This textbook presents all the basics for the first two years of a course in mathematical analysis, from the natural numbers to Stokes-Cartan Theorem.

The main novelty which distinguishes this book is the choice of introducing the Kurzweil-Henstock integral from the very beginning. Although this approach requires a small additional effort by the student, it will be compensated by a substantial advantage in the development of the theory, and later on when learning about more advanced topics.

The text guides the reader with clarity in the discovery of the many different subjects, providing all necessary tools – no preliminaries are needed. Both students and their instructors will benefit from this book and its novel approach, turning their course in mathematical analysis into a gratifying and successful experience.

About the Author

Alessandro Fonda obtained his PhD at the International School for Advanced Studies (SISSA-Trieste) in 1988, under the supervision of Jean Mawhin. Then he first got a research position in Belgium, before going back to Italy, at the University of Trieste, becoming full professor in 2002.

He obtained two prizes from the Acad�mie Royale de Belgique for his monographs "Periodic solutions of scalar second order differential equations with a singularity" in 1993 and "Playing around resonance. An invitation to the search of periodic solutions for second order ordinary differential equations" in 2017.

He has been invited to give plenary lectures at several conferences in Europe and in the USA.

His research interests are mainly concentrated on existence and multiplicity problems for boundary value problems. He recently gave an important contribution to the study of the periodic problem for Hamiltonian systems by providing some generalizations of the Poincar�-Birkhoff Theorem in higher dimensions. He also studied problems related to differential inclusions, persistence in dynamical systems, and global behaviour of the solutions to planar systems.

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