test Bank. |
| consider the initial value problem: Applied Algebra and Functional Analysis Anthony N. Michel, Charles J. Herget, 1993-01-01 A valuable reference. — American Scientist. Excellent graduate-level treatment of set theory, algebra and analysis for applications in engineering and science. Fundamentals, algebraic structures, vector spaces and linear transformations, metric spaces, normed spaces and inner product spaces, linear operators, more. A generous number of exercises have been integrated into the text. 1981 edition. |
| consider the initial value problem: Numerical Methods for Scientists and Engineers H.M. Antia, 2002-05-01 This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. |
| consider the initial value problem: Calculus Volume 3 Edwin Herman, Gilbert Strang, 2016-03-30 Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations. |
| consider the initial value problem: Stability Analysis In Terms Of Two Measures Vangipuram Lakshmikantham, 1993-09-30 The problems of modern society are both complex and multidisciplinary. In spite of the apparent diversity of problems, tools developed in one context are often adaptable to an entirely different situation. The concepts of Lyapunov stability have given rise to many new notions that are important in applications. Relative to each concept, there exists a sufficient literature parallel to Lyapunov's theory of stability. It is natural to ask whether we can find a notion and develop the corresponding theory which unifies and includes a variety of known concepts of stability in a single set up. The answer is yes and it is the development of stability theory in terms of two measures. It is in this spirit the authors see the importance of the present monograph. Its aim is to present a systematic account of recent developments in the stability theory in terms of two distinct measures, describe the current state of the art, show the essential unity achieved by wealth of applications, and provide a unified general structure applicable to several nonlinear problems. |
| consider the initial value problem: The Heat Equation D. V. Widder, 1976-01-22 The Heat Equation |
| consider the initial value problem: Elementary Differential Equations William E. Boyce, Richard C. DiPrima, Douglas B. Meade, 2017-08-14 With Wiley's Enhanced E-Text, you get all the benefits of a downloadable, reflowable eBook with added resources to make your study time more effective, including: Embedded & searchable equations, figures & tables Math XML Index with linked pages numbers for easy reference Redrawn full color figures to allow for easier identification Elementary Differential Equations, 11th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two ] or three ] semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. |
CONSIDER Definition & Meaning - Merriam-Webster
The meaning of CONSIDER is to think about carefully. How to use consider in a sentence. Synonym Discussion of Consider.
CONSIDER | English meaning - Cambridge Dictionary
CONSIDER definition: 1. to spend time thinking about a possibility or making a decision: 2. to give attention to a…. Learn more.
CONSIDER definition and meaning | Collins English Dictionary
If you consider a person or thing to be something, you have the opinion that this is what they are. We don't consider our customers to be mere consumers; we consider them to be our friends. [ …
CONSIDER - Definition & Meaning - Reverso English Dictionary
Consider definition: think about something seriously or carefully. Check meanings, examples, usage tips, pronunciation, domains, and related words. Discover expressions like "consider it …
What does consider mean? - Definitions.net
To consider means to think about or carefully contemplate something, often with the intention of making a decision or forming an opinion. It involves thoroughly examining different aspects, …
Consider - definition of consider by The Free Dictionary
1. to think carefully about, esp. in order to make a decision; contemplate; ponder. 2. to regard as or deem to be: I consider the matter settled. 3. to think, believe, or suppose. 4. to bear in mind; …
Consider - Definition, Meaning & Synonyms - Vocabulary.com
Consider is a verb that simply means to think about, look at, or judge. Consider, for a moment, the perks of house sitting for your pool-owning neighbors before you immediately refuse their …
Consider Definition & Meaning | Britannica Dictionary
CONSIDER meaning: 1 : to think about (something or someone) carefully especially in order to make a choice or decision; 2 : to think about (something that is important in understanding …
Consider Definition & Meaning - YourDictionary
To think carefully about (something), especially before making a decision; I needed more time to consider my options. We considered taking the train instead of the bus. To think about in order …
CONSIDER Synonyms: 173 Similar and Opposite Words | Merriam ...
Some common synonyms of consider are contemplate, study, and weigh. While all these words mean "to think about in order to arrive at a judgment or decision," consider may suggest giving …
CONSIDER Definition & Meaning - Merriam-Webster
The meaning of CONSIDER is to think about carefully. How to use consider in a sentence. Synonym Discussion of Consider.
CONSIDER | English meaning - Cambridge Dictionary
CONSIDER definition: 1. to spend time thinking about a possibility or making a decision: 2. to give attention to a…. Learn more.
CONSIDER definition and meaning | Collins English Dictionary
If you consider a person or thing to be something, you have the opinion that this is what they are. We don't consider our customers to be mere consumers; we consider them to be our friends. [ …
CONSIDER - Definition & Meaning - Reverso English Dictionary
Consider definition: think about something seriously or carefully. Check meanings, examples, usage tips, pronunciation, domains, and related words. Discover expressions like "consider it …
What does consider mean? - Definitions.net
To consider means to think about or carefully contemplate something, often with the intention of making a decision or forming an opinion. It involves thoroughly examining different aspects, …
Consider - definition of consider by The Free Dictionary
1. to think carefully about, esp. in order to make a decision; contemplate; ponder. 2. to regard as or deem to be: I consider the matter settled. 3. to think, believe, or suppose. 4. to bear in mind; …
Consider - Definition, Meaning & Synonyms - Vocabulary.com
Consider is a verb that simply means to think about, look at, or judge. Consider, for a moment, the perks of house sitting for your pool-owning neighbors before you immediately refuse their …
Consider Definition & Meaning | Britannica Dictionary
CONSIDER meaning: 1 : to think about (something or someone) carefully especially in order to make a choice or decision; 2 : to think about (something that is important in understanding …
Consider Definition & Meaning - YourDictionary
To think carefully about (something), especially before making a decision; I needed more time to consider my options. We considered taking the train instead of the bus. To think about in order …
CONSIDER Synonyms: 173 Similar and Opposite Words | Merriam ...
Some common synonyms of consider are contemplate, study, and weigh. While all these words mean "to think about in order to arrive at a judgment or decision," consider may suggest giving …
