Keskin A.Ü. Ordinary Differential Equations for Engineers: Problems with MatLAB Solutions

Springer, 2019. — xiii+786 p. — ISBN: 978-3-319-95243-7.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.
(перевод)
В монографии представлен учебный материал в области дифференциальных уравнений при рассмотрении приложений и тем в области электротехнической и биомедицинской инженерии. Книга содержит задачи с различными уровнями сложности, в том числе и математические моделирования. Целевая аудитория состоит из продвинутых студентов и аспирантов, а также преподавателей, но книга также может быть полезна для практикующих инженеров.Disclaimer
About the AuthorBasic Concepts
Definitions and PreliminariesFirst Order Ordinary Differential Equations
Fundamentals of First Order ODEs
Direction Fields
Systems of First Order ODEs
Applications of First Order ODEsSecond and Higher Order Ordinary Differential Equations
Linearity and the Wronskian
Linear Second-Order ODEs
Reduction of Order
Cauchy-Euler ODEs
Method of Undetermined Coefficients
Variation of ParametersSeries Solutions of Second-Order Ordinary Differential Equations
Power Series and Convergence
Taylor Series and Polynomials
Ordinary and Singular Points
Series Solutions Near an Ordinary Point
Series Solutions Near a Singular Point; the Method of FrobeniusSpecial Differential Equations, Functions, and Polynomials
Gamma Function
Bessel Equation, Bessel Functions, and Polynomials
Chebyshev Equation, Chebyshev Functions, and Polynomials
Legendre Equation, Legendre Functions and Polynomials
Laguerre Equation and Polynomials
Hermite Equation and PolynomialsLaplace Transform Methods
Laplace Transform and Its Properties
Inverse Laplace Transforms, Initial and Final Values
Solutions of Linear ODEs Using Laplace Transforms
Applications of Laplace Transform MethodsSystems of First-Order Linear Equations
Review of Matrices, Linear Independence, Eigenvalues, Eigenvectors
Order Reduction of Second- and Higher Order ODEs in Matrix Form
Homogeneous Systems with Constant Coefficients
The Matrix Exponential Function
The Jordan Form
Matrix Methods and Solutions of Nonhomogeneous ODEs in MatLABNumerical Solutions of Differential Equations
Euler Methods
Second-Order Methods
Numerical Solution of Second-Order ODEs (Backward Euler Method)
Fourth and Higher Order Numerical Methods
Variable Step Size Methods
Multistep Methods
Runge-Kutta-Nystrom (RKN) Method
Stiff ODEs
Numerical Solution of Implicit ODEsNonlinear Ordinary Differential Equations
Phase Plane Analysis of Linear Systems
Autonomous Equations and Stability
Almost (Locally) Linear Systems
Limit Cycles, Competing Species, ChaosMore Applications of ODEs
Buoyancy Problem
Mass-Spring Systems
Numerical Solutions: Flame Propagation, Logistic Growth, Vertical Projectile
Belousov-Zhabotinsky Oscillating Chemical Reac
Electric Circuits
Hodgin-Huxley and Fitzhugh-Nagumo Spiking Neuron Models
Mixing Tank and Chemical Reactions in a Batch Reactor
Modeling Quadrotor Dynamics
Pendulum Problems
Satellite OrbitsAppendix: Mathematical Formulas and Tables
Index