Differential Equations : An Introduction to Modern Methods and Applications (PCK UNBND/)

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Differential Equations : An Introduction to Modern Methods and Applications (PCK UNBND/)

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 682 p.
  • 言語 ENG
  • 商品コード 9780471936954
  • DDC分類 515

Table of Contents

    1 Introduction                                 1  (39)
1.1 Some Basic Mathematical Models; 1 (10)
Direction Fields
1.2 Solutions of Some Differential 11 (11)
Equations
1.3 Numerical Approximations: Euler's 22 (11)
Method
1.4 Classification of Differential 33 (7)
Equations
2 First Order Differential Equations 40 (87)
2.1 Linear Equations; Method of 41 (8)
Integrating Factors
2.2 Separable Equations 49 (7)
2.3 Modeling with First Order Equations 56 (15)
2.4 Differences Between Linear and 71 (10)
Nonlinear Equations
2.5 Autonomous Equations and Population 81 (14)
Dynamics
2.6 Exact Equations and Integrating 95 (8)
Factors
2.7 Accuracy of Numerical Methods 103(8)
2.8 Improved Euler and Runge-Kutta Methods 111(16)
Projects 119(1)
2.P.1 Harvesting a Renewable Resource 119(1)
2.P.2 Designing a Drip Dispenser for a 120(2)
Hydrology Experiment
2.P.3 A Mathematical Model of a 122(2)
Groundwater Contaminant Source
2.P.4 Monte Carlo Option Pricing: 124(3)
Pricing Financial Options by Flipping a
Coin
3 Systems of Two First Order Equations 127(83)
3.1 Systems of Two Linear Algebraic 128(11)
Equations
3.2 Systems of Two First Order Linear 139(9)
Differential Equations
3.3 Homogeneous Linear Systems with 148(16)
Constant Coefficients
3.4 Complex Eigenvalues 164(11)
3.5 Repeated Eigenvalues 175(12)
3.6 A Brief Introduction to Nonlinear 187(7)
Systems
3.7 Numerical Methods for Systems of 194(16)
First Order Equations
Projects 199(1)
3.P.1 Eigenvalue-Placement Design of a 199(3)
Satellite Attitude Control System
3.P.2 Estimating Rate Constants for an 202(2)
Open Two-Compartment Model
3.P.3 The Ray Theory of Wave Propagation 204(4)
3.P.4 A Blood-Brain Pharmacokinetic 208(2)
Model
4 Second Order Linear Equations 210(96)
4.1 Definitions and Examples 210(13)
4.2 Theory of Second Order Linear 223(9)
Homogeneous Equations
4.3 Linear Homogeneous Equations with 232(11)
Constant Coefficients
4.4 Characteristic Equations with Complex 243(9)
Roots
4.5 Mechanical and Electrical Vibrations 252(11)
4.6 Nonhomogeneous Equations; Method of 263(9)
Undetermined Coefficients
4.7 Forced Vibrations, Frequency 272(11)
Response, and Resonance
4.8 Variation of Parameters 283(23)
Projects 293(1)
4.P.1 A Vibration Insulation Problem 293(1)
4.P.2 Linearization of a Nonlinear 294(2)
Mechanical System
4.P.3 A Spring-Mass Event Problem 296(1)
4.P.4 Uniformly Distributing Points on 297(4)
a Sphere
4.P.5 Euler-Lagrange Equations 301(5)
5 The Laplace Transform 306(84)
5.1 Definition of the Laplace Transform 307(9)
5.2 Properties of the Laplace Transform 316(7)
5.3 The Inverse Laplace Transform 323(9)
5.4 Solving Differential Equations with 332(8)
Laplace Transforms
5.5 Discontinuous Functions and Periodic 340(9)
Functions
5.6 Differential Equations with 349(7)
Discontinuous Forcing Functions
5.7 Impulse Functions 356(7)
5.8 Convolution Integrals and Their 363(9)
Applications
5.9 Linear Systems and Feedback Control 372(18)
Projects 382(1)
5.P.1 An Electric Circuit Problem 382(1)
5.P.2 Effects of Pole Locations on Step 382(3)
Responses of Second Order Systems
5.P.3 The Watt Governor, Feedback 385(5)
Control, and Stability
6 Systems of First Order Linear Equations 390(82)
6.1 Definitions and Examples 391(11)
6.2 Basic Theory of First Order Linear 402(10)
Systems
6.3 Homogeneous Linear Systems with 412(11)
Constant Coefficients
6.4 Complex Eigenvalues 423(10)
6.5 Fundamental Matrices and the 433(11)
Exponential of a Matrix
6.6 Nonhomogeneous Linear Systems 444(7)
6.7 Defective Matrices 451(21)
Projects 459(1)
6.P.1 A Compartment Model of Heat Flow 459(3)
in a Rod
6.P.2 Earthquakes and Tall Buildings 462(2)
6.P.3 Controlling a Spring-Mass System 464(8)
to Equilibrium
7 Nonlinear Differential Equations and 472(65)
Stability
7.1 Autonomous Systems and Stability 472(10)
7.2 Almost Linear Systems 482(11)
7.3 Competing Species 493(11)
7.4 Predator-Prey Equations 504(9)
7.5 Periodic Solutions and Limit Cycles 513(11)
7.6 Chaos and Strange Attractors: The 524(13)
Lorenz Equations
Projects 532(1)
7.P.1 Modeling of Epidemics 532(2)
7.P.2 Harvesting in a Competitive 534(2)
Environment
7.P.3 The Rossler System 536(1)
A Matrices and Linear Algebra 537(46)
A.1 Matrices 537(9)
A.2 Systems of Linear Algebraic 546(17)
Equations, Linear Independence, and Rank
A.3 Determinants and Inverses 563(8)
A.4 The Eigenvalue Problem 571(12)
B Complex Variables 583(4)
Answers To Selected Problems 587(86)
References 673(2)
Index 675