MATLAB THROUGH EXAMPLES. INTEGRALS AND DIFFERENTIAL EQUATIONS

This book provides the necessary material for working with integral calculus and differential equations using MATLAB. Regarding integral calculus, it delves into methods of integration in one variable, including immediate integrals, integrals by substitution, integrals by parts, integrals by reduction, cyclic integrals, line integrals, improper integrals, and Riemann integrals, with applications to calculating curve lengths and calculating surfaces and volumes of revolution. This book also covers methods of integration in several variables and their applications to calculating areas of plane figures, surfaces, and volumes. Additionally, it develops approximate methods of numerical integration. Furthermore, it explores differential equations, developing analytical methods for separable, exact, homogeneous, and linear equations. Numerical solutions for first-order and higher-order ordinary differential equations are also presented. The course also covers higher-order homogeneous linear equations with constant coefficients, non-homogeneous equations with constant coefficients solved by variation of parameters, non-homogeneous equations with variable coefficients, and Cauchy-Euler equations. Systems of homogeneous and non-homogeneous linear equations with constant coefficients, differential equations, and nonlinear systems are also developed using approximate numerical methods such as Euler and Runge-Kutta, as well as equations solved using orthogonal methods and the Laplace transform. A wide variety of examples and exercises solved using MATLAB software are presented.