Author: Javier Vinuesa MuñozPublisher:
ISBN:
Category :
Languages : es
Pages :
Book Description
Estudio de la transformada de Laplace con Mathematica
Author: Javier Vinuesa MuñozEstudio de la transformada de Laplace
Author: Vanessa María Montero ContiosoPublisher:
ISBN:
Category :
Languages : es
Pages : 90
Book Description
En la actualidad, podemos encontrar diversas situaciones cuyo comportamiento puede ser modelado y estudiado a través de las ecuaciones diferenciales. Lejos de ser un problema puramente matemático, las ecuaciones diferenciales son usadas por físicos, biólogos, ingenieros, y científicos en general para entender problemas de algún determinado interés. De hecho, existen métodos de resolución de ecuaciones diferenciales, problemas de valores iniciales, problemas de contorno y ecuaciones en derivadas parciales que se estudian en el Grado en Matemáticas. A lo largo de este documento vamos a mostrar un método alternativo de resolución a este tipo de problemas que no se ha estudiado con detalle en dicha titulación, aunque nos restringiremos a los casos lineales. Este método permite ahorrarnos los numerosos cálculos que implican la derivación y la integración, pudiendo optimizar la resolución y convirtiéndolo en un proceso más efectivo. Se presenta al lector el método de la transformada de Laplace junto con todas sus propiedades acompañadas de ejemplos, con la motivación de poder usarlas como ayuda en la resolución de problemas que involucren algunos tipos de ecuaciones diferenciales. La estructura de este trabajo permite poder usarlo como herramienta tanto para aplicar como para entender la transformada de Laplace. Empezamos con una definición y varias propiedades para seguir con la transformada inversa y la aplicación a la resolución de problemas y finalizamos con varios ejemplos donde se muestra todo lo anterior. Además, se dedica un capítulo a estudiar la relación de la transformada de Laplace con la variable compleja. Tratamos de justificar todos los enunciados de forma completa, clara y concisa.
Applied Laplace Transforms and z-Transforms for Scientists and Engineers
Author: Urs GrafPublisher: Birkhäuser
ISBN: 9783034895934
Category : Mathematics
Languages : en
Pages : 500
Book Description
The theory of Laplace transformation is an important part of the mathematical background required for engineers, physicists and mathematicians. Laplace transformation methods provide easy and effective techniques for solving many problems arising in various fields of science and engineering, especially for solving differential equations. What the Laplace transformation does in the field of differential equations, the z-transformation achieves for difference equations. The two theories are parallel and have many analogies. Laplace and z transformations are also referred to as operational calculus, but this notion is also used in a more restricted sense to denote the operational calculus of Mikusinski. This book does not use the operational calculus of Mikusinski, whose approach is based on abstract algebra and is not readily accessible to engineers and scientists. The symbolic computation capability of Mathematica can now be used in favor of the Laplace and z-transformations. The first version of the Mathematica Package LaplaceAndzTransforrns developed by the author appeared ten years ago. The Package computes not only Laplace and z-transforms but also includes many routines from various domains of applications. Upon loading the Package, about one hundred and fifty new commands are added to the built-in commands of Mathematica. The code is placed in front of the already built-in code of Laplace and z-transformations of Mathematica so that built-in functions not covered by the Package remain available. The Package substantially enhances the Laplace and z-transformation facilities of Mathematica. The book is mainly designed for readers working in the field of applications.
Problem-Based Learning: A Didactic Strategy in the Teaching of System Simulation
Author: Lorenzo Cevallos-TorresPublisher: Springer
ISBN: 3030133931
Category : Technology & Engineering
Languages : en
Pages : 144
Book Description
This book describes and outlines the theoretical foundations of system simulation in teaching, and as a practical contribution to teaching-and-learning models. It presents various methodologies used in teaching, the goal being to solve real-life problems by creating simulation models and probability distributions that allow correlations to be drawn between a real model and a simulated model. Moreover, the book demonstrates the role of simulation in decision-making processes connected to teaching and learning.
Green’s Functions in the Theory of Ordinary Differential Equations
Author: Alberto CabadaPublisher: Springer Science & Business Media
ISBN: 1461495067
Category : Mathematics
Languages : en
Pages : 180
Book Description
This book provides a complete and exhaustive study of the Green’s functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value problems. Classic methods of lower and upper solutions are explored, with a particular focus on monotone iterative techniques that flow from them. In addition, Cabada proves the existence of positive solutions by constructing operators defined in cones. The book will be of interest to graduate students and researchers interested in the theoretical underpinnings of boundary value problem solutions.
Differential Equations and Boundary Value Problems
Author: Charles Henry EdwardsPublisher: Pearson Educación
ISBN: 9789684444386
Category : Computers
Languages : en
Pages : 816
Book Description
For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course while maintaining the solid foundation of algebraic techniques that are still essential to science and engineering students. It reflects the new excitement in differential equations as the availability of technical computing environments likeMaple, Mathematica, and MATLAB reshape the role and applications of the discipline. New technology has motivated a shift in emphasis from traditional, manual methods to both qualitative and computer-based methods that render accessible a wider range of realistic applications. With this in mind, the text augments core skills with conceptual perspectives that students will need for the effective use of differential equations in their subsequent work and study.
The Information
Author: James GleickPublisher: Vintage
ISBN: 0307379574
Category : Science
Languages : en
Pages : 400
Book Description
From the bestselling author of the acclaimed Chaos and Genius comes a thoughtful and provocative exploration of the big ideas of the modern era: Information, communication, and information theory. Acclaimed science writer James Gleick presents an eye-opening vision of how our relationship to information has transformed the very nature of human consciousness. A fascinating intellectual journey through the history of communication and information, from the language of Africa’s talking drums to the invention of written alphabets; from the electronic transmission of code to the origins of information theory, into the new information age and the current deluge of news, tweets, images, and blogs. Along the way, Gleick profiles key innovators, including Charles Babbage, Ada Lovelace, Samuel Morse, and Claude Shannon, and reveals how our understanding of information is transforming not only how we look at the world, but how we live. A New York Times Notable Book A Los Angeles Times and Cleveland Plain Dealer Best Book of the Year Winner of the PEN/E. O. Wilson Literary Science Writing Award
The obstacle problem
Author: Luis Angel CaffarelliPublisher: Edizioni della Normale
ISBN: 9788876422492
Category : Mathematics
Languages : en
Pages : 0
Book Description
The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.
Two-Point Boundary Value Problems: Lower and Upper Solutions
Author: C. De CosterPublisher: Elsevier
ISBN: 0080462472
Category : Mathematics
Languages : en
Pages : 502
Book Description
This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction.· Presents the fundamental features of the method· Construction of lower and upper solutions in problems· Working applications and illustrated theorems by examples· Description of the history of the method and Bibliographical notes
Higher Order Dynamic Mode Decomposition and Its Applications
Author: Jose Manuel VegaPublisher: Academic Press
ISBN: 0128227664
Category : Technology & Engineering
Languages : en
Pages : 322
Book Description
Higher Order Dynamic Mode Decomposition and Its Applications provides detailed background theory, as well as several fully explained applications from a range of industrial contexts to help readers understand and use this innovative algorithm. Data-driven modelling of complex systems is a rapidly evolving field, which has applications in domains including engineering, medical, biological, and physical sciences, where it is providing ground-breaking insights into complex systems that exhibit rich multi-scale phenomena in both time and space. Starting with an introductory summary of established order reduction techniques like POD, DEIM, Koopman, and DMD, this book proceeds to provide a detailed explanation of higher order DMD, and to explain its advantages over other methods. Technical details of how the HODMD can be applied to a range of industrial problems will help the reader decide how to use the method in the most appropriate way, along with example MATLAB codes and advice on how to analyse and present results. - Includes instructions for the implementation of the HODMD, MATLAB codes, and extended discussions of the algorithm - Includes descriptions of other order reduction techniques, and compares their strengths and weaknesses - Provides examples of applications involving complex flow fields, in contexts including aerospace engineering, geophysical flows, and wind turbine design