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by César Pérez López
MATLAB Differential Equations
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Title
Copyright
Contents at a Glance
Contents
About the Author
Coming Soon
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 Environment
Chapter 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 Parameters
Non-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 Methods
The 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 Feval
Local 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
Ordinary Differential Equations with Initial Values
Ordinary Differential Equations with Boundary Values
Partial Differential Equations
Chapter 8: Symbolic Differential and Integral Calculus
Symbolic Computation with MATLAB. Symbolic Variables
Symbolic Functions. Substitution and Functional Operations
Mathematical Analysis Functions. Limits, Continuity, and Series
Derivatives, Integrals and Differential Equations
Linear Algebra: Simplifying and Solving Equations
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