Description
Taylor & Francis Applied Differential Equations The Primary Course 2015 Edition by Vladimir A. Dobrushkin
A Contemporary Approach to Teaching Differential EquationsApplied Differential Equations: An Introduction presents a contemporary treatment of ordinary differential equations (ODEs) and an introduction to partial differential equations (PDEs), including their applications in engineering and the sciences. Designed for a two-semester undergraduate course, the text offers a true alternative to books published for past generations of students. It enables students majoring in a range of fields to obtain a solid foundation in differential equations. The text covers traditional material, along with novel approaches to mathematical modeling that harness the capabilities of numerical algorithms and popular computer software packages. It contains practical techniques for solving the equations as well as corresponding codes for numerical solvers. Many examples and exercises help students master effective solution techniques, including reliable numerical approximations.This book describes differential equations in the context of applications and presents the main techniques needed for modeling and systems analysis. It teaches students how to formulate a mathematical model, solve differential equations analytically and numerically, analyze them qualitatively, and interpret the results. Table of contents :- First-Order EquationsIntroductionSeparable EquationsEquations with Homogeneous CoefficientsExact Differential EquationsIntegrating FactorsFirst-Order Linear Differential EquationsEquations Reducible to first OrderExistence and UniquenessReview Questions for Chapter 1Applications of First Order ODEApplications in MathematicsCurves of PursuitChemical ReactionsPopulation ModelsMechanicsElectricityApplications in PhysicsThermodynamicsFlow ProblemsReview Questions for Chapter 2Mathematical Modeling and Numerical MethodsMathematical ModelingCompartment AnalysisDifference EquationsEuler's MethodsError EstimatesThe Runge-Kutta MethodsMultistep MethodsError Analysis and StabilityReview Questions for Chapter 3Second-order EquationsSecond and Higher Order Linear EquationsLinear Independence and WronskiansThe Fundamental Set of SolutionsEquations with Constant CoefficientsComplex RootsRepeated Roots. Reduction of OrderNonhomogenous EquationsVariation of ParametersOperator MethodReview Questions for Chapter 4Laplace TransformsThe Laplace TransformProperties of the Laplace TransformConvolutionDiscontinuous and Impulse FunctionsThe Inverse Laplace TransformApplications to Homogenous EquationsApplications to Non-homogenous EquationsInternal EquationsReview Questions for Chapter 5Series of SolutionsReview of Power SeriesThe RecurrencePower Solutions about an Ordinary PointEuler EquationsSeries Solutions Near a Regular Singular PointEquations of Hypergeometric TypeBessel's EquationsLegendre's EquationOrthogonal PolynomialsReview Questions for Chapter 6Applications of Higher Order Differential EquationsBoundary Value ProblemsSome Numerical MethodsDynamicsDynamics of Rotational MotionHarmonic MotionModeling: Forced OscillationsModeling of Electric CircuitsSome Variational ProblemsReview Questions for Chapter 7Appendix: Software PackagesAnswers to ProblemsBibliographyIndex