Applications Of Differential Transform To Real World Problems

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Applications of Differential Transform to Real World Problems

Author : Yogeshwari F Patel
Publisher : CRC Press
ISBN 13 : 1000629562
Total Pages : 307 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Applications of Differential Transform to Real World Problems by : Yogeshwari F Patel

Download or read book Applications of Differential Transform to Real World Problems written by Yogeshwari F Patel and published by CRC Press. This book was released on 2022-08-08 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an invaluable resource for applied researchers to find the analytical solution of differential equations describing the dynamical system with less computational effort and time. It describes the basic concepts of the differential transform method and solution of various real-world problems described by simple to complicated differential equations. It provides a computational technique that is not only conceptually simple and easy to use but also readily adaptable for computer coding. Different chapters of the book deal with the basic differential equations involved in the physical phenomena as well as a complicated system of differential equations described by the mathematical model. The book offers comprehensive coverage of the most essential topics, including Basic concepts and fundamental properties of the proposed technique with proof The solution of linear, nonlinear, homogeneous, and nonhomogeneous ordinary differential equations (ODEs) and partial differential equations (PDEs) The initial and boundary value problems Real-world ODE and PDE problems are also discussed Applications of Differential Transform to Real World Problems is primarily aimed at undergraduates, graduates, and researchers studying differential equations. Scientists dealing with complicated differential equations or systems of differential equations will also find this book useful.

Differential Transformation Method for Mechanical Engineering Problems

Author : Mohammad Hatami
Publisher : Academic Press
ISBN 13 : 0128053402
Total Pages : 422 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Differential Transformation Method for Mechanical Engineering Problems by : Mohammad Hatami

Download or read book Differential Transformation Method for Mechanical Engineering Problems written by Mohammad Hatami and published by Academic Press. This book was released on 2016-11-17 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Transformation Method for Mechanical Engineering Problems focuses on applying DTM to a range of mechanical engineering applications. The authors modify traditional DTM to produce two additional methods, multi-step differential transformation method (Ms-DTM) and the hybrid differential transformation method and finite difference method (Hybrid DTM-FDM). It is then demonstrated how these can be a suitable series solution for engineering and physical problems, such as the motion of a spherical particle, nanofluid flow and heat transfer, and micropolar fluid flow and heat transfer. Presents the differential transformation method and why it holds an advantage over higher-order Taylor series methods Includes a full mathematical introduction to DTM, Ms-DTM, and Hybrid DTM Covers the use of these methods for solving a range of problems in areas such as nanofluid flow, heat transfer, and motion of a spherical particle in different conditions Provides numerous examples and exercises which will help the reader fully grasp the practical applications of these new methods

Differential Equations and Their Applications

Author : M. Braun
Publisher : Springer Science & Business Media
ISBN 13 : 1468401734
Total Pages : 351 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Differential Equations and Their Applications by : M. Braun

Download or read book Differential Equations and Their Applications written by M. Braun and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two major changes in the Third Edition of Differential Equations and Their Applications. First, we have completely rewritten the section on singular solutions of differential equations. A new section, 2.8.1, dealing with Euler equations has been added, and this section is used to motivate a greatly expanded treatment of singular equations in sections 2.8.2 and 2.8.3. Our second major change is in Section 2.6, where we have switched to the metric system of units. This change was requested by many of our readers. In addition to the above changes, we have updated the material on population models, and have revised the exercises in this section. Minor editorial changes have also been made throughout the text. New York City March,1983 Martin Braun vi Preface to the First Edition This textbook is a unique blend of the theory of differential equations and their exciting application to "real world" problems. First, and foremost, it is a rigorous study of ordinary differential equations and can be fully understood by anyone who has completed one year of calculus. However, in addition to the traditional applications, it also contains many exciting "real life" problems. These applications are completely self contained. First, the problem to be solved is outlined clearly, and one or more differential equations are derived as a model for this problem. These equations are then solved, and the results are compared with real world data. The following applications are covered in this text.

500 Examples and Problems of Applied Differential Equations

Author : Ravi P. Agarwal
Publisher : Springer Nature
ISBN 13 : 3030263843
Total Pages : 388 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis 500 Examples and Problems of Applied Differential Equations by : Ravi P. Agarwal

Download or read book 500 Examples and Problems of Applied Differential Equations written by Ravi P. Agarwal and published by Springer Nature. This book was released on 2019-09-24 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights an unprecedented number of real-life applications of differential equations together with the underlying theory and techniques. The problems and examples presented here touch on key topics in the discipline, including first order (linear and nonlinear) differential equations, second (and higher) order differential equations, first order differential systems, the Runge–Kutta method, and nonlinear boundary value problems. Applications include growth of bacterial colonies, commodity prices, suspension bridges, spreading rumors, modeling the shape of a tsunami, planetary motion, quantum mechanics, circulation of blood in blood vessels, price-demand-supply relations, predator-prey relations, and many more. Upper undergraduate and graduate students in Mathematics, Physics and Engineering will find this volume particularly useful, both for independent study and as supplementary reading. While many problems can be solved at the undergraduate level, a number of challenging real-life applications have also been included as a way to motivate further research in this vast and fascinating field.

Beyond Perturbation

Author : Shijun Liao
Publisher : CRC Press
ISBN 13 : 1135438293
Total Pages : 335 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Beyond Perturbation by : Shijun Liao

Download or read book Beyond Perturbation written by Shijun Liao and published by CRC Press. This book was released on 2003-10-27 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.

Differential Equations and Their Applications

Author : M. Braun
Publisher : Springer Science & Business Media
ISBN 13 : 1468493604
Total Pages : 530 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Differential Equations and Their Applications by : M. Braun

Download or read book Differential Equations and Their Applications written by M. Braun and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a unique blend of the theory of differential equations and their exciting application to "real world" problems. First, and foremost, it is a rigorous study of ordinary differential equations and can be fully un derstood by anyone who has completed one year of calculus. However, in addition to the traditional applications, it also contains many exciting "real life" problems. These applications are completely self contained. First, the problem to be solved is outlined clearly, and one or more differential equa tions are derived as a model for this problem. These equations are then solved, and the results are compared with real world data. The following applications are covered in this text. I. In Section 1.3 we prove that the beautiful painting "Disciples of Emmaus" which was bought by the Rembrandt Society of Belgium for $170,000 was a modem forgery. 2. In Section 1.5 we derive differential equations which govern the population growth of various species, and compare the results predicted by our models with the known values of the populations. 3. In Section 1.6 we derive differential equations which govern the rate at which farmers adopt new innovations. Surprisingly, these same differen tial equations govern the rate at which technological innovations are adopted in such diverse industries as coal, iron and steel, brewing, and railroads.

Differential Equations and Their Applications

Author : Martin Braun
Publisher : Springer Science & Business Media
ISBN 13 : 1468492292
Total Pages : 558 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Differential Equations and Their Applications by : Martin Braun

Download or read book Differential Equations and Their Applications written by Martin Braun and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are three major changes in the Third Edition of Differential Equations and Their Applications. First, we have completely rewritten the section on singular solutions of differential equations. A new section, 2.8.1, dealing with Euler equations has been added, and this section is used to motivate a greatly expanded treatment of singular equations in sections 2.8.2 and 2.8.3. Our second major change is the addition of a new section, 4.9, dealing with bifurcation theory, a subject of much current interest. We felt it desirable to give the reader a brief but nontrivial introduction to this important topic. Our third major change is in Section 2.6, where we have switched to the metric system of units. This change was requested by many of our readers. In addition to the above changes, we have updated the material on population models, and have revised the exercises in this section. Minor editorial changes have also been made throughout the text. New York City Martin Braun Nooember, 1982 Preface to the First Edition This textbook is a unique blend of the theory of differential equations and their exciting application to "real world" problems. First, and foremost, it is a rigorous study of ordinary differential equations and can be fully understood by anyone who has completed one year of calculus. However, in addition to the traditional applications, it also contains many exciting "real life" problems. These applications are completely self contained.

Introduction to Inverse Problems for Differential Equations

Author : Alemdar Hasanov Hasanoğlu
Publisher : Springer Nature
ISBN 13 : 303079427X
Total Pages : 521 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Introduction to Inverse Problems for Differential Equations by : Alemdar Hasanov Hasanoğlu

Download or read book Introduction to Inverse Problems for Differential Equations written by Alemdar Hasanov Hasanoğlu and published by Springer Nature. This book was released on 2021-08-02 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties. For the second edition, the authors have added two new chapters focusing on real-world applications of inverse problems arising in wave and vibration phenomena. They have also revised the whole text of the first edition.

500 Examples and Problems of Applied Differential Equations

Author : Ravi P. Agarwal
Publisher :
ISBN 13 : 9783030263850
Total Pages : 388 pages
Book Rating : 4.2/5 (638 download)

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Book Synopsis 500 Examples and Problems of Applied Differential Equations by : Ravi P. Agarwal

Download or read book 500 Examples and Problems of Applied Differential Equations written by Ravi P. Agarwal and published by . This book was released on 2019 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights an unprecedented number of real-life applications of differential equations together with the underlying theory and techniques. The problems and examples presented here touch on key topics in the discipline, including first order (linear and nonlinear) differential equations, second (and higher) order differential equations, first order differential systems, the Runge-Kutta method, and nonlinear boundary value problems. Applications include growth of bacterial colonies, commodity prices, suspension bridges, spreading rumors, modeling the shape of a tsunami, planetary motion, quantum mechanics, circulation of blood in blood vessels, price-demand-supply relations, predator-prey relations, and many more. Upper undergraduate and graduate students in Mathematics, Physics and Engineering will find this volume particularly useful, both for independent study and as supplementary reading. While many problems can be solved at the undergraduate level, a number of challenging real-life applications have also been included as a way to motivate further research in this vast and fascinating field.

Engineering Differential Equations

Author : Bill Goodwine
Publisher : Springer Science & Business Media
ISBN 13 : 1441979190
Total Pages : 762 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Engineering Differential Equations by : Bill Goodwine

Download or read book Engineering Differential Equations written by Bill Goodwine and published by Springer Science & Business Media. This book was released on 2010-11-11 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.

Differential Equations: Methods and Applications

Author : Belkacem Said-Houari
Publisher : Springer
ISBN 13 : 3319257358
Total Pages : 212 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Differential Equations: Methods and Applications by : Belkacem Said-Houari

Download or read book Differential Equations: Methods and Applications written by Belkacem Said-Houari and published by Springer. This book was released on 2016-01-11 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory.To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included.The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations.

New Trends in Fractional Differential Equations with Real-World Applications in Physics

Author : Jagdev Singh
Publisher : Frontiers Media SA
ISBN 13 : 2889663043
Total Pages : 172 pages
Book Rating : 4.8/5 (896 download)

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Book Synopsis New Trends in Fractional Differential Equations with Real-World Applications in Physics by : Jagdev Singh

Download or read book New Trends in Fractional Differential Equations with Real-World Applications in Physics written by Jagdev Singh and published by Frontiers Media SA. This book was released on 2020-12-30 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.

Applied Differential Equations

Author : Vladimir A. Dobrushkin
Publisher : CRC Press
ISBN 13 : 1000606244
Total Pages : 706 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Applied Differential Equations by : Vladimir A. Dobrushkin

Download or read book Applied Differential Equations written by Vladimir A. Dobrushkin and published by CRC Press. This book was released on 2022-09-21 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book started as a collection of lecture notes for a course in differential equations taught by the Division of Applied Mathematics at Brown University. To some extent, it is a result of collective insights given by almost every instructor who taught such a course over the last 15 years. Therefore, the material and its presentation covered in this book were practically tested for many years. This text is designed for a two-semester sophomore or junior level course in differential equations. It offers novel approaches in presentation and utilization of computer capabilities. This text intends to provide a solid background in differential equations for students majoring in a breadth of fields. Differential equations are described in the context of applications. The author stresses differential equations constitute an essential part of modeling by showing their applications, including numerical algorithms and syntax of the four most popular software packages. Students learn how to formulate a mathematical model, how to solve differential equations (analytically or numerically), how to analyze them qualitatively, and how to interpret the results. In writing this textbook, the author aims to assist instructors and students through: Showing a course in differential equations is essential for modeling real-life phenomena Stressing the mastery of traditional solution techniques and presenting effective methods, including reliable numerical approximations Providing qualitative analysis of ordinary differential equations. The reader should get an idea of how all solutions to the given problem behave, what are their validity intervals, whether there are oscillations, vertical or horizontal asymptotes, and what is their long-term behavior The reader will learn various methods of solving, analysis, visualization, and approximation, exploiting the capabilities of computers Introduces and employs MapleTM, Mathematica®, MatLab®, and Maxima This textbook facilitates the development of the student’s skills to model real-world problems Ordinary and partial differential equations is a classical subject that has been studied for about 300 years. The beauty and utility of differential equations and their application in mathematics, biology, chemistry, computer science, economics, engineering, geology, neuroscience, physics, the life sciences, and other fields reaffirm their inclusion in myriad curricula. A great number of examples and exercises make this text well suited for self-study or for traditional use by a lecturer in class. Therefore, this textbook addresses the needs of two levels of audience, the beginning and the advanced.

Textbook on Ordinary Differential Equations

Author : Ramakanta Meher
Publisher : CRC Press
ISBN 13 : 1000824020
Total Pages : 290 pages
Book Rating : 4.0/5 (8 download)

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Book Synopsis Textbook on Ordinary Differential Equations by : Ramakanta Meher

Download or read book Textbook on Ordinary Differential Equations written by Ramakanta Meher and published by CRC Press. This book was released on 2022-12-29 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many scientific and real-world problems that occur in science, engineering, and medicine can be represented in differential equations. There is a vital role for differential equations in studying the behavior of different types of real-world problems. Thus, it becomes crucial to know the existence and uniqueness properties of differential equations and various methods of finding differential equation solutions in explicit form. It is also essential to know different kinds of differential equations in terms of eigenvalues, termed eigenvalue problems, and some special functions used in finding the solution to differential equations. The study of nonlinear problems also plays a significant role in different real-world situations. There is a necessity to know the behavior of solutions of nonlinear differential equations. Still, there are very few forms of differential equations whose solution can be found in explicit form. For the differential equations whose solutions cannot be found in explicit form, one has to study the properties of solutions of the given differential equation to guess an approximate solution of it. This book aims to introduce all the necessary topics of differential equations in one book so that laymen can easily understand the subject and apply it in their research areas. The novel approach used in this book is the introduction of different analytical methods for finding the solution of differential equations with sufficient theorems, corollaries, and examples, and the geometrical interpretations in each topic. This textbook is intended to study the theory and methods of finding the explicit solutions to differential equations, wherever possible, and in the absence of finding explicit solutions, it is intended to study the properties of solutions to the given differential equations. This book is based on syllabi of the theory of differential equations prescribed for postgraduate students of mathematics and applied mathematics in different institutions and universities of India and abroad. This book will be helpful for competitive examinations as well.

Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems

Author : Chakraverty, S.
Publisher : IGI Global
ISBN 13 : 1466649925
Total Pages : 442 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems by : Chakraverty, S.

Download or read book Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems written by Chakraverty, S. and published by IGI Global. This book was released on 2014-01-31 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book provides the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications"--Provided by publisher.

Fixed Point Theory and Fractional Calculus

Author : Pradip Debnath
Publisher : Springer Nature
ISBN 13 : 9811906688
Total Pages : 358 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Fixed Point Theory and Fractional Calculus by : Pradip Debnath

Download or read book Fixed Point Theory and Fractional Calculus written by Pradip Debnath and published by Springer Nature. This book was released on 2022-05-10 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.

Partial Differential Equations

Author : Thomas Hillen
Publisher : John Wiley & Sons
ISBN 13 : 1118438434
Total Pages : 610 pages
Book Rating : 4.1/5 (184 download)

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Book Synopsis Partial Differential Equations by : Thomas Hillen

Download or read book Partial Differential Equations written by Thomas Hillen and published by John Wiley & Sons. This book was released on 2014-08-21 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including: • Classification of second-order linear PDEs • Derivation of heat, wave, and Laplace’s equations • Fourier series • Separation of variables • Sturm-Liouville theory • Fourier transforms Each chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources. Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels.