MATLAB Differential Equations

Contents at a Glance --
Contents --
About the Author --
Chapter 1: Introducing MATLAB and the MATLAB Working Environment --
Introduction --
Developing Algorithms and Applications --
Data Access and Analysis --
Data Visualization --
Numerical Calculation --
Publication of Results and Distribution of Applications --
The MATLAB working environment --
Help in MATLAB --
Numerical Computation with MATLAB --
Symbolic Calculations with MATLAB --
Graphics with MATLAB --
General Notation --
Help with Commands --
MATLAB and Programming Commands to Escape and Exit to the MS-DOS EnvironmentChapter 2: First Order Differential Equations. Exact Equations, Separation of Variables, Homogeneous and Linear Equations --
First Order Differential Equations --
Separation of Variables --
Homogeneous Differential Equations --
Exact Differential Equations --
Linear Differential Equations --
Chapter 3: Higher Order Differential Equations. The Laplace Transform and Special Types of Equations --
Ordinary High-Order Equations --
Linear Higher-Order Equations. Homogeneous Equations with Constant Coefficients Non-Homogeneous Equations with Constant Coefficients. Variation of ParametersNon-Homogeneous Equations with Variable Coefficients. Cauchy�Euler Equations --
The Laplace Transform --
Orthogonal Polynomials --
Chebychev Polynomials of the First and Second Kind --
Legendre Polynomials --
Associated Legendre Polynomials --
Hermite Polynomials --
Generalized Laguerre Polynomials --
Laguerre Polynomials --
Jacobi Polynomials --
Gegenbauer Polynomials --
Bessel and Airy Functions --
Chapter 4: Differential Equations Via Approximation Methods Higher Order Equations and Approximation MethodsThe Taylor Series Method --
The Runge�Kutta Method --
Chapter 5: Systems of Differential Equations and Finite Difference Equations --
Systems of Linear Homogeneous Equations with Constant Coefficients --
Systems of Linear Non-Homogeneous Equations with Constant Coefficients --
Finite Difference Equations --
Partial Differential Equations --
Chapter 6: Numerical Calclus with MATLAB. Applications to Differential Equations --
MATLAB and Programming --
Text Editor --
Scripts Functions and M-Files. Function, Eval and FevalLocal and Global Variables --
Data Types --
Flow Control: FOR Loops, WHILE and IF ELSEIF --
The FOR Loop --
The WHILE Loop --
IF ELSEIF ELSE END Loops --
Switch and Case --
Continue --
Break --
Try ... Catch --
Return --
Subfunctions --
Ordinary Differential Equations Using Numerical Analysis --
Euler�s Method --
Heun�s Method --
The Taylor Series Method --
Chapter 7: Ordinary and Partial Differential Equations with Initial and Boundary Values --
Numerical Solutions of Differential Equations