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Boyces Elementary Differential Equations and Boundary Value Problems 11th Edition, Global Edition [Mīkstie vāki]

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  • Formāts: Paperback / softback, 624 pages, height x width x depth: 276x219x20 mm, weight: 1274 g
  • Izdošanas datums: 26-May-2017
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1119382874
  • ISBN-13: 9781119382874
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  • Formāts: Paperback / softback, 624 pages, height x width x depth: 276x219x20 mm, weight: 1274 g
  • Izdošanas datums: 26-May-2017
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1119382874
  • ISBN-13: 9781119382874
Citas grāmatas par šo tēmu:
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.
Preface vii
1 Introduction
1(23)
1.1 Some Basic Mathematical Models; Direction Fields
1(8)
1.2 Solutions of Some Differential Equations
9(7)
1.3 Classification of Differential Equations
16(8)
2 First-Order Differential Equations
24(77)
2.1 Linear Differential Equations; Method of Integrating Factors
24(9)
2.2 Separable Differential Equations
33(6)
2.3 Modeling with First-Order Differential Equations
39(11)
2.4 Differences Between Linear and Nonlinear Differential Equations
50(8)
2.5 Autonomous Differential Equations and Population Dynamics
58(11)
2.6 Exact Differential Equations and Integrating Factors
69(6)
2.7 Numerical Approximations: Euler's Method
75(8)
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 with Constant Coefficients
101(7)
3.2 Solutions of Linear Homogeneous Equations; the Wronskian
108(10)
3.3 Complex Roots of the Characteristic Equation
118(7)
3.4 Repeated Roots; Reduction of Order
125(6)
3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
131(9)
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 Differential Equations
167(5)
4.2 Homogeneous Differential Equations with Constant Coefficients
172(7)
4.3 The Method of Undetermined Coefficients
179(4)
4.4 The Method of Variation of Parameters
183(4)
5 Series Solutions of Second-Order Linear Equations
187(52)
5.1 Review of Power Series
187(6)
5.2 Series Solutions Near an Ordinary Point, Part I
193(10)
5.3 Series Solutions Near an Ordinary Point, Part II
203(6)
5.4 Euler Equations; Regular Singular Points
209(8)
5.5 Series Solutions Near a Regular Singular Point, Part I
217(5)
5.6 Series Solutions Near a Regular Singular Point, Part II
222(6)
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 Discontinuous Forcing Functions
262(6)
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 Equations; Linear Independence, Eigenvalues, Eigenvectors
293(9)
7.4 Basic Theory of Systems of First-Order Linear Equations
302(5)
7.5 Homogeneous Linear Systems with Constant Coefficients
307(10)
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 Stability
386(75)
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 Lorenz Equations
452(9)
10 Partial Differential Equations and Fourier Series
461(66)
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 Conduction in a Rod
486(8)
10.6 Other Heat Conduction Problems
494(8)
10.7 The Wave Equation: Vibrations of an Elastic String
502(10)
10.8 Laplace's Equation
512(15)
11 Boundary Value Problems and Sturm-Liouville Theory
527(44)
11.1 The Occurrence of Two-Point Boundary Value Problems
527(6)
11.2 Sturm-Liouville Boundary Value Problems
533(10)
11.3 Nonhomogeneous Boundary Value Problems
543(11)
11.4 Singular Sturm-Liouville Problems
554(6)
11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion
560(4)
11.6 Series of Orthogonal Functions: Mean Convergence
564(7)
Answers To Problems 571(31)
Index 602