Elementary Differential Equations and Boundary Value Problems, - International Adaptatio

Klappentext 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.  Zusammenfassung 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. Inhaltsverzeichnis 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 n¿¿ 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, Par...

List of contents

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 n¿¿ 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 

Product details

• Authors: Boyce, W Boyce, William E Boyce, William E. Boyce, William E. (Rensselaer Polytechnic Institut Boyce, William E. Diprima Boyce, Boyce William E., Richard C Diprima, Richard C. Diprima, DiPrima Richard C., Douglas Meade, Douglas B. Meade, Meade Douglas B.
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Paperback / Softback
• Released: 31.08.2022
• EAN: 9781119820512
• ISBN: 978-1-119-82051-2
• No. of pages: 736
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Mathematik, Mathematics, Differentialgleichung, Differentialgleichungen, Differential equations, Randwertproblem