Introduction to Partial Differential Equations

Author: Aslak Tveito
Publisher: Springer Science & Business Media
ISBN: 0387227733
Format: PDF, ePub, Mobi
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Combining both the classical theory and numerical techniques for partial differential equations, this thoroughly modern approach shows the significance of computations in PDEs and illustrates the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between these techniques. The authors present the material at an easy pace and exercises ranging from the straightforward to the challenging have been included. In addition there are some "projects" suggested, either to refresh the students memory of results needed in this course, or to extend the theories developed in the text. Suitable for undergraduate and graduate students in mathematics and engineering.

An Introduction to Partial Differential Equations

Author: Michael Renardy
Publisher: Springer Science & Business Media
ISBN: 0387216871
Format: PDF
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Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.

Introduction to Symmetry Analysis

Author: Brian J. Cantwell
Publisher: Cambridge University Press
ISBN: 9781139431712
Format: PDF, ePub
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Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-B├Ącklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries.

Introduction to Numerical Methods in Differential Equations

Author: Mark H. Holmes
Publisher: Springer Science & Business Media
ISBN: 0387681213
Format: PDF
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This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.

A First Course in the Numerical Analysis of Differential Equations

Author: A. Iserles
Publisher: Cambridge University Press
ISBN: 0521734908
Format: PDF
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lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

Partial Differential Equations with Numerical Methods

Author: Stig Larsson
Publisher: Springer Science & Business Media
ISBN: 3540887059
Format: PDF, ePub
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The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

Numerical Methods for Elliptic and Parabolic Partial Differential Equations

Author: Peter Knabner
Publisher: Springer Science & Business Media
ISBN: 0387217622
Format: PDF, Mobi
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This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Applied Partial Differential Equations

Author: J. R. Ockendon
Publisher: Oxford University Press on Demand
ISBN: 9780198527718
Format: PDF, Mobi
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Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This revised edition of Applied Partial Differential Equations contains many new sections and exercises including transform methods, free surface flows, linear elasticity and complex characteristics.

Differential Equations and Dynamical Systems

Author: Lawrence Perko
Publisher: Springer Science & Business Media
ISBN: 1461300037
Format: PDF, Mobi
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This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations.