Differential Equations With Applications: Class Notes With Detailed Examples by Jigarkumar Patel

Differential Equations With Applications: Class Notes With Detailed Examples

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File Size: 43566 KB.
Print Length: 503 pages.
Language: English.
ASIN: B074333T5K.
Formats: PDF, ePUB & mobi.

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Differential Equations With Applications: Class Notes With Detailed Examples

This book is different than most math books because it is based on a student’s class notes that have been reviewed and updated by the professor who taught the course! Therefore, this book is structured and presented in a way that teaches the material with a series of detailed examples, from simple to increasing complexity. Solution techniques are generalized and simple, step-by-step procedures are listed and used to solve a series of problems, from simple to advanced. All topics are presented in a logical way that gives the reader a clear understanding of the important concepts and the relationship between topics.

This book should be considered a reference for students taking a course in Differential Equations (DEs). Statements of theorem and important results are included; however, proofs are not included because the primary emphasis is on problems and applications. This book includes an impressive list of topics:

FIRST-ORDER DE
* First Order Linear DE
* 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.

Throughout the book, short reviews are included where needed. In addition, the appendix includes some supporting material (integration-by-parts (tabular-method), complex numbers, linear independence, and matrices).

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