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This book provides an up-to-date description of the methods needed
to face the existence of solutions to some nonlinear boundary value
problems. All important and interesting aspects of the theory of
periodic solutions of ordinary differential equations related to
the physical and mathematical question of resonance are treated.
The author has chosen as a model example the periodic problem for a
second order scalar differential equation. In a paedagogical style
the author takes the reader step by step from the basics to the
most advanced existence results in the field.
This book provides an up-to-date description of the methods needed
to face the existence of solutions to some nonlinear boundary value
problems. All important and interesting aspects of the theory of
periodic solutions of ordinary differential equations related to
the physical and mathematical question of resonance are treated.
The author has chosen as a model example the periodic problem for a
second order scalar differential equation. In a paedagogical style
the author takes the reader step by step from the basics to the
most advanced existence results in the field.
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.
This beginners' course provides students with a general and
sufficiently easy to grasp theory of the Kurzweil-Henstock
integral. The integral is indeed more general than Lebesgue's in
RN, but its construction is rather simple, since it makes use of
Riemann sums which, being geometrically viewable, are more easy to
be understood. The theory is developed also for functions of
several variables, and for differential forms, as well, finally
leading to the celebrated Stokes-Cartan formula. In the appendices,
differential calculus in RN is reviewed, with the theory of
differentiable manifolds. Also, the Banach-Tarski paradox is
presented here, with a complete proof, a rather peculiar argument
for this type of monographs.
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