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Elementary Differential Equations and Boundary Value Problems Wileyplus Registration Card plus Print Companion 11 PSC/LSL

  • Formaat: kõrgus x laius x paksus: 2625x2125x0.73 mm
  • Ilmumisaeg: 12-Nov-2016
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119336619
  • ISBN-13: 9781119336617
Teised raamatud teemal:
  • Formaat: kõrgus x laius x paksus: 2625x2125x0.73 mm
  • Ilmumisaeg: 12-Nov-2016
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119336619
  • ISBN-13: 9781119336617
Teised raamatud teemal:

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Elementary Differential Equations and Boundary Value Problems, 11th Edition, 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(79)
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(12)
2.4 Differences Between Linear and Nonlinear Differential Equations
51(7)
2.5 Autonomous Differential Equations and Population Dynamics
58(12)
2.6 Exact Differential Equations and Integrating Factors
70(6)
2.7 Numerical Approximations: Euler's Method
76(7)
2.8 The Existence and Uniqueness Theorem
83(8)
2.9 First-Order Difference Equations
91(12)
3 Second-Order Linear Differential Equations
103(66)
3.1 Homogeneous Differential Equations with Constant Coefficients
103(7)
3.2 Solutions of Linear Homogeneous Equations; the Wronskian
110(10)
3.3 Complex Roots of the Characteristic Equation
120(7)
3.4 Repeated Roots; Reduction of Order
127(6)
3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
133(9)
3.6 Variation of Parameters
142(5)
3.7 Mechanical and Electrical Vibrations
147(12)
3.8 Forced Periodic Vibrations
159(10)
4 Higher-Order Linear Differential Equations
169(20)
4.1 General Theory of nth Order Linear Differential Equations
169(5)
4.2 Homogeneous Differential Equations with Constant Coefficients
174(7)
4.4 The Method of Undetermined Coefficients
181(4)
4.5 The Method of Variation of Parameters
185(4)
5 Series Solutions of Second-Order Linear Equations
189(52)
5.1 Review of Power Series
189(6)
5.2 Series Solutions Near an Ordinary Point, Part I
195(10)
5.3 Series Solutions Near an Ordinary Point, Part II
205(6)
5.4 Euler Equations; Regular Singular Points
211(8)
5.5 Series Solutions Near a Regular Singular Point, Part I
219(5)
5.6 Series Solutions Near a Regular Singular Point, Part II
224(6)
5.7 Bessel's Equation
230(11)
6 The Laplace Transform
241(40)
6.1 Definition of the Laplace Transform
241(7)
6.2 Solution of Initial Value Problems
248(9)
6.3 Step Functions
257(7)
6.4 Differential Equations with Discontinuous Forcing Functions
264(6)
6.5 Impulse Functions
270(5)
6.6 The Convolution Integral
275(6)
7 Systems of First-Order Linear Equations
281(73)
7.1 Introduction
281(5)
7.2 Matrices
286(9)
7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
295(9)
7.4 Basic Theory of Systems of First-Order Linear Equations
304(5)
7.5 Homogeneous Linear Systems with Constant Coefficients
309(10)
7.6 Complex-Valued Eigenvalues
319(10)
7.7 Fundamental Matrices
329(8)
7.8 Repeated Eigenvalues
337(8)
7.9 Nonhomogeneous Linear Systems
345(9)
8 Numerical Methods
354(34)
8.1 The Euler or Tangent Line Method
354(9)
8.2 Improvements on the Euler Method
363(4)
8.3 The Runge-Kutta Method
367(4)
8.4 Multistep Methods
371(5)
8.5 Systems of First-Order Equations
376(2)
8.6 More on Errors; Stability
378(10)
9 Nonlinear Differential Equations and Stability
388(75)
9.1 The Phase Plane: Linear Systems
388(10)
9.2 Autonomous Systems and Stability
398(9)
9.3 Locally Linear Systems
407(10)
9.4 Competing Species
417(11)
9.5 Predator-Prey Equations
428(7)
9.6 Liapunov's Second Method
435(9)
9.7 Periodic Solutions and Limit Cycles
444(10)
9.8 Chaos and Strange Attractors: The Lorenz Equations
454(9)
10 Partial Differential Equations and Fourier Series
463(66)
10.1 Two-Point Boundary Value Problems
463(6)
10.2 Fourier Series
469(8)
10.3 The Fourier Convergence Theorem
477(5)
10.4 Even and Odd Functions
482(6)
10.5 Separation of Variables; Heat Conduction in a Rod
488(8)
10.6 Other Heat Conduction Problems
496(8)
10.7 The Wave Equation: Vibrations of an Elastic String
504(10)
10.8 Laplace's Equation
514(15)
11 Boundary Value Problems and Sturm-Liouville Theory
529(44)
11.1 The Occurrence of Two-Point Boundary Value Problems
529(6)
11.2 Sturm-Liouville Boundary Value Problems
535(10)
11.3 Nonhomogeneous Boundary Value Problems
545(11)
11.4 Singular Sturm-Liouville Problems
556(6)
11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion
562(4)
11.6 Series of Orthogonal Functions: Mean Convergence
566(7)
Answers to Problems 573(35)
Index 608