Download or read book Differential Equations and Linear Algebra written by Gilbert Strang and published by Wellesley-Cambridge Press. This book was released on 2015-02-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.
Download or read book Differential Equations with MATLAB written by Mark McKibben and published by CRC Press. This book was released on 2014-09-08 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance. The first part of the book presents systems of linear ODEs. The text develops mathematical models from ten disparate fields, including pharmacokinetics, chemistry, classical mechanics, neural networks, physiology, and electrical circuits. Focusing on linear PDEs, the second part covers PDEs that arise in the mathematical modeling of phenomena in ten other areas, including heat conduction, wave propagation, fluid flow through fissured rocks, pattern formation, and financial mathematics. The authors engage students by posing questions of all types throughout, including verifying details, proving conjectures of actual results, analyzing broad strokes that occur within the development of the theory, and applying the theory to specific models. The authors’ accessible style encourages students to actively work through the material and answer these questions. In addition, the extensive use of MATLAB® GUIs allows students to discover patterns and make conjectures.
Download or read book Computational Partial Differential Equations Using MATLAB written by Jichun Li and published by CRC Press. This book was released on 2019-09-26 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this popular text for an Numerical Analysis course, the authors introduce several major methods of solving various partial differential equations (PDEs) including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques including the classic finite difference method, finite element method, and state-of-the-art numercial methods.The text uniquely emphasizes both theoretical numerical analysis and practical implementation of the algorithms in MATLAB. This new edition includes a new chapter, Finite Value Method, the presentation has been tightened, new exercises and applications are included, and the text refers now to the latest release of MATLAB. Key Selling Points: A successful textbook for an undergraduate text on numerical analysis or methods taught in mathematics and computer engineering. This course is taught in every university throughout the world with an engineering department or school. Competitive advantage broader numerical methods (including finite difference, finite element, meshless method, and finite volume method), provides the MATLAB source code for most popular PDEs with detailed explanation about the implementation and theoretical analysis. No other existing textbook in the market offers a good combination of theoretical depth and practical source codes.
Download or read book Differential Equations written by P. Mohana Shankar and published by CRC Press. This book was released on 2018-04-17 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book takes a problem solving approach in presenting the topic of differential equations. It provides a complete narrative of differential equations showing the theoretical aspects of the problem (the how's and why's), various steps in arriving at solutions, multiple ways of obtaining solutions and comparison of solutions. A large number of comprehensive examples are provided to show depth and breadth and these are presented in a manner very similar to the instructor's class room work. The examples contain solutions from Laplace transform based approaches alongside the solutions based on eigenvalues and eigenvectors and characteristic equations. The verification of the results in examples is additionally provided using Runge-Kutta offering a holistic means to interpret and understand the solutions. Wherever necessary, phase plots are provided to support the analytical results. All the examples are worked out using MATLAB® taking advantage of the Symbolic Toolbox and LaTex for displaying equations. With the subject matter being presented through these descriptive examples, students will find it easy to grasp the concepts. A large number of exercises have been provided in each chapter to allow instructors and students to explore various aspects of differential equations.
Download or read book Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB written by Alexander Stanoyevitch and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Partial Differential Equations Using MATLAB written by Jichun Li and published by CRC Press. This book was released on 2008-10-20 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as state-of-the-art numerical
Download or read book Solving ODEs with MATLAB written by Lawrence F. Shampine and published by Cambridge University Press. This book was released on 2003-04-28 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.
Download or read book A Compendium of Partial Differential Equation Models written by William E. Schiesser and published by Cambridge University Press. This book was released on 2009-03-16 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.
Download or read book An Introduction to Partial Differential Equations with MATLAB written by Matthew P. Coleman and published by CRC Press. This book was released on 2016-04-19 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Partial Differential Equations with MATLAB, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat,
Download or read book Partial Differential Equations written by Mark S. Gockenbach and published by SIAM. This book was released on 2010-12-02 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.
Download or read book Introduction to Partial Differential Equations with MATLAB written by Jeffery M. Cooper and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value problems with constant coeffi cients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter.
Download or read book Ordinary and Partial Differential Equation Routines in C C Fortran Java Maple and MATLAB written by H.J. Lee and published by CRC Press. This book was released on 2003-11-24 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a set of ODE/PDE integration routines in the six most widely used computer languages, enabling scientists and engineers to apply ODE/PDE analysis toward solving complex problems. This text concisely reviews integration algorithms, then analyzes the widely used Runge-Kutta method. It first presents a complete code before discussin
Download or read book Simulation of ODE PDE Models with MATLAB OCTAVE and SCILAB written by Alain Vande Wouwer and published by Springer. This book was released on 2014-06-07 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs). Special attention is paid to the numerical method of lines (MOL), a popular approach to the solution of time-dependent PDEs, which proceeds in two basic steps: spatial discretization and time integration. Besides conventional finite-difference and element techniques, more advanced spatial-approximation methods are examined in some detail, including nonoscillatory schemes and adaptive-grid approaches. A MOL toolbox has been developed within MATLAB®/OCTAVE/SCILAB. In addition to a set of spatial approximations and time integrators, this toolbox includes a collection of application examples, in specific areas, which can serve as templates for developing new programs. Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB provides a practical introduction to some advanced computational techniques for dynamic system simulation, supported by many worked examples in the text, and a collection of codes available for download from the book’s page at www.springer.com. This text is suitable for self-study by practicing scientists and engineers and as a final-year undergraduate course or at the graduate level.
Download or read book Ordinary Differential Equations for Engineers written by Ali Ümit Keskin and published by Springer. This book was released on 2018-09-01 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Download or read book Numerical Computing with MATLAB written by Cleve B. Moler and published by SIAM. This book was released on 2010-08-12 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revised textbook for introductory courses in numerical methods, MATLAB and technical computing, which emphasises the use of mathematical software.
Download or read book Differential Equation Solutions with MATLAB written by Dingyü Xue and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-04-06 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses the solutions of differential equations with MATLAB. Analytical solutions of differential equations are explored first, followed by the numerical solutions of different types of ordinary differential equations (ODEs), as well as the universal block diagram based schemes for ODEs. Boundary value ODEs, fractional-order ODEs and partial differential equations are also discussed.
Download or read book Stability of Linear Delay Differential Equations written by Dimitri Breda and published by Springer. This book was released on 2014-10-21 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.
