Borres M.C. Differential Equationss: Theory and Applications

Arcler Press, 2019. — xii, 411 p. — ISBN: 978-1-77361-596-7.
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This book examines several aspects of differential equation including an extensive explanation of higher order differential equation. It includes applications of differential equations in mechanics and different types of differential equations. Provides the reader with clear understanding of theory and application of differential equations.Basic Concepts of Differential EquationsThe Bernoulli Equation
Differential Equations of Higher Order
The WronskianFundamental Concepts of Partial Differential EquationsClassification of Second Order PDE
Summary and Discussion
Classification of Second Order PDEApplication of Differential Equations in MechanicsProjectile Motion
Summary and DiscussionElliptic Differential EquationBoundary Value Problem (BVPs)
Some Important Mathematical Tools
Properties of Harmonic Functions
Separation of Variables
Dirichlet Problem for a Rectangle
The Neumann Problem for a Rectangle
Interior Dirichlet Problem for a Circle
Exterior Dirichlet Problem for a Circle
Interior Neumann Problem for a Circle
Solution of Laplace Equation in Cylindrical Coordinates
Solution of Laplace Equation in Spherical Coordinates
Miscellaneous Example
Summary and DiscussionsHyperbolic Differential EquationSolution of One-Dimensional Wave Equation by Canonical Reduction
The Initial Value Problem; D’alembert’s Solution
Summary and DiscussionParabolic Differential EquationsBoundary Conditions
Elementary Solutions of The Diffusion Equation
Dirac Delta Function
Separation of Variables Method
Maximum-Minimum Principle and Consequences
Miscellaneous Example
Boundary ConditionsLaplace Transform MethodsTransform of Some Elementary Functions
Properties of Laplace Transform
Transform of a Periodic Function
Transform of Error Function
Transform of Bessel’s Function
Transform of Dirac Delta Function
Convolution Theorem (Faltung Theorem)Green’s FunctionThe Eigenfunction Method
Summary and Discussion