Ordinary differential equations / / Michael D. Greenberg

• Autore: Greenberg Michael D. <1935->
• Pubblicazione: Hoboken, New Jersey : , : Wiley, , 2012; ©2012
• Descrizione fisica: 1 online resource (549 p.)
• Disciplina: 515/.352
• Soggetto topico: Differential equations; Differential equations, Partial
• Soggetto genere / forma: Electronic books.
• Note generali: Includes index.
• Nota di contenuto: Cover; 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 ; exponential 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 ; 1.7 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 ; 2.2 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 ; 2.5.3 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 ; 2.10 Particular Solution By Variation Of Parameters
• Sommario/riassunto: Features 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
• Titolo autorizzato: Ordinary differential equations
• ISBN: 1-118-24341-2; 1-118-24340-4; 1-118-24338-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910464840803321
• Lo trovi qui: Univ. Federico II