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Author: Luis Manuel Braga da Costa Campos
Publisher: CRC Press
ISBN: 0429595158
Category : Technology & Engineering
Languages : en
Pages : 261
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Book Description
Classification and Examples of Differential Equations and their Applications is the sixth book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This sixth book consists of one chapter (chapter 10 of the set). It contains 20 examples related to the preceding five books and chapters 1 to 9 of the set. It includes two recollections: the first with a classification of differential equations into 500 standards and the second with a list of 500 applications. The ordinary differential equations are classified in 500 standards concerning methods of solution and related properties, including: (i) linear differential equations with constant or homogeneous coefficients and finite difference equations; (ii) linear and non-linear single differential equations and simultaneous systems; (iii) existence, unicity and other properties; (iv) derivation of general, particular, special, analytic, regular, irregular, and normal integrals; (v) linear differential equations with variable coefficients including known and new special functions. The theory of differential equations is applied to the detailed solution of 500 physical and engineering problems including: (i) one- and multidimensional oscillators, with damping or amplification, with non-resonant or resonant forcing; (ii) single, non-linear, and parametric resonance; (iii) bifurcations and chaotic dynamical systems; (iv) longitudinal and transversal deformations and buckling of bars, beams, and plates; (v) trajectories of particles; (vi) oscillations and waves in non-uniform media, ducts, and wave guides. Provides detailed solution of examples of differential equations of the types covered in tomes l-5 of the set (Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six -volume Set) Includes physical and engineering problems that extend those presented in the tomes 1-6 (Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set) Includes a classification of ordinary differential equations and their properties into 500 standards that can serve as a look-up table of methods of solution Covers a recollection of 500 physical and engineering problems and sub-cases that involve the solution of differential equations Presents the problems used as examples including formulation, solution, and interpretation of results
Author: LUIS MANUEL. BRAGA DA COSTA CAMPOS
Publisher:
ISBN: 9781032653761
Category :
Languages : en
Pages : 0
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Book Description
This is the sixth book of Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-Volume Set, in the Mathematics and Physics for Science and Technology series. This book contains examples of the various types of differential equations in earlier book set and their application to physical and engineering problems.
Author: Luis Manuel Braga da Costa Campos
Publisher: CRC Press
ISBN: 0429595158
Category : Technology & Engineering
Languages : en
Pages : 261
Get Book Here
Book Description
Classification and Examples of Differential Equations and their Applications is the sixth book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This sixth book consists of one chapter (chapter 10 of the set). It contains 20 examples related to the preceding five books and chapters 1 to 9 of the set. It includes two recollections: the first with a classification of differential equations into 500 standards and the second with a list of 500 applications. The ordinary differential equations are classified in 500 standards concerning methods of solution and related properties, including: (i) linear differential equations with constant or homogeneous coefficients and finite difference equations; (ii) linear and non-linear single differential equations and simultaneous systems; (iii) existence, unicity and other properties; (iv) derivation of general, particular, special, analytic, regular, irregular, and normal integrals; (v) linear differential equations with variable coefficients including known and new special functions. The theory of differential equations is applied to the detailed solution of 500 physical and engineering problems including: (i) one- and multidimensional oscillators, with damping or amplification, with non-resonant or resonant forcing; (ii) single, non-linear, and parametric resonance; (iii) bifurcations and chaotic dynamical systems; (iv) longitudinal and transversal deformations and buckling of bars, beams, and plates; (v) trajectories of particles; (vi) oscillations and waves in non-uniform media, ducts, and wave guides. Provides detailed solution of examples of differential equations of the types covered in tomes l-5 of the set (Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six -volume Set) Includes physical and engineering problems that extend those presented in the tomes 1-6 (Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set) Includes a classification of ordinary differential equations and their properties into 500 standards that can serve as a look-up table of methods of solution Covers a recollection of 500 physical and engineering problems and sub-cases that involve the solution of differential equations Presents the problems used as examples including formulation, solution, and interpretation of results
Author: Deborah E. Richards
Publisher: Nova Science Publishers
ISBN: 9781634826433
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book includes research on the Lax-Milgram theorem, which can be used to prove existence and uniqueness of weak solutions to partial differential equations and several examples of its application to relevant boundary value problems are presented. The authors also investigate nonlinear control problems for couple partial differential equations arising from climate and circulation dynamics in the equatorial zone; the integration of partial differential equations (PDE) with the help of non-commutative analysis over octonions and Cayley-Dickson algebras; and the existence and properties of solutions, applications in sequential optimal control with pointwise in time state constraints.
Author: Jiri Lebl
Publisher:
ISBN: 9781706230236
Category :
Languages : en
Pages : 468
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Book Description
Version 6.0. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See https: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions.
Author: Gerhard Kristensson
Publisher: Springer Science & Business Media
ISBN: 1441970207
Category : Mathematics
Languages : en
Pages : 225
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Book Description
Second Order Differential Equations presents a classical piece of theory concerning hypergeometric special functions as solutions of second-order linear differential equations. The theory is presented in an entirely self-contained way, starting with an introduction of the solution of the second-order differential equations and then focusingon the systematic treatment and classification of these solutions. Each chapter contains a set of problems which help reinforce the theory. Some of the preliminaries are covered in appendices at the end of the book, one of which provides an introduction to Poincaré-Perron theory, and the appendix also contains a new way of analyzing the asymptomatic behavior of solutions of differential equations. This textbook is appropriate for advanced undergraduate and graduate students in Mathematics, Physics, and Engineering interested in Ordinary and Partial Differntial Equations. A solutions manual is available online.
Author: E. C. Zachmanoglou
Publisher: Courier Corporation
ISBN: 048613217X
Category : Mathematics
Languages : en
Pages : 434
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Book Description
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.
Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
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Book Description
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Author: Luis Manuel Braga da Costa Campos
Publisher: CRC Press
ISBN: 0429593864
Category : Mathematics
Languages : en
Pages : 268
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Book Description
Classification and Examples of Differential Equations and their Applications is the sixth book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This sixth book consists of one chapter (chapter 10 of the set). It contains 20 examples related to the preceding five books and chapters 1 to 9 of the set. It includes two recollections: the first with a classification of differential equations into 500 standards and the second with a list of 500 applications. The ordinary differential equations are classified in 500 standards concerning methods of solution and related properties, including: (i) linear differential equations with constant or homogeneous coefficients and finite difference equations; (ii) linear and non-linear single differential equations and simultaneous systems; (iii) existence, unicity and other properties; (iv) derivation of general, particular, special, analytic, regular, irregular, and normal integrals; (v) linear differential equations with variable coefficients including known and new special functions. The theory of differential equations is applied to the detailed solution of 500 physical and engineering problems including: (i) one- and multidimensional oscillators, with damping or amplification, with non-resonant or resonant forcing; (ii) single, non-linear, and parametric resonance; (iii) bifurcations and chaotic dynamical systems; (iv) longitudinal and transversal deformations and buckling of bars, beams, and plates; (v) trajectories of particles; (vi) oscillations and waves in non-uniform media, ducts, and wave guides. Provides detailed solution of examples of differential equations of the types covered in tomes l-5 of the set (Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six -volume Set) Includes physical and engineering problems that extend those presented in the tomes 1-6 (Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set) Includes a classification of ordinary differential equations and their properties into 500 standards that can serve as a look-up table of methods of solution Covers a recollection of 500 physical and engineering problems and sub-cases that involve the solution of differential equations Presents the problems used as examples including formulation, solution, and interpretation of results
Author: Earl A. Coddington
Publisher: SIAM
ISBN: 9781611971439
Category : Mathematics
Languages : en
Pages : 353
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Book Description
Linear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering. Three recurrent themes run through the book. The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions. The use of power series, beginning with the matrix exponential function leads to the special functions solving classical equations. Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions.
Author: Tai-Ran Hsu
Publisher: John Wiley & Sons
ISBN: 1119071208
Category : Technology & Engineering
Languages : en
Pages : 541
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Book Description
A resource book applying mathematics to solve engineering problems Applied Engineering Analysis is a concise textbookwhich demonstrates how toapply mathematics to solve engineering problems. It begins with an overview of engineering analysis and an introduction to mathematical modeling, followed by vector calculus, matrices and linear algebra, and applications of first and second order differential equations. Fourier series and Laplace transform are also covered, along with partial differential equations, numerical solutions to nonlinear and differential equations and an introduction to finite element analysis. The book also covers statistics with applications to design and statistical process controls. Drawing on the author's extensive industry and teaching experience, spanning 40 years, the book takes a pedagogical approach and includes examples, case studies and end of chapter problems. It is also accompanied by a website hosting a solutions manual and PowerPoint slides for instructors. Key features: Strong emphasis on deriving equations, not just solving given equations, for the solution of engineering problems. Examples and problems of a practical nature with illustrations to enhance student’s self-learning. Numerical methods and techniques, including finite element analysis. Includes coverage of statistical methods for probabilistic design analysis of structures and statistical process control (SPC). Applied Engineering Analysis is a resource book for engineering students and professionals to learn how to apply the mathematics experience and skills that they have already acquired to their engineering profession for innovation, problem solving, and decision making.
