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Simulating the behavior of a human heart, predicting tomorrow's
weather, optimizing the aerodynamics of a sailboat, finding the
ideal cooking time for a hamburger: to solve these problems,
cardiologists, meteorologists, sportsmen, and engineers can count
on math help. This book will lead you to the discovery of a magical
world, made up of equations, in which a huge variety of important
problems for our life can find useful answers.
The volume is a follow-up to the INdAM meeting "Special metrics and
quaternionic geometry" held in Rome in November 2015. It offers a
panoramic view of a selection of cutting-edge topics in
differential geometry, including 4-manifolds, quaternionic and
octonionic geometry, twistor spaces, harmonic maps, spinors,
complex and conformal geometry, homogeneous spaces and
nilmanifolds, special geometries in dimensions 5-8, gauge theory,
symplectic and toric manifolds, exceptional holonomy and integrable
systems. The workshop was held in honor of Simon Salamon, a leading
international scholar at the forefront of academic research who has
made significant contributions to all these subjects. The articles
published here represent a compelling testimony to Salamon's
profound and longstanding impact on the mathematical community.
Target readership includes graduate students and researchers
working in Riemannian and complex geometry, Lie theory and
mathematical physics.
The volume is a follow-up to the INdAM meeting "Special metrics and
quaternionic geometry" held in Rome in November 2015. It offers a
panoramic view of a selection of cutting-edge topics in
differential geometry, including 4-manifolds, quaternionic and
octonionic geometry, twistor spaces, harmonic maps, spinors,
complex and conformal geometry, homogeneous spaces and
nilmanifolds, special geometries in dimensions 5-8, gauge theory,
symplectic and toric manifolds, exceptional holonomy and integrable
systems. The workshop was held in honor of Simon Salamon, a leading
international scholar at the forefront of academic research who has
made significant contributions to all these subjects. The articles
published here represent a compelling testimony to Salamon's
profound and longstanding impact on the mathematical community.
Target readership includes graduate students and researchers
working in Riemannian and complex geometry, Lie theory and
mathematical physics.
This textbook covers topics of undergraduate mathematics in
abstract algebra, geometry, topology and analysis with the purpose
of connecting the underpinning key ideas. It guides STEM students
towards developing knowledge and skills to enrich their scientific
education. In doing so it avoids the common mechanical approach to
problem-solving based on the repetitive application of dry
formulas. The presentation preserves the mathematical rigour
throughout and still stays accessible to undergraduates. The
didactical focus is threaded through the assortment of subjects and
reflects in the book's structure. Part 1 introduces the
mathematical language and its rules together with the basic
building blocks. Part 2 discusses the number systems of common
practice, while the backgrounds needed to solve equations and
inequalities are developed in Part 3. Part 4 breaks down the
traditional, outdated barriers between areas, exploring in
particular the interplay between algebra and geometry. Two
appendices form Part 5: the Greek etymology of frequent terms and a
list of mathematicians mentioned in the book. Abundant examples and
exercises are disseminated along the text to boost the learning
process and allow for independent work. Students will find
invaluable material to shepherd them through the first years of an
undergraduate course, or to complement previously learnt subject
matters. Teachers may pick'n'mix the contents for planning lecture
courses or supplementing their classes.
This work is a textbook on Mathematical Analysis written by expert
lecturers in the field. This textbook, other than the classical
differentiation and integration tools for functions of several real
variables, metric spaces, ordinary differential equations, implicit
function and so on, also provides opportunities to go deeper into
certain topics: among them, the Ascoli-Arzela theorem, the
regularity of convex functions in R^n, L^p spaces and absolutely
continuous functions, all topics that are paramount in modern
Mathematical Analysis. Other instances include the Weierstrass
theorem on polynomial approximation of continuous functions or
Peano's existence theorem (typically only existence, without
uniqueness) for nonlinear ODEs and systems under general
assumptions. The content is discussed in an elementary way and, at
a successive stage, some topics are examined from several, more
penetrating, angles. The agile organization of the subject matter
helps instructors to effortlessly determine which parts to present
during lectures and where to stop. The authors believe that any
textbook can contribute to the success of a lecture course only to
a point, and the choices made by lecturers are decisive in this
respect. The book is addressed to graduate or undergraduate honors
students in Mathematics, Physics, Astronomy, Computer Science,
Statistics and Probability, attending Mathematical Analysis courses
at the Faculties of Science, Engineering, Economics and
Architecture.
This textbook aims at introducing readers, primarily
students enrolled in undergraduate Mathematics or Physics
courses, to the topics and methods of classical Mathematical
Physics, including Classical Mechanics, its Lagrangian and
Hamiltonian formulations, Lyapunov stability, plus the
Liouville theorem and the Poincaré recurrence theorem among
others. The material also rigorously covers the theory of Special
Relativity. The logical-mathematical structure of the physical
theories of concern is introduced in an axiomatic way,
starting from a limited number of physical assumptions.
Special attention is paid to themes with a major impact on
Theoretical and Mathematical Physics beyond Analytical
Mechanics, such as the Galilean symmetry of classical Dynamics and
the Poincaré symmetry of relativistic Dynamics, the
far-fetching relationship between symmetries and constants of
motion, the coordinate-free nature of the underpinning mathematical
objects, or the possibility of describing Dynamics in a
global way while still working in local coordinates. Based on
the author’s established teaching experience, the text was
conceived to be flexible and thus adapt to different
curricula and to the needs of a wide range of students and
instructors.
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