عنوان

A first course in differential equations with modeling applications /

0495108243

9780495108245

b528696

A first course in differential equations with modeling applications /

[Book]

Dennis G. Zill

9th ed

Belmont, CA :

Brooks/Cole, Cengage Learning,

©2009

xiii, 362, 23, 16, 7 pages :

color illustrations ;

29 cm

Includes index

Preface -- 1. Introduction to differential equations -- 1.1. Definitions and terminology -- 1.2. Initial-value problems -- 1.3. Differential equations as mathematical models -- Chapter 1 in review -- 2. First-order differential equations -- 2.1. Solution curves without a solution -- 2.1.1. Direction fields -- 2.1.2. Autonomous first-order Des -- 2.2. Separable variables -- 2.3. Linear equations -- 2.4. Exact equations -- 2.5. Solutions by substitutions -- 2.6. A numerical method -- Chapter 2 in review -- 3. Modeling with first-order differential equations -- 3.1. Linear models -- 3.2. Nonlinear models -- 3.3. Modeling with systems of first-order DEs -- Chapter 3 in review -- 4. Higher-order differential equations -- 4.1. Preliminary theory--linear equations -- 4.1.1. Initial-value and boundary-value problems -- 4.1.2. Homogeneous equations -- 4.1.3. Nonhomogeneous equations -- 4.2. Reduction of order -- 4.3. Homogeneous linear equations with constant coefficients -- 4.4. Undetermined coefficients--superposition approach -- 4.5. Undetermined coefficients--annihilator approach -- 4.6. Variation of parameters -- 4.7. Cauchy-Euler equation -- 4.8. Solving systems of linear DEs by elimination -- 4.9. Nonlinear differential equations -- Chapter 4 in review -- 5. Modeling with higher-order differential equations -- 5.1. Linear models : initial-value problems -- 5.1.1. Spring/mass systems : free undamped motion -- 5.1.2. Spring/mass systems : free damped motion -- 5.1.3. Spring/mass systems : driven motion -- 5.1.4. Series circuit analogue -- 5.2. Linear models : boundary-value problems -- 5.3. Nonlinear models -- Chapter 5 in review -- 6. Series solutions of linear equations -- 6.1. Solutions about ordinary points -- 6.1.1. Review of power series -- 6.1.2. Power series solutions -- 6.2. Solutions about singular points -- 6.3. Special functions -- 6.3.1. Bessel's equation -- 6.3.2. Legendre's equation -- Chapter 6 in review -- 7. The Laplace transform -- 7.1. Definition of the Laplace transform -- 7.2. Inverse transforms and transforms of derivatives -- 7.2.1. Inverse transforms -- 7.2.2. Transforms of derivatives -- 7.3. Operational properties I -- 7.3.1. Translation on the s-axis -- 7.3.2. Translation on the t-axis -- 7.4. Operational properties II -- 7.4.1. Derivatives of a transform -- 7.4.2. Transforms of integrals -- 7.4.3. Transform of a periodic function -- 7.5. The Dirac delta function -- 7.6. Systems of linear differential equations -- Chapter 7 in review -- 8. Systems of linear first-order differential equations -- 8.1. Preliminary theory--linear systems -- 8.2. Homogeneous linear systems -- 8.2.1. Distinct real eigenvalues -- 8.2.2. Repeated eigenvalues -- 8.2.3. Complex eigenvalues -- 8.3. Nonhomogeneous linear systems -- 8.3.1. Undetermined coefficients -- 8.3.2. Variation of parameters -- 8.4. Matrix exponential -- Chapter 8 in review -- 9. Numerical solutions of ordinary differential equations -- 9.1. Euler methods and error analysis -- 9.2. Runge-Kutta methods -- 9.3. Multistep methods -- 9.4. Higher-order equations and systems -- 9.5. Second-order boundary-value problems -- Chapter 9 in review -- Appendices -- I. Gamma function -- II. Matrices -- III. Laplace transforms -- Answers for selected odd-numbered problems -- Index

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Differential equations, Textbooks

Zill, Dennis G.,1940-

20160718043449.0

[Book]

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