Differential Equation Solutions with MATLAB®

by Dingyü Xue

Author	: Dingyü Xue
Publisher	: Walter de Gruyter GmbH & Co KG
Total Pages	: 417
Release	: 2020-04-06
Genre	: Computers
ISBN	: 3110675315

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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.

Differential Equations and Linear Algebra

by Gilbert Strang

Author	: Gilbert Strang
Publisher	: Wellesley-Cambridge Press
Total Pages	: 0
Release	: 2015-02-12
Genre	: Mathematics
ISBN	: 9780980232790

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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.

Solving ODEs with MATLAB

by Lawrence F. Shampine

Author	: Lawrence F. Shampine
Publisher	: Cambridge University Press
Total Pages	: 276
Release	: 2003-04-28
Genre	: Computers
ISBN	: 9780521530941

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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.

Computational Partial Differential Equations Using MATLAB®

by Jichun Li

Author	: Jichun Li
Publisher	: CRC Press
Total Pages	: 423
Release	: 2019-09-26
Genre	: Mathematics
ISBN	: 0429556535

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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.

Numerical Computing with MATLAB

by Cleve B. Moler

Author	: Cleve B. Moler
Publisher	: SIAM
Total Pages	: 340
Release	: 2010-08-12
Genre	: Computers
ISBN	: 0898716608

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A revised textbook for introductory courses in numerical methods, MATLAB and technical computing, which emphasises the use of mathematical software.

Computational Partial Differential Equations Using MATLAB

by Jichun Li

Author	: Jichun Li
Publisher	: CRC Press
Total Pages	: 376
Release	: 2008-10-20
Genre	: Mathematics
ISBN	: 1420089056

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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

Ordinary Differential Equations for Engineers

by Ali Ümit Keskin

Author	: Ali Ümit Keskin
Publisher	: Springer
Total Pages	: 791
Release	: 2018-09-01
Genre	: Technology & Engineering
ISBN	: 3319952439

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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.

Fractional-Order Control Systems

by Dingyü Xue

Author	: Dingyü Xue
Publisher	: Walter de Gruyter GmbH & Co KG
Total Pages	: 455
Release	: 2017-07-10
Genre	: Mathematics
ISBN	: 3110497190

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This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design. It presents original research to find high-precision solutions to fractional-order differentiations and differential equations. Numerical algorithms and their implementations are proposed to analyze multivariable fractional-order control systems. Through high-quality MATLAB programs, it provides engineers and applied mathematicians with theoretical and numerical tools to design control systems. Contents Introduction to fractional calculus and fractional-order control Mathematical prerequisites Definitions and computation algorithms of fractional-order derivatives and Integrals Solutions of linear fractional-order differential equations Approximation of fractional-order operators Modelling and analysis of multivariable fractional-order transfer function Matrices State space modelling and analysis of linear fractional-order Systems Numerical solutions of nonlinear fractional-order differential Equations Design of fractional-order PID controllers Frequency domain controller design for multivariable fractional-order Systems Inverse Laplace transforms involving fractional and irrational Operations FOTF Toolbox functions and models Benchmark problems for the assessment of fractional-order differential equation algorithms

Partial Differential Equations

by Mark S. Gockenbach

Author	: Mark S. Gockenbach
Publisher	: SIAM
Total Pages	: 665
Release	: 2010-12-02
Genre	: Mathematics
ISBN	: 0898719356

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A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.