O'Reilly logo

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

MATLAB Differential Equations

Book Description

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java.

MATLAB Differential Equations introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to the MATLAB environment and MATLAB programming, this book provides all the material needed to work on differential equations using MATLAB. It includes techniques for solving ordinary and partial differential equations of various kinds, and systems of such equations, either symbolically or using numerical methods (Euler’s method, Heun’s method, the Taylor series method, the Runge–Kutta method,…). It also describes how to implement mathematical tools such as the Laplace transform, orthogonal polynomials, and special functions (Airy and Bessel functions), and find solutions of finite difference equations.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents at a Glance
  5. Contents
  6. About the Author
  7. Coming Soon
  8. Chapter 1: Introducing MATLAB and the MATLAB Working Environment
    1. Introduction
      1. Developing Algorithms and Applications
      2. Data Access and Analysis
      3. Data Visualization
      4. Numerical Calculation
      5. Publication of Results and Distribution of Applications
    2. The MATLAB working environment
    3. Help in MATLAB
    4. Numerical Computation with MATLAB
    5. Symbolic Calculations with MATLAB
    6. Graphics with MATLAB
    7. General Notation
    8. Help with Commands
    9. MATLAB and Programming
    10. Commands to Escape and Exit to the MS-DOS Environment
  9. Chapter 2: First Order Differential Equations. Exact Equations, Separation of Variables, Homogeneous and Linear Equations
    1. First Order Differential Equations
    2. Separation of Variables
    3. Homogeneous Differential Equations
    4. Exact Differential Equations
    5. Linear Differential Equations
  10. Chapter 3: Higher Order Differential Equations. The Laplace Transform and Special Types of Equations
    1. Ordinary High-Order Equations
    2. Linear Higher-Order Equations. Homogeneous Equations with Constant Coefficients
    3. Non-Homogeneous Equations with Constant Coefficients. Variation of Parameters
    4. Non-Homogeneous Equations with Variable Coefficients. Cauchy–Euler Equations
    5. The Laplace Transform
    6. Orthogonal Polynomials
      1. Chebychev Polynomials of the First and Second Kind
      2. Legendre Polynomials
      3. Associated Legendre Polynomials
      4. Hermite Polynomials
      5. Generalized Laguerre Polynomials
      6. Laguerre Polynomials
      7. Jacobi Polynomials
      8. Gegenbauer Polynomials
    7. Bessel and Airy Functions
  11. Chapter 4: Differential Equations Via Approximation Methods
    1. Higher Order Equations and Approximation Methods
    2. The Taylor Series Method
    3. The Runge–Kutta Method
  12. Chapter 5: Systems of Differential Equations and Finite Difference Equations
    1. Systems of Linear Homogeneous Equations with Constant Coefficients
    2. Systems of Linear Non-Homogeneous Equations with Constant Coefficients
    3. Finite Difference Equations
    4. Partial Differential Equations
  13. Chapter 6: Numerical Calclus with MATLAB. Applications to Differential Equations
    1. MATLAB and Programming
    2. Text Editor
    3. Scripts
    4. Functions and M-Files. Function, Eval and Feval
    5. Local and Global Variables
    6. Data Types
    7. Flow Control: FOR Loops, WHILE and IF ELSEIF
      1. The FOR Loop
      2. The WHILE Loop
      3. IF ELSEIF ELSE END Loops
      4. Switch and Case
      5. Continue
      6. Break
      7. Try ... Catch
      8. Return
    8. Subfunctions
    9. Ordinary Differential Equations Using Numerical Analysis
      1. Euler’s Method
      2. Heun’s Method
      3. The Taylor Series Method
  14. Chapter 7: Ordinary and Partial Differential Equations with Initial and Boundary Values
    1. Numerical Solutions of Differential Equations
    2. Ordinary Differential Equations with Initial Values
    3. Ordinary Differential Equations with Boundary Values
    4. Partial Differential Equations
  15. Chapter 8: Symbolic Differential and Integral Calculus
    1. Symbolic Computation with MATLAB. Symbolic Variables
    2. Symbolic Functions. Substitution and Functional Operations
    3. Mathematical Analysis Functions. Limits, Continuity, and Series
    4. Derivatives, Integrals and Differential Equations
    5. Linear Algebra: Simplifying and Solving Equations