MAPLE THROUGH EXAMPLES: INTEGRALS AND DIFFERENTIAL EQUATIONS

This book provides the necessary material for working with integral calculus and differential equations using Maple. Regarding integral calculus, it delves into the methods of integration in one variable, including immediate integrals, integrals by substitution, integrals by parts, integrals by reduction, cyclic integrals, line integrals, improper integrals, Eulerian integrals, elliptic integrals, trigonometric integrals, Fresnel integrals, hypergeometric integrals, exponential integrals, logarithmic integrals, and Riemann integrals, with applications to calculating the lengths of curves and the areas 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. Furthermore, it explores differential equations in depth, developing 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 are also developed, as are differential equations and nonlinear systems using approximate numerical methods such as Euler and Runge-Kutta, equations solved using orthogonal methods, and special equations such as Airy and Bessel. Finally, partial differential equations are addressed. A wide variety of examples and exercises solved using Maple software are presented.