LEADER 05450nam 2200697 450 001 9910464840803321 005 20200520144314.0 010 $a1-118-24341-2 010 $a1-118-24340-4 010 $a1-118-24338-2 035 $a(CKB)3710000000121790 035 $a(EBL)818224 035 $a(SSID)ssj0001225067 035 $a(PQKBManifestationID)12521180 035 $a(PQKBTitleCode)TC0001225067 035 $a(PQKBWorkID)11269016 035 $a(PQKB)11027556 035 $a(SSID)ssj0001333799 035 $a(PQKBManifestationID)16036926 035 $a(PQKBTitleCode)TC0001333799 035 $a(PQKBWorkID)11386252 035 $a(PQKB)23124397 035 $a(MiAaPQ)EBC818224 035 $a(Au-PeEL)EBL818224 035 $a(CaPaEBR)ebr10881242 035 $a(CaONFJC)MIL615348 035 $a(OCoLC)881162528 035 $a(EXLCZ)993710000000121790 100 $a20140619h20122012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOrdinary differential equations /$fMichael D. Greenberg 210 1$aHoboken, New Jersey :$cWiley,$d2012. 210 4$dİ2012 215 $a1 online resource (549 p.) 300 $aIncludes index. 311 $a1-118-23002-7 327 $aCover; Title Page; Copyright; Contents; Preface; 1 First-Order Differential Equations; 1.1 Motivation And Overview; 1.1.1 Introduction; 1.1.2 Modeling; 1.1.3 The order of a differential equation; 1.1.4 Linear and nonlinear equations; 1.1.5 Ourplan; 1.1.6 Direction field; 1.1.7 Computer software; 1.2 Linear First-Order Equations; 1.2.1 The simplest case; 1.2.2 The homogeneous equation; 1.2.3 Solving the full equation by the integrating factor method; 1.2.4 Existence and uniqueness for the linear equation; 1.3 Applications Of Linear First-Order Equations; 1.3.1 Population dynamics 327 $aexponential model1.3.2 Radioactive decay; carbon dating; 1.3.3 Mixing problems; a one-compartment model; 1.3.4 The phase line, equilibrium points, and stability; 1.3.5 Electrical circuits; 1.4 Nonlinear First-Order Equations That Are Separable; 1.5 Existence And Uniqueness; 1.5.1 An existence and uniqueness theorem; 1.5.2 Illustrating the theorem; 1.5.3 Application to free fall; physical significance of nonuniqueness; 1.6 Applications Of Nonlinear First-Order Equations; 1.6.1 The logistic model of population dynamics; 1.6.2 Stability of equilibrium points and linearized stability analysis 327 $a1.7 Exact Equations And Equations That Can Be Made Exact1.7.1 Exact differential equations; 1.7.2 Making an equation exact; integrating factors; 1.8 Solution By Substitution; 1.8.1 Bernoulli's equation; 1.8.2 Homogeneous equations; 1.9 Numerical Solution By Euler's Method; 1.9.1 Euler's method; 1.9.2 Convergence of Euler's method; 1.9.3 Higher-order methods; Chapter 1 Review; 2 Higher-Order Linear Equations; 2.1 Linear Differential Equations Of Second Order; 2.1.1 Introduction; 2.1.2 Operator notation and linear differential operators; 2.1.3 Superposition principle 327 $a2.2 Constant-Coefficient Equations2.2.1 Constant coefficients; 2.2.2 Seeking a general solution; 2.2.3 Initial value problem; 2.3 Complex Roots; 2.3.1 Complex exponential function; 2.3.2 Complex characteristic roots; 2.4 Linear Independence; Existence, Uniqueness, General Solution; 2.4.1 Linear dependence and linear independence; 2.4.2 Existence, uniqueness, and general solution; 2.4.3 Abel's formula and Wronskian test for linear independence; 2.4.4 Building a solution method on these results; 2.5 Reduction Of Order; 2.5.1 Deriving the formula; 2.5.2 The method rather than the formula 327 $a2.5.3 About the method of reduction of order2.6 Cauchy-Euler Equations; 2.6.1 General solution; 2.6.2 Repeated roots and reduction of order; 2.6.3 Complex roots; 2.7 The General Theory For Higher-Order Equations; 2.7.1 Theorems for nth-order linear equations; 2.7.2 Constant-coefficient equations; 2.7.3 Cauchy-Euler equations; 2.8 Nonhomogeneous Equations; 2.8.1 General solution; 2.8.2 The scaling and superposition of forcing functions; 2.9 Particular Solution By Undetermined Coefficients; 2.9.1 Undetermined coefficients; 2.9.2 A special case; the complex exponential method 327 $a2.10 Particular Solution By Variation Of Parameters 330 $aFeatures a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various 606 $aDifferential equations$vTextbooks 606 $aDifferential equations, Partial$vTextbooks 608 $aElectronic books. 615 0$aDifferential equations 615 0$aDifferential equations, Partial 676 $a515/.352 700 $aGreenberg$b Michael D.$f1935-$040789 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910464840803321 996 $aOrdinary differential equations$91942497 997 $aUNINA