A First Course in Differential Equations : With Modeling Applications (9TH)

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A First Course in Differential Equations : With Modeling Applications (9TH)

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  • 製本 Hardcover:ハードカバー版/ページ数 362 p.
  • 言語 ENG,ENG
  • 商品コード 9780495108245
  • DDC分類 515.35

Table of Contents

Preface                                            ix
Introduction to Differential Equations 1 (33)
Definitions and Terminology 2 (11)
Initial-Value Problems 13 (6)
Differential Equations as Mathematical 19 (15)
Models
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)
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)
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)
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)
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)
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)
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)
in Review 337(2)
Numerical Solutions of Ordinary 339(1)
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(4)
in Review 362
Appendices
Gamma Function 1 (2)
Matrices 3 (18)
Laplace Transforms 21
Answers for Selected Odd-Numbered Problems 1
Index