Mathematica is a platform for scientific computing that helps you to work in virtually all areas of the experimental sciences and engineering. In particular, this software presents quite extensive capabilities and implements a large number of commands enabling you to efficiently handle problems involving Mathematical Analysis. Using Mathematica you will be able to solve a wide range of differential equations algebraically. Mathematica also implements numerical methods for the approximate solution of differential equations. The book begins with a practical introduction in Mathematica. Through successive chapters it delves into topics such as limits, numerical series, power series, continuity, differentiability and integration of functions of one and several variables and their applications in calculating areas and volumes. It also works in the field of differential equations, partial differential equations, systems of differential equations and difference equations. The concepts are illustrated with many examples and end of each chapter a number of exercises are solved to understand the theoretical concepts.