# krainaksiazek differential equations methods and applications 20123748

- znaleziono 99 produktów w 6 sklepach

### Differential Equations: An Introduction to Modern Methods and Applications 3e Student Solutions Manual

**Książki**

Sklep: KrainaKsiazek.pl

### Optimal Control of Partial Differential Equations II: Theory and Applications Birkhäuser

**Książki / Literatura obcojęzyczna**

This volume contains the contributions of participants of the conference "Optimal Control of Partial Differential Equations" which, under the chairmanship of the editors, took place at the Mathematisches Forschungsinstitut Oberwolfach from May 18 to May 24, 1986. The great variety of topics covered by the contributions strongly indicates that also in the future it will be impossible to develop a unifying control theory of partial differential equations. On the other hand, there is a strong tendency to treat prob lems which are directly connected to practical applications. So this volume contains real-world applications like optimal cooling laws for the production of rolled steel or concrete solutions for the problem of optimal shape design in mechanics and hydrody namics. Another main topic is the construction of numerical methods. This includes applications of the finite element method as well as of Quasi-Newton-methods to con strained and unconstrained control problems. Also, very complex problems arising in the theory of free boundary value problems are treated. ]~inally, some contribu tions show how practical problems stimulate the further development of the theory; in particular, this is the case for fields like suboptimal control, necessary optimality conditions and sensitivity analysis. As usual, the lectures and stimulating discussions took place in the pleasant at mosphere of the Mathematisches Forschungsinstitut Oberwolfach. Special thanks of the participants are returned to the Director as well as to the staff of the institute.

Sklep: Libristo.pl

### Perturbation Methods for Differential Equations Birkhäuser

**Książki / Literatura obcojęzyczna**

Many differential equations with nonlinearities or variable coefficients do not permit the construction of exact solutions. This book introduces several perturbation methods that can be used to develop approximate solutions of such equations. To accommodate an interdisciplinary readership, the author focuses almost exclusively on procedures, underlying ideas and applications, and minimizes technical proofs.§The book begins with an introduction to the idea of asymptotic approximations to the evaluation of transcendental functions and the solution of differential equations, as well as a discussion of the regular perturbation approach. What follows is a systematic and unified treatment of the resolution of the nonuniformities produced, as a rule, by the regular perturbation method. Several singular perturbation methods are examined, including the methods of: strained parameters, averaging, matched asymptotic expansions, multiple scales, and quantum-field-theoretic renormalization.§Methods treated are applied to ordinary and partial differential equations arising in various problems of solid mechanics, fluid dynamics, and plasma physics. Background material is provided in each chapter along with illustrative examples, problems, and selected solutions. A comprehensive bibliography and index complete the work.§Perturbation Methods for Differential Equations serves as a textbook for graduate students and advanced undergraduate students in applied mathematics, physics, and engineering who want to enhance their expertise with mathematical methods via a one- or two-semester course. Researchers in these areas will also find the book an excellent reference.

Sklep: Libristo.pl

### Numerical Methods For Elliptic And Parabolic Partial Differential Equations

**Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Calculus & mathematical analysis>Differential calculus & equationsKsi...**

Provides An Introduction To Numerical Methods For Partial Differential Equations, Interweaving Both Theory And Applications Throughout. This Text Covers Finite Difference, Finite Element And Finite Volume Methods. It Is Useful For Graduate Students In Mathematics, Engineering And Physics.

Sklep: Gigant.pl

### Introduction to Computation and Modeling for Differential Equations John Wiley & Sons Inc

**Książki / Literatura obcojęzyczna**

"Introduction to Computation and Modeling for Differential Equations, Second Edition" provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique "Five-M" approach: Modeling, Mathematics, Methods, MATLAB(R), and Multiphysics. This approach facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation, and it also illustrates how a problem is solved numerically using the appropriate mathematical methods. The "Second Edition" includes new topical coverage on variational formulation, the finite element method, examples of discretization, Anstaz methods for parabolic PDEs and elliptic PDEs, Galerkin's method for the model problem, and finite difference and volume methods. Many new real-world examples from scientific and engineering applications, including mechanics, fluid dynamics, solid mechanics, chemical engineering, electromagnetic field theory, and control theory have been added. All presented examples are solved through the use of MATLAB and the interactive scientific computing program Comsol Multiphysics. Numerous illustrations aid in the visualization of the solutions, and a related website features select solutions to problems and MATLAB datasets.

Sklep: Libristo.pl

### Fractional Differential Equations BERTRAMS

**Książki / Literatura obcojęzyczna**

This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research. A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. The key features include: a unique survey of many applications of fractional calculus; presents basic theory; includes a unified presentation of selected classical results, which are important for applications; provides many examples; contains a separate chapter of fractional order control systems, which opens new perspectives in control theory; the first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches; and, includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives.

Sklep: Libristo.pl

### Introduction to Linear Algebra and Differential Equations Dover Publications

**Książki / Literatura obcojęzyczna**

Preface 1. Complex Numbers 1.1 Introduction 1.2 The Algebra of Complex Numbers 1.3 The Geometry of Complex Numbers 1.4 Two-dimensional Vectors 1.5 Functions of a Complex Variable 1.6 Exponential Function 1.7 Power Series 2. Linear Algebraic Equations 2.1 Introduction 2.2 Matrices 2.3 Elimination Method 2.4 Determinants 2.5 Inverse of a Matrix 2.6 Existence and Uniqueness Theorems 3. Vector Spaces 3.1 Introduction 3.2 Three-dimensional Vectors 3.3 Axioms of a Vector Space 3.4 Dependence and Independence of Vectors 3.5 Basis and Dimension 3.6 Scalar Product 3.7 Orthonormal Bases 3.8 Infinite-dimensional Vector Spaces 4. Linear Transformations 4.1 Introduction 4.2 Definitions and Examples 4.3 Matrix Representations 4.4 Changes of Bases 4.5 Characteristic Values and Characteristic Vectors 4.6 Symmetric and Hermitian Matrices 4.7 Jordan Forms 5. First Order Differential Equations 5.1 Introduction 5.2 An Example 5.3 Basic Definitions 5.4 First Order Linear Equations 5.5 First Order Nonlinear Equations 5.6 Applications of First Order Equations 5.7 Numerical Methods 5.8 Existence and Uniqueness 6. Linear Differential Equations 6.1 Introduction 6.2 General Theorems 6.3 Variation of Parameters 6.4 Equations with Constant Coefficients 6.5 Method of Undetermined Coefficients 6.6 Applications 6.7 Green's Functions 7. Laplace Transforms 7.1 Introduction 7.2 Existence of the Transform 7.3 Transforms of Certain Functions 7.4 Inversion of the Transform 7.5 Solution of Differential Equations 7.6 Applications 7.7 Uniqueness of the Transform 8. Power-Series Methods 8.1 Introduction 8.2 Solution near Ordinary Points 8.3 Solution near Regular Singular Points 8.4 Bessel Functions 8.5 Boundary-value Problems 8.6 Convergence Theorems 9. Systems of Differential Equations 9.1 Introduction 9.2 First Order Systems 9.3 Linear First Order Systems 9.4 Linear First Order Systems with Constant Coefficients 9.5 Higher Order Linear Systems 9.6 Existence and Uniqueness Theorem Answers and Hints for Selected Exercises; Index

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### Differential Equations and Linear Algebra Cambridge University Press

**Książki / Literatura obcojęzyczna**

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.

Sklep: Libristo.pl

### Linear Partial Differential Equations for Scientists and Engineers Birkhäuser

**Książki / Literatura obcojęzyczna**

One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics.§This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications.§Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition will primarily serve as a textbook for the first two courses in PDEs, or in a course on advanced engineering mathematics. The book may also be used as a reference for graduate students, researchers, and professionals in modern applied mathematics, mathematical physics, and engineering. Readers will gain a solid mathematical background in PDEs, sufficient to start interdisciplinary collaborative research in a variety of fields.§Also by L. Debnath: Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition, ISBN 0-8176-4323-0.

Sklep: Libristo.pl

### Advanced Topics in Computational Partial Differential Equations Springer, Berlin

**Książki / Literatura obcojęzyczna**

The book is suitable for readers with a background in basic finite element and finite difference methods for partial differential equations who wants gentle introductions to advanced topics like parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to compute solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment, so to take advantage of these examples some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through discretization methods, algorithms, software design, verification, and computational examples.

Sklep: Libristo.pl

### Differential Equations Dover Publications

**Książki / Literatura obcojęzyczna**

Chapter 1. First Order Equations 1.1 Introduction 1.2 Variable separate 1.3 Geometric interpretation of first order equations 1.4 Existence and uniqueness theorem 1.5 Families of curves and envelopes 1.6 Clairaut equations Chapter 2. Special Methods for First Order Equations 2.1 Homogeneous equations--substitutions 2.2 Exact equations 2.3 Line integrals 2.4 First order linear equations--integrating factors 2.5 Orthogonal families 2.6 Review of power series 2.7 Series solutions Chapter 3. Linear Equations 3.1 Introduction 3.2 Two theorems on linear algebraic equations 3.3 General theory of linear equations 3.4 Second order equations with constant coefficients 3.5 Applications Chapter 4. Special Methods for Linear Equations 4.1 Complex-valued solutions 4.2 Linear differential operators 4.3 Homogeneous equations with constant coefficients 4.4 Method of undetermined coefficients 4.5 Inverse operators 4.6 Variation of parameters method Chapter 5. The Laplace Transform 5.1 Review of improper integrals 5.2 The Laplace transform 5.3 Properties of the transform 5.4 Solution of equations by transforms Chapter 6. Picard's Existence Theorem 6.1 Review 6.2 Outline of the Picard method 6.3 Proof of existence and uniqueness 6.4 Approximations to solutions Chapter 7. Systems of Equations 7.1 Geometric interpretation of a system 7.2 Other interpretations of a system 7.3 A system equivalent to M(x,y)dx+N(x,y)dy=0 7.4 Existence and uniqueness theorems 7.5 Existence theorem for nth order equations 7.6 Polygonal approximations for systems 7.7 Linear systems 7.8 Operator methods 7.9 Laplace transform methods Index

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### Mathematical Physics with Partial Differential Equations ACADEMIC PRESS

**Książki / Literatura obcojęzyczna**

"Mathematical Physics with Partial Differential Equations" is for advanced undergraduate and beginning graduate students taking a course on mathematical physics taught out of math departments. The text presents some of the most important topics and methods of mathematical physics. The premise is to study in detail the three most important partial differential equations in the field - the heat equation, the wave equation, and Laplace's equation. The most common techniques of solving such equations are developed in this book, including Green's functions, the Fourier transform, and the Laplace transform, which all have applications in mathematics and physics far beyond solving the above equations. The book's focus is on both the equations and their methods of solution. Ordinary differential equations and PDEs are solved including Bessel Functions, making the book useful as a graduate level textbook. The book's rigor supports the vital sophistication for someone wanting to continue further in areas of mathematical physics. This title: examines in depth both the equations and their methods of solution; presents physical concepts in a mathematical framework; contains detailed mathematical derivations and solutions - reinforcing the material through repetition of both the equations and the techniques; and, includes several examples solved by multiple methods-highlighting the strengths and weaknesses of various techniques and providing additional practice.

Sklep: Libristo.pl

### Analysis and Topology in Nonlinear Differential Equations Springer, Berlin

**Książki / Literatura obcojęzyczna**

This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in Joăo Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is perceptible throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novel applications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fully nonlinear equations and systems with different nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type. Also treated are analytic aspects as well as applications such as diffusion problems in mathematical genetics and finance and evolution equations related to electromechanical devices.

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### Fundamentals of Differential Equations and Boundary Value Problems Pearson Education Limited

**Książki / Literatura obcojęzyczna**

Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available computer software. Fundamentals of Differential Equations, Eighth Edition is suitable for a one-semester sophomore- or junior-level course. Fundamentals of Differential Equations with Boundary Value Problems,'Sixth Edition, contains enough material for a two-semester course that covers and builds on boundary value problems. The Boundary Value Problems version consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm-Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory).

Sklep: Libristo.pl

### Linear Ordinary Differential Equations Society for Industrial and Applied Mathematics

**Książki / Literatura obcojęzyczna**

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.

Sklep: Libristo.pl

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