微分方程式と境界値問題(グローバル版テキスト)<br>Boyce's Elementary Differential Equations and Boundary Value Problems -- Paperback / softback (Global Edi)

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微分方程式と境界値問題(グローバル版テキスト)
Boyce's Elementary Differential Equations and Boundary Value Problems -- Paperback / softback (Global Edi)

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Full Description


Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) 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. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study.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. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.

Table of Contents

Preface                                            vii
1 Introduction 1 (23)
1.1 Some Basic Mathematical Models; 1 (8)
Direction Fields
1.2 Solutions of Some Differential 9 (7)
Equations
1.3 Classification of Differential 16 (8)
Equations
2 First-Order Differential Equations 24 (77)
2.1 Linear Differential Equations; Method 24 (9)
of Integrating Factors
2.2 Separable Differential Equations 33 (6)
2.3 Modeling with First-Order 39 (11)
Differential Equations
2.4 Differences Between Linear and 50 (8)
Nonlinear Differential Equations
2.5 Autonomous Differential Equations and 58 (11)
Population Dynamics
2.6 Exact Differential Equations and 69 (6)
Integrating Factors
2.7 Numerical Approximations: Euler's 75 (8)
Method
2.8 The Existence and Uniqueness Theorem 83 (7)
2.9 First-Order Difference Equations 90 (11)
3 Second-Order Linear Differential Equations 101(66)
3.1 Homogeneous Differential Equations 101(7)
with Constant Coefficients
3.2 Solutions of Linear Homogeneous 108(10)
Equations; the Wronskian
3.3 Complex Roots of the Characteristic 118(7)
Equation
3.4 Repeated Roots; Reduction of Order 125(6)
3.5 Nonhomogeneous Equations; Method of 131(9)
Undetermined Coefficients
3.6 Variation of Parameters 140(5)
3.7 Mechanical and Electrical Vibrations 145(12)
3.8 Forced Periodic Vibrations 157(10)
4 Higher-Order Linear Differential Equations 167(20)
4.1 General Theory of nth Order Linear 167(5)
Differential Equations
4.2 Homogeneous Differential Equations 172(7)
with Constant Coefficients
4.3 The Method of Undetermined 179(4)
Coefficients
4.4 The Method of Variation of Parameters 183(4)
5 Series Solutions of Second-Order Linear 187(52)
Equations
5.1 Review of Power Series 187(6)
5.2 Series Solutions Near an Ordinary 193(10)
Point, Part I
5.3 Series Solutions Near an Ordinary 203(6)
Point, Part II
5.4 Euler Equations; Regular Singular 209(8)
Points
5.5 Series Solutions Near a Regular 217(5)
Singular Point, Part I
5.6 Series Solutions Near a Regular 222(6)
Singular Point, Part II
5.7 Bessel's Equation 228(11)
6 The Laplace Transform 239(40)
6.1 Definition of the Laplace Transform 239(7)
6.2 Solution of Initial Value Problems 246(9)
6.3 Step Functions 255(7)
6.4 Differential Equations with 262(6)
Discontinuous Forcing Functions
6.5 Impulse Functions 268(5)
6.6 The Convolution Integral 273(6)
7 Systems of First-Order Linear Equations 279(73)
7.1 Introduction 279(6)
7.2 Matrices 285(8)
7.3 Systems of Linear Algebraic 293(9)
Equations; Linear Independence,
Eigenvalues, Eigenvectors
7.4 Basic Theory of Systems of 302(5)
First-Order Linear Equations
7.5 Homogeneous Linear Systems with 307(10)
Constant Coefficients
7.6 Complex-Valued Eigenvalues 317(10)
7.7 Fundamental Matrices 327(8)
7.8 Repeated Eigenvalues 335(8)
7.9 Nonhomogeneous Linear Systems 343(9)
8 Numerical Methods 352(34)
8.1 The Euler or Tangent Line Method 352(9)
8.2 Improvements on the Euler Method 361(4)
8.3 The Runge-Kutta Method 365(4)
8.4 Multistep Methods 369(5)
8.5 Systems of First-Order Equations 374(2)
8.6 More on Errors; Stability 376(10)
9 Nonlinear Differential Equations and 386(75)
Stability
9.1 The Phase Plane: Linear Systems 386(10)
9.2 Autonomous Systems and Stability 396(9)
9.3 Locally Linear Systems 405(10)
9.4 Competing Species 415(11)
9.5 Predator-Prey Equations 426(7)
9.6 Liapunov's Second Method 433(9)
9.7 Periodic Solutions and Limit Cycles 442(10)
9.8 Chaos and Strange Attractors: The 452(9)
Lorenz Equations
10 Partial Differential Equations and 461(66)
Fourier Series
10.1 Two-Point Boundary Value Problems 461(6)
10.2 Fourier Series 467(8)
10.3 The Fourier Convergence Theorem 475(5)
10.4 Even and Odd Functions 480(6)
10.5 Separation of Variables; Heat 486(8)
Conduction in a Rod
10.6 Other Heat Conduction Problems 494(8)
10.7 The Wave Equation: Vibrations of an 502(10)
Elastic String
10.8 Laplace's Equation 512(15)
11 Boundary Value Problems and 527(44)
Sturm-Liouville Theory
11.1 The Occurrence of Two-Point Boundary 527(6)
Value Problems
11.2 Sturm-Liouville Boundary Value 533(10)
Problems
11.3 Nonhomogeneous Boundary Value 543(11)
Problems
11.4 Singular Sturm-Liouville Problems 554(6)
11.5 Further Remarks on the Method of 560(4)
Separation of Variables: A Bessel Series
Expansion
11.6 Series of Orthogonal Functions: Mean 564(7)
Convergence
Answers To Problems 571(31)
Index 602