differential equations i essentials vol 1

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Ordinary Differential Equations In The Complex Domain

Author : Einar Hille
ISBN : 0486696200
Genre : Mathematics
File Size : 52. 67 MB
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Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.

Essential Partial Differential Equations

Author : David F. Griffiths
ISBN : 9783319225692
Genre : Mathematics
File Size : 89. 35 MB
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This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.

Computational Differential Equations

Author : K. Eriksson
ISBN : 0521567386
Genre : Mathematics
File Size : 31. 37 MB
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Textbook for teaching computational mathematics.

Computer Methods For Ordinary Differential Equations And Differential Algebraic Equations

Author : Uri M. Ascher
ISBN : 9780898714128
Genre : Mathematics
File Size : 61. 48 MB
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This book contains all the material necessary for a course on the numerical solution of differential equations.

Essentials Of Partial Differential Equations

Author : Marin Marin
ISBN : 9783319906478
Genre : Technology & Engineering
File Size : 85. 13 MB
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This book offers engineering students an introduction to the theory of partial differential equations and then guiding them through the modern problems in this subject. Divided into two parts, in the first part readers already well-acquainted with problems from the theory of differential and integral equations gain insights into the classical notions and problems, including differential operators, characteristic surfaces, Levi functions, Green’s function, and Green’s formulas. Readers are also instructed in the extended potential theory in its three forms: the volume potential, the surface single-layer potential and the surface double-layer potential. Furthermore, the book presents the main initial boundary value problems associated with elliptic, parabolic and hyperbolic equations. The second part of the book, which is addressed first and foremost to those who are already acquainted with the notions and the results from the first part, introduces readers to modern aspects of the theory of partial differential equations.

An Introduction To Ordinary Differential Equations

Author : Ravi P. Agarwal
ISBN : 0387712763
Genre : Mathematics
File Size : 66. 49 MB
Format : PDF
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Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.

Visualdsolve

Author : Dan Schwalbe
ISBN : UVA:X006073311
Genre : Mathematics
File Size : 33. 16 MB
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This book/software package is a comprehensive Mathematica package for the visualization of solutions to ordinary differential equations. It includes well-known DE visualization tools such as solution plots and orbits, as well as some new ideas such as the modeling of shaded gray regions in the phase plane. VisualDSolve is an excellent resource for anyone seeking a greater understanding of solutions to ordinary differential equations.

Ordinary Differential Equations In The Complex Domain

Author : Einar Hille
ISBN : 0486696200
Genre : Mathematics
File Size : 77. 99 MB
Format : PDF, Kindle
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Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.

Riccati Differential Equations

Author : Reid
ISBN : 9780080955957
Genre : Mathematics
File Size : 27. 94 MB
Format : PDF, ePub
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Riccati Differential Equations

Stochastic Differential Equations And Applications

Author : Avner Friedman
ISBN : 9781483217871
Genre : Mathematics
File Size : 28. 13 MB
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Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume is divided into nine chapters. Chapters 1 to 5 deal with the basic theory of stochastic differential equations, including discussions of the Markov processes, Brownian motion, and the stochastic integral. Chapter 6 examines the connections between solutions of partial differential equations and stochastic differential equations, while Chapter 7 describes the Girsanov’s formula that is useful in the stochastic control theory. Chapters 8 and 9 evaluate the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity. This book is intended primarily for undergraduate and graduate mathematics students.

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