DIFFERENTIAL EQUATIONS AND NUMERICAL CALCULUS METHODS WITH MATLAB

This book delves into the solution of differential equations using MATLAB, from both numerical and analytical perspectives, and their applications. It covers topics such as the application of numerical computation methods to solve differential and partial differential equations, including the Euler, Heun, and Taylor methods. These methods are also extended to the solution of linear and nonlinear equations and systems, optimization and zeros of functions, and numerical differentiation and integration. Furthermore, it explores analytical methods for solving differential equations as separable equations, exact equations, and homogeneous and linear equations. It also addresses higher-order homogeneous linear equations with constant coefficients, nonhomogeneous equations with constant coefficients by variation of parameters, nonhomogeneous equations with variable coefficients, and the Cauchy-Euler equations. The course also covers systems of homogeneous and non-homogeneous linear equations with constant coefficients, differential equations, and nonlinear systems using approximate numerical methods such as Euler and Runge-Kutta, as well as equations using orthogonal methods and Laplace transforms. A wide variety of examples and exercises solved using MATLAB software are presented.