This book consists of two parts. The first part presents the material of Applied Mathematics that is typically taught to first-year students of Engineering and Physical Sciences at Greek Universities. Special emphasis has been placed on applications and exercises to clearly understand how we apply theory in solving mathematical problems encountered in the science we study.

The second part develops the Mathematica Symbolic Algebra package, which allows us to work and attempt to solve mathematical problems using a computer within an ideal environment. Essentially, it is a programming language that unifies the user's ability to simultaneously use symbolic, numerical, and graphical methods to solve mathematical problems.

Writing a book that deals with Applied Mathematics, especially for first-year students, must overcome two very fundamental difficulties. The first concerns the presentation of mathematical concepts, which must be done with clarity and completeness, while the second concerns convincing first-year students that what they read are the keys to opening doors that will lead them to solve the mathematical problems they will encounter in their science, both during their studies and later as professionals.

I hope and wish that the combination of acquiring knowledge of both the mathematical concepts presented in the first part of the book and the Symbolic Algebra package developed in the second part will serve as the impetus needed for the reader to explore the magical world of mathematics in a modern way.