Fundamentals of differential equations

Başlık:

Yazar:

Nagle, R. Kent

ISBN:

9780201338683

Ek Yazar:

Nagle, R. Kent

Basım Bilgisi:

5. bs.

Yayın Bilgisi:

Reading, Mass. : Addison-Wesley , 2000.

Fiziksel Tanım:

xxii, 684, 10, 32, 8 s. : ill. ; 24 sm. + 1 computer optical disc (4 3/4 in.)

Özet:

DIFFERENTIAL EQUATİONS NAGLE- SAFF-SNIDER CONTENTS 2.3 Linear Equations 54 2.4 Exact Equations 63 *2.5 Special Integrating Factors 73 *2.6 Substitutions and Transformations 77 Chapter Summary 86 Review Problems 87 Technical Writing Exercises 88 Group Projects for Chapter 2 89 A. The Snowplow Problem 89 B. Two Snowplows 89 C. Asymptotic Behavior of Solutions to Linear Equations 90 D. Torricelli’s Law of Fluid Flow 90 E. Clairaut Equations and Singular Solutions 92 CHAPTER 3 MATHEMATICAL MODELS AND NUMERICAL METHODS INVOLVING FIRST ORDER EQUATIONS 93 3.1 Mathematical Modeling 93 3.2 Compartmental Analysis 95 3.3 Heating and Cooling of Buildings 107 3.4 Newtonian Mechanics 114 3.5 Improved Euler’s Method 124 3.6 Higher-Order Numerical Methods: Taylor and Runge-Kutta 135 3.7 Professional Codes for Solving Initial Value Problems 144 Group Projects for Chapter 3 148 A. Delay Differential Equations 148 B. Aquaculture 149 C. Curve of Pursuit 150 D. Aircraft Guidance in a Crosswind 151 E. Stability of Numerical Methods 152 F. Period Doubling and Chaos 153 G. Bang-Bang Controls 155 CHAPTER 4 LINEAR SECOND ORDER EQUATIONS 156 4.1 Introduction: The Mass-Spring Oscillator 156 4.2 Linear Differential Operators 161 4.3 Fundamental Solutions of Homogeneous Equations 168 *4.4 Reduction of Order 178 4.5 Homogeneous Linear Equations with Constant Coefficients 183 4.6 Auxiliary Equations with Complex Roots 191 4.7 Superposition and Nonhomogeneous Equations 200 4.8 Method of Undetermined Coefficients 204 4.9 Variation of Parameters 213 *4.10 Qualitative Considerations for Variable-Coefficient and Nonlinear Equations 218 *4.11 A Closer Look at Free Mechanical Vibrations 230 *4.12 A Closer Look at Forced Mechanical Vibrations 240 Chapter Summary 248 Review Problems 250 Technical Writing Exercises 251 Group Projects for Chapter 4 252 A. Undetermined Coefficients Using Complex Arithmetic 252 B. An Alternative to the Method of Undetermined Coefficients 253 C. Convolution Method 254 D. Linearization of Nonlinear Problems 255 E. Nonlinear Equations Solvable by First Order Techniques 256 F. Apollo Reentry 257 G. Simple Pendulum 258 H. Asymptotic Behavior of Solutions 259 CHAPTER 5 INTRODUCTION TO SYSTEMS AND PHASE PLANE ANALYSIS 261 5.1 Interconnected Fluid Tanks 261 *5.2 Introduction to the Phase Plane 263 5.3 Elimination Method for Systems 278 5.4 Coupled Mass-Spring Systems 286 5.5 Electrical Circuits 293 5.6 Numerical Methods for Higher-Order Equations and Systems 301 5.7 Dynamical Systems, Poincare Maps, and Chaos 315 Chapter Summary 325 Review Problems 327 Group Projects for Chapter 5 328 A. Designing a Landing System for Interplanetary Travel 328 B. Things That Bob 329 C. Effects of Hunting on Predator-Prey Systems 330 D. Periodic Solutions to Volterra-Lotka Systems 331 E. Hamiltonian Systems 332 F. Limit Cycles 334 G. Strange Behavior of Competing Species-Part 1 335 H. Cleaning Up the Great Lakes 336 CHAPTER 6 THEORY OF HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONS 6.1 Basic Theory of Linear Differential Equations 338 6.2 Homogeneous Linear Equations with Constant Coefficients 347 6.3 Undetermined Coefficients and the Annihilator Method 354 6.4 Method of Variation of Parameters 360 Chapter Summary 364 Review Problems 366 Technical Writing Exercises 366 Group Projects for Chapter 6 367 A. Justifying the Method of Undetermined Coefficients 367 B. Transverse Vibrations of Beam 367 CHAPTER 7 LAPLACE TRANSFORMS 369 7.1 Introduction: A Mixing Problem 369 7.2 Definition of the Laplace Transform 373 7.3 Properties of the Laplace Transform 382 7.4 Inverse Laplace Transform 388 7.5 Solving Initial Value Problems 398 7.6 Transforms of Discontinuous and Periodic Functions 406 *7.7 Convolution 420 *7.8 Impulses and the Dirac Delta Function 429 *7.9 Solving Linear Systems with Laplace Transforms 436 Chapter Summary 439 Review Problems 440 Technical Writing Exercises 441 Group Projects for Chapter 7 A. Duhamel ‘s Formulas B. Frequency Response Modeling C. Determining System Parameters CHAPTER 8 SERIES SOLUTIONS OF DIFFERENTIAL EQUATIONS 447 8.1 Introduction: The Taylor Polynomial Approximation 447 8.2 Power Series and Analytic Functions 453 8.3 Power Series Solutions to Linear Differential Equations 462 8.4 Equations with Analytic Coefficients 473 *8.5 Cauchy-Euler (Equidimensional) Equations Revisited 479 8.6 Method of Frobenius 483 8.7 Finding a Second Linearly Independent Solution 495 8.8 Special Functions 507 Chapter Summary 520 Review Problems 521 Technical Writing Exercises 522 Group Projects for Chapter 8 523 A. Spherically Symmetric Solutions to Schrödinger’s Equation for the Hydrogen Atom - - 523 B. Airy’s Equation 524 C. Buckling of a Tower 524 D. Aging Spring and Bessel Functions 525 CHAPTER 9 MATRIX METHODS FOR LINEAR SYSTEMS 527 9.1 Introduction 527 9.2 Review 1: Linear Algebraic Equations 532 9.3 Review 2: Matrices and Vectors 536 9.4 Linear Systems in Normal Form 548 9.5 Homogeneous Linear Systems with Constant Coefficients 557 9.6 Complex Eigenvalues 569 9.7 Nonhomogeneous Linear Systems 575 9.8 The Matrix Exponential Function 582 Chapter Summary 591 Review Problems 594 Technical Writing Exercises 595 Group Projects for Chapter 9 596 A. Uncoupling Normal Systems 596 B. Matrix Laplace Transform Method 596 C. Undamped Second Order Systems 598 D. Strange Behavior of Competing Species-Part II 599 CHAPTER 1O PARTIAL DIFFERENTIAL EQUATIONS 600 10.1 Introduction: A Model for Heat Flow 600 10.2 Method of Separation of Variables 603 10.3 Fourier Series 613 10.4 Fourier Cosine and Sine Series 631 10.5 The Heat Equation 636 10.6 The Wave Equation 649 10.7 Laplace’s Equation 662 Chapter Summary 675 Technical Writing Exercises 677 Group Projects for Chapter 10 678 A. Steady-State Temperature Distribution in a Circular Cylinder 678 B. A Laplace Transform Solution of the Wave Equation 679 C. Green ‘s Function 680 D. Numerical Method for AM =fon a Rectangle 682 APPENDICES A-l A. Newton’s Method A-l B. Simpson’s Rule A-3 C. Cramer’s Rule A-5 D. Method of Least Squares A-6 E. Runge-Kutta Procedure for n Equations A-9 ANSWERS TO ODD-NUMBERED PROBLEMS B-l INDEX 1-1

Konu Terimi:

Diferansiyel denklemler_Ders kitapları

Differential equations_Textbooks

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