MATLAB Differential Equations

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. What you’ll learn* How to use the MATLAB environment * How to program the MATLAB language from first principles * How to solve ordinary and partial differential equations symbolically * How to solve ordinary and partial differential equations numerically, and graph their solutions * How to solve finite difference equations and general recurrence equations * How MATLAB can be used to investigate convergence of sequences and series and analytical properties of functions, with working examples Who this book is for This book is for anyone who wants to work in a practical, hands-on manner with MATLAB to solve differential equations. You'll already understand the core topics of undergraduate level applied mathematics, and have access to an installed version of MATLAB, but no previous experience of MATLAB is assumed. Table of Contents1. Introducing MATLAB and Differential Equations 2. First Order Differential Equations 3. Differential Equations of Superior Order. 4. Differential Equations Through Approximate Methods 5. Differential Equations Systems and Equations in Finite Differences 6. Numerical Calculus with MATLAB 7. Differential Equations with Initial Values et al. 8. Symbolic Differential and Integral Calculus 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. What you’ll learn How to use the MATLAB environmentHow to program the MATLAB language from first principlesHow to solve ordinary and partial differential equations symbolicallyHow to solve ordinary and partial differential equations numerically, and graph their solutionsHow to solve finite difference equations and general recurrence equationsHow MATLAB can be used to investigate convergence of sequences and series and analytical properties of functions, with working examplesWho this book is for This book is for anyone who wants to work in a practical, hands-on manner with MATLAB to solve differential equations. Youll already understand the core topics of undergraduate level applied mathematics, and have access to an installed version of MATLAB, but no previous experience of MATLAB is assumed. Table of Contents 1. Introducing MATLAB and Differential Equations 2. First Order Differential Equations 3. Differential Equations of Superior Order. 4. Differential Equations Through Approximate Methods 5. Differential Equations Systems and Equations in Finite Differences 6. Numerical Calculus with MATLAB 7. Differential Equations with Initial Values et al. 8. Symbolic Differential and Integral Calculus 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. César Pérez López. Chapter 5: Systems of Differential Equations and Finite Difference EquationsSystems 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 Chapter 2: First Order Differential Equations. Exact Equations, Separation of Variables, Homogeneous and Linear EquationsFirst 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 Switch and CaseContinue; 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; Exercise 7-1; Exercise 7-2; Exercise 7-3; Chapter 8: Symbolic Differential and Integral Calculus Non-Homogeneous Equations with Variable Coefficients. Cauchy-Euler EquationsThe 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