Ordinary Differential Equations Applications In Engineering
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Ordinary Differential Equations with Applications
Ordinary differential equations (ODEs) arise in many contexts of mathematics and science (social as well as natural). Mathematical descriptions of change use differentials and derivatives. Various differentials, derivatives, and functions become related to each other via equations, and thus a differential equation is a result that describes dynamically changing phenomena, evolution, and variation. Often, quantities are defined as the rate of change of other quantities (for example, derivatives of displacement with respect to time), or gradients of quantities, which is how they enter differential equations. Ordinary differential equations are equations to be solved in which the unknown element is a function, rather than a number, and in which the known information relates that function to its derivatives. Few such equations admit an explicit answer, but there is a wealth of qualitative information describing the solutions and their dependence on the defining equation. Systems of differential equations form the basis of mathematical models in a wide range of fields - from engineering and physical sciences to finance and biological sciences. Differential equations are relations between unknown functions and their derivatives. Computing numerical solutions to differential equations is one of the most important tasks in technical computing, and one of the strengths of MATLAB. The book explains the origins of various types of differential equations. The scope of the book is limited to linear differential equations of the first order, linear differential equation of higher order, partial differential equations and special methods of solution of differential equations of second order, keeping in view the requirement of students.
Ordinary Differential Equations for Engineers
This monograph presents teaching material in the field of differential equations while addressing applications and topics in electrical and biomedical engineering primarily. The book contains problems with varying levels of difficulty, including Matlab simulations. The target audience comprises advanced undergraduate and graduate students as well as lecturers, but the book may also be beneficial for practicing engineers alike.
Ordinary Differential Equations and Applications II: with Maple Illustrations
Author: Benjamin Oyediran Oyelami
language: en
Publisher: Bentham Science Publishers
Release Date: 2024-12-19
Ordinary Differential Equations and Applications II: With Maple Illustrations integrates fundamental theories of Ordinary Differential Equations (ODEs) with practical applications and Maple-based solutions. This comprehensive textbook covers vector-valued differential equations, matrix solutions, stability methods, and periodic systems. Using Maple and MapleSim software, readers learn symbolic solutions, plotting techniques, 2D/3D animation for ODE problems, and simulations for engineering systems. This book is ideal for undergraduate and postgraduate students in mathematics, physics, economics, and engineering, as well as researchers and professionals needing advanced applications of ODEs. Key Features: - Comprehensive introduction to ODE concepts and real-life applications - Solutions for initial value problems using Maple and MapleSim software - Analysis of stability using Routh-Hurwitz and Lyapunov methods - Models of neural firing, avian influenza, and biological populations - Practical guidance on MapleSim for multi-domain simulations, code generation, and Monte Carlo simulation