Differential Equations With Applications: Class Notes With Detailed Examples: Version 2
Paperback
ISBN13: 9781695453982
Publisher: Independently Published
Published: Sep 29 2019
Pages: 470
Weight: 2.04
Height: 0.95 Width: 8.00 Depth: 10.00
Language: English
* Separable DE
* Substitution Methods (Bernoulli DE, Homogeneous DE, Special Substitution)
* Exact DE With & Without Integrating Factor
* Strategies for First-Order DE
* Existence and Uniqueness Theorem SECOND-ORDER DE
* Second-Order DE with Constant Coefficients (Characteristic Eqns., Existence & Uniqueness, Wronskian Determinant)
* Higher-Order DE with Constant Coefficients
* Non-Homogeneous DE with Constant Coefficients (Undetermined Coefficients, Variation of Parameters)
* Euler's DE
* Reduction of Order
* Mechanical and Electrical Vibrations (Spring Mass System, Electrical Vibrations) SERIES SOLUTIONS of DE
* Power Series (Review)
* Series Solution near an Ordinary Point
* Types of Singular Points
* Series Solution near Regular Singular Point
* Bessel's DE LAPLACE TRANSFORM of DE
* Improper Integration
* Definition of Laplace Transform and Gamma Functions
* Step Functions
* Impulse Functions
* Convolution Integrals SYSTEMS of FIRST-ORDER DE
* Systems of First-Order Linear DEs
* Eigenvalues and Eigenvectors
* Homogeneous and Non-Homogeneous Systems
* The Phase Plane
* Locally Linear Systems
* Competing Species
* Predator-Prey Systems The last, and perhaps most interesting, chapter of this book includes phase portraits and discusses the stability of equilibrium solutions for non-linear systems of differential equations. The book concludes with fascinating applications such as competing species and predator-prey systems.
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