Ordinary differential equations for engineers : problems with MATLAB solutions

Intro
 Preface
 Disclaimer
 Contents
 About the Author
 1 Basic Concepts
 1.1 Definitions and Preliminaries
 2 First Order Ordinary Differential Equations
 2.1 Fundamentals of First Order ODEs
 2.2 Direction Fields
 2.3 Systems of First Order ODEs
 2.4 Applications of First Order ODEs
 References
 3 Second and Higher Order Ordinary Differential Equations
 3.1 Linearity and the Wronskian
 3.2 Linear Second-Order ODEs
 3.3 Reduction of Order
 3.4 Cauchy-Euler ODEs
 3.5 Method of Undetermined Coefficients
 3.6 Variation of Parameters
 References 4 Series Solutions of Second-Order Ordinary Differential Equations4.1 Power Series and Convergence
 4.2 Taylor Series and Polynomials
 4.3 Ordinary and Singular Points
 4.4 Series Solutions Near an Ordinary Point
 4.5 Series Solutions Near a Singular Point
 the Method of Frobenius
 References
 5 Special Differential Equations, Functions, and Polynomials
 5.1 Gamma Function
 5.2 Bessel Equation, Bessel Functions, and Polynomials
 5.3 Chebyshev Equation, Chebyshev Functions, and Polynomials
 5.4 Legendre Equation, Legendre Functions and Polynomials
 5.5 Laguerre Equation and Polynomials 5.6 Hermite Equation and PolynomialsReferences
 6 Laplace Transform Methods
 6.1 Laplace Transform and Its Properties
 6.2 Inverse Laplace Transforms, Initial and Final Values
 6.3 Solutions of Linear ODEs Using Laplace Transforms
 6.4 Applications of Laplace Transform Methods
 References
 7 Systems of First-Order Linear Equations
 7.1 Review of Matrices, Linear Independence, Eigenvalues, Eigenvectors
 7.2 Order Reduction of Second- and Higher Order ODEs in Matrix Form
 7.3 Homogeneous Systems with Constant Coefficients
 7.4 The Matrix Exponential Function
 7.5 The Jordan Form 7.6 Matrix Methods and Solutions of Nonhomogeneous ODEs in MATLABReferences
 8 Numerical Solutions of Differential Equations
 8.1 Euler Methods
 8.2 Second-Order Methods
 8.3 Numerical Solution of Second-Order ODEs (Backward Euler Method)
 8.4 Fourth and Higher Order Numerical Methods
 8.5 Variable Step Size Methods
 8.6 Multistep Methods
 8.7 Runge-Kutta-Nystrom (RKN) Method
 8.8 Stiff ODEs
 8.9 Numerical Solution of Implicit ODEs
 References
 9 Nonlinear Ordinary Differential Equations
 9.1 Phase Plane Analysis of Linear Systems
 9.2 Autonomous Equations and Stability 9.3 Almost (Locally) Linear Systems9.4 Limit Cycles, Competing Species, Chaos
 References
 10 More Applications of ODEs
 10.1 Buoyancy Problem
 10.2 Mass-Spring Systems
 10.3 Numerical Solutions: Flame Propagation, Logistic Growth, Vertical Projectile
 10.4 Belousov-Zhabotinsky Oscillating Chemical Reactions
 10.5 Electric Circuits
 10.6 Hodgin-Huxley and Fitzhugh-Nagumo Spiking Neuron Models
 10.7 Mixing Tank and Chemical Reactions in a Batch Reactor
 10.8 Modeling Quadrotor Dynamics
 10.9 Pendulum Problems
 10.10 Satellite Orbits
 References
 Appendix: Mathematical Formulas and Tables