Differential Equations with Boundary-Value Problems (7TH)

Differential Equations with Boundary-Value Problems (7TH)

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  • 製本 Hardcover:ハードカバー版/ページ数 526 p.
  • 言語 ENG,ENG
  • 商品コード 9780495108368
  • DDC分類 515.35

Full Description


DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 7th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.

Table of Contents

Preface                                            xi
Introduction To Differential Equations 1 (33)
Definitions and Terminology 2 (11)
Initial-Value Problems 13 (6)
Differential Equations as Mathematical 19 (15)
Models
Chapter 1 In Review 32 (2)
First-Order Differential Equations 34 (48)
Solution Curves Without a Solution 35 (9)
Direction Fields 35 (2)
Autonomous First-Order DEs 37 (7)
Separable Variables 44 (9)
Linear Equations 53 (9)
Exact Equations 62 (8)
Solutions by Substitutions 70 (5)
A Numerical Method 75 (7)
Chapter 2 In Review 80 (2)
Modeling With First-Order Differential 82 (35)
Equations
Linear Models 83 (11)
Nonlinear Models 94 (11)
Modeling with Systems of First-Order DEs 105(12)
Chapter 3 In Review 113(4)
Higher-Order Differential Equations 117(64)
Preliminary Theory---Linear Equations 118(12)
Initial-Value and Boundary-Value 118(2)
Problems
Homogeneous Equations 120(5)
Nonhomogeneous Equations 125(5)
Reduction of Order 130(3)
Homogeneous Linear Equations with 133(7)
Constant Coefficients
Undetermined Coefficients---Superposition 140(10)
Approach
Undetermined Coefficients---Annihilator 150(7)
Approach
Variation of Parameters 157(5)
Cauchy-Euler Equation 162(7)
Solving Systems of Linear DEs by 169(5)
Elimination
Nonlinear Differential Equations 174(7)
Chapter 4 In Review 178(3)
Modeling With Higher-Order Differential 181(38)
Equations
Linear Models: Initial-Value Problems 182(17)
Spring/Mass Systems: Free Undamped 182(4)
Motion
Spring/Mass Systems: Free Damped Motion 186(3)
Spring/Mass Systems: Driven Motion 189(3)
Series Circuit Analogue 192(7)
Linear Models: Boundary-Value Problems 199(8)
Nonlinear Models 207(12)
Chapter 5 In Review 216(3)
Series Solutions Of Linear Equations 219(36)
Solutions About Ordinary Points 220(11)
Review of Power Series 220(3)
Power Series Solutions 223(8)
Solutions About Singular Points 231(10)
Special Functions 241(14)
Bessel's Equation 241(7)
Legendre's Equation 248(5)
Chapter 6 In Review 253(2)
The Laplace Transform 255(48)
Definition of the Laplace Transform 256(6)
Inverse Transforms and Transforms of 262(8)
Derivatives
Inverse Transforms 262(3)
Transforms of Derivatives 265(5)
Operational Properties I 270(12)
Translation on the s-Axis 271(3)
Translation on the t-Axis 274(8)
Operational Properties II 282(10)
Derivatives of a Transform 282(1)
Transforms of Integrals 283(4)
Transform of a Periodic Function 287(5)
The Dirac Delta Function 292(3)
Systems of Linear Differential Equations 295(8)
Chapter 7 In Review 300(3)
Systems Of Linear First-Order Differential 303(36)
Equations
Preliminary Theory---Linear Systems 304(7)
Homogeneous Linear Systems 311(15)
Distinct Real Eigenvalues 312(3)
Repeated Eigenvalues 315(5)
Complex Eigenvalues 320(6)
Nonhomogeneous Linear Systems 326(8)
Undetermined Coefficients 326(3)
Variation of Parameters 329(5)
Matrix Exponential 334(5)
Chapter 8 In Review 337(2)
Numerical Solutions Of Ordinary 339(24)
Differential Equations
Euler Methods and Error Analysis 340(5)
Runge-Kutta Methods 345(5)
Multistep Methods 350(3)
Higher-Order Equations and Systems 353(5)
Second-Order Boundary-Value Problems 358(5)
Chapter 9 In Review 362(1)
Plane Autonomous Systems 363(34)
Autonomous Systems 364(6)
Stability of Linear Systems 370(8)
Linearization and Local Stability 378(10)
Autonomous Systems as Mathematical Models 388(9)
Chapter 10 In Review 395(2)
Orthogonal Functions And Fourier Series 397(35)
Orthogonal Functions 398(5)
Fourier Series 403(5)
Fourier Cosine and Sine Series 408(8)
Sturm-Liouville Problem 416(7)
Bessel and Legendre Series 423(9)
Fourier-Bessel Series 424(3)
Fourier-Legendre Series 427(3)
Chapter 11 In Review 430(2)
Boundary-Value Problems In Rectangular 432(39)
Coordinates
Separable Partial Differential Equations 433(4)
Classical PDEs and Boundary-Value Problems 437(6)
Heat Equation 443(2)
Wave Equation 445(5)
Laplace's Equation 450(5)
Nonhomogeneous Boundary-Value Problems 455(6)
Orthogonal Series Expansions 461(5)
Higher-Dimensional Problems 466(5)
Chapter 12 In Review 469(2)
Boundary-Value Problems In Other Coordinate 471(17)
Systems
Polar Coordinates 472(5)
Polar and Cylindrical Coordinates 477(6)
Spherical Coordinates 483(5)
Chapter 13 In Review 486(2)
Integral Transforms 488(23)
Error Function 489(1)
Laplace Transform 490(8)
Fourier Integral 498(6)
Fourier Transforms 504(7)
Chapter 14 In Review 510(1)
Numerical Solutions Of Partial Differential 511
Equations
Laplace's Equation 512(5)
Heat Equation 517(5)
Wave Equation 522
Chapter 15 In Review 526
Appendices
I. Gamma Function 1 (2)
II. Matrices 3 (18)
III. Laplace Transforms 21
Answers for Selected Odd-Numbered Problems 1 (1)
Index 1