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Elementary Differential Equations and Boundary Value Problems, International Adaptation de Douglas B. Meade

Elementary Differential Equations and Boundary Value Problems, International Adaptation

Autor Douglas B. Meade, Richard C. Diprima, William E. Boyce
en Limba Engleză Paperback – 23 iun 2022

Analiza modelelor matematice de bază constituie punctul de plecare în această a 12-a ediție a volumului Elementary Differential Equations and Boundary Value Problems, International Adaptation. Subliniem faptul că textul este redactat din perspectiva matematicianului aplicat, reușind să echilibreze rigoarea teoretică necesară unui curs universitar cu utilitatea practică a metodelor de aproximare. Notăm cu interes progresia logică a materiei: de la clasificarea ecuațiilor și studiul ecuațiilor de ordinul întâi (inclusiv dinamica populațiilor și metoda lui Euler), până la tratarea complexă a ecuațiilor liniare de ordinul doi și a sistemelor neomogene. Această ediție internațională rafinează expunerea teoriei elementare, punând un accent sporit pe metodele de soluționare care și-au dovedit eficiența într-o gamă largă de aplicații științifice. Cititorii familiarizați cu Applied Differential Equations de Vladimir A. Dobrushkin vor aprecia în acest volum o structură similar de riguroasă, însă Elementary Differential Equations and Boundary Value Problems, International Adaptation se distinge prin integrarea mai profundă a analizei existenței și unicității soluțiilor în contextul modelelor fizice reale. Structura manualului este concepută pentru a sprijini parcursul academic al studenților STEM, oferind o tranziție lină de la calculul diferențial clasic către subiecte avansate precum transformata Laplace sau sistemele autonome. Considerăm că organizarea capitolelor, care include secțiuni dedicate ecuațiilor exacte și factorilor integranți, reflectă o experiență pedagogică consolidată de-a lungul a numeroase ediții, transformând acest titlu într-un instrument de referință pentru programa universitară actuală.

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Specificații

ISBN-13: 9781119820512
ISBN-10: 1119820510
Pagini: 736
Dimensiuni: 215 x 275 x 29 mm
Greutate: 1.57 kg
Ediția:12. Auflage
Editura: John Wiley & Sons, Inc.
Locul publicării:Hoboken, United States

De ce să citești această carte

Este manualul standard pentru studenții de la facultățile de profil tehnic sau matematic care urmează cursuri de ecuații diferențiale. Cititorul câștigă o înțelegere profundă a metodelor de rezolvare, beneficiind de un echilibru între teorie și aplicații practice. Ediția a 12-a aduce claritate și o structură adaptată cerințelor academice internaționale moderne, fiind esențială pentru pregătirea examenelor și fundamentarea cunoștințelor de inginerie sau fizică.

Cuprins

TABLE OF CONTENTS 1 Introduction 1.1 Some Basic Mathematical Models 1.2 Solutions of Some Differential Equations 1.3 Classification of Differential Equations 2 First-Order Differential Equations 2.1 Linear Differential Equations; Method of Integrating Factors 2.2 Separable Differential Equations 2.3 Modeling with First-Order Linear Differential Equations 2.4 Differences Between Linear and Nonlinear Differential Equations 2.5 Autonomous Differential Equations and Population Dynamics 2.6 Exact Differential Equations and Integrating Factors 2.7 Numerical Approximations: Euler's Method 2.8 The Existence and Uniqueness Theorem 2.9 First-Order Difference Equations 3 Second-Order Linear Differential Equations 3.1 Homogeneous Differential Equations with Constant Coefficients 3.2 Solutions of Linear Homogeneous Equations; the Wronskian 3.3 Complex Roots of the Characteristic Equation 3.4 Repeated Roots; Reduction of Order 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients 3.6 Variation of Parameters 3.7 Mechanical and Electrical Vibrations 3.8 Forced Periodic Vibrations 3.9 Central Gravitational Forces and Kepler's Laws 4 Higher-Order Linear Differential Equations 4.1 General Theory of nth Order Linear Differential Equations 4.2 Homogeneous Differential Equations with Constant Coefficients 4.3 The Method of Undetermined Coefficients 4.4 The Method of Variation of Parameters 5 Series Solutions of First-Order and Second-Order Linear Equations 5.1 Review of Power Series 5.2 Series Solution of First Order Equations 5.3 Series Solutions Near an Ordinary Point, Part I 5.4 Series Solutions Near an Ordinary Point, Part II 5.5 Euler Equations; Regular Singular Points 5.6 Series Solutions Near a Regular Singular Point, Part I 5.7 Series Solutions Near a Regular Singular Point, Part II 5.8 Bessel's Equation 6 Systems of First-Order Linear Equations 6.1 Introduction 6.2 Matrices 6.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors 6.4 Basic Theory of Systems of First-Order Linear Equations 6.5 Homogeneous Linear Systems with Constant Coefficients 6.6 Complex-Valued Eigenvalues 6.7 Fundamental Matrices 6.8 Repeated Eigenvalues 6.9 Nonhomogeneous Linear Systems 7 The Laplace Transform 7.1 Definition of the Laplace Transform 7.2 Solution of Initial Value Problems 7.3 Step Functions 7.4 Differential Equations with Discontinuous Forcing Functions 7.5 Impulse Functions 7.6 The Convolution Integral 8 Numerical Methods of Solving First Order Equations 8.1 The Euler or Tangent Line Method 8.2 Improvements on the Euler Method 8.3 The Runge-Kutta Method 8.4 Multistep Methods 8.5 Systems of First-Order Equations 8.6 More on Errors; Stability 9 Nonlinear Differential Equations and Stability 9.1 The Phase Plane: Linear Systems 9.2 Autonomous Systems and Stability 9.3 Locally Linear Systems 9.4 Competing Species 9.5 Predator - Prey Equations 9.6 Lyapunov's Second Method 9.7 Periodic Solutions and Limit Cycles 9.8 Chaos and Strange Attractors: The Lorenz Equations 10 Partial Differential Equations and Fourier Series 10.1 Two-Point Boundary Value Problems 10.2 Fourier Series 10.3 The Fourier Convergence Theorem 10.4 Even and Odd Functions 10.5 Separation of Variables; Heat Conduction in a Rod 10.6 Other Heat Conduction Problems 10.7 The Wave Equation: Vibrations of an Elastic String 10.8 Laplace's Equation A APPENDIX 537 B APPENDIX 541 11 Boundary Value Problems and Sturm-Liouville Theory 11.1 The Occurrence of Two-Point Boundary Value Problems 11.2 Sturm-Liouville Boundary Value Problems 11.3 Nonhomogeneous Boundary Value Problems 11.4 Singular Sturm-Liouville Problems 11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion 11.6 Series of Orthogonal Functions: Mean Convergence Web Appendix Special Functions: On Legendre Polynomials and Functions ANSWERS TO PROBLEMS INDEX

Descriere

Boyce's Elementary Differential Equations and Boundary Value Problems is written from the viewpoint of the applied mathematician, with diverse interest in differential equations, ranging from quite theoretical to intensely practical-and usually a combination of both. The intended audience for the text is undergraduate STEM students taking an introductory course in differential equations. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent, while a basic familiarity with matrices is helpful. This new edition of the book aims to preserve, and to enhance the qualities that have made previous editions so successful. It offers a sound and accurate exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications.