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Books by professors of the ICMC group on FDEs
Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations as well, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more.
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These are lecture notes on Ordinary Differential Equations by professors Hermínio Cassago Junior and Luiz Augusto da Costa Ladeira. It was intended to be a textbook for sophomore in the various courses of the campus of the University of São Paulo at São Carlos. Today, it is also used in other faculties and universities. The textbook covers linear differential equations of first and second orders, Laplace transform, systems of linear differential and equations, and an introduction to non-linear differential equation of first order.
Differential and integral calculus is not a sequence of rules to memorize, but a theory based entirely on the notion of real number. All of its central results are a consequence of the so-called Axiom of Completeness, about which the reader will find a clear discussion in this book. It is the understanding of theoretical concepts that allows an understanding of how differential and integral calculus applies to other sciences and practical situations. The subjects dealt with throughout the chapters are: basic conceptualization; studies of the concepts of limit and continuity; differential calculus and some of its applications; Riemann integral, integral calculus techniques and definition of logarithm and exponential functions; presentation of sequences and numerical series and power series. At the end of each chapter, the reader will find exercises whose answers are found at the end of the volume.
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This is a textbook entitled "Linear Algebra and Ordinary Differential Equations" by professor Luiz Augusto da costa Ladeira was specially elaborated for freshman of some engineering courses of our campus which prefer to offer an integrated view of these matters rather than a more deep approach treating Linear Algebra and ODEs separately. Within the contents of the textbook, the student finds first order equations, vector spaces, linear differential equations, linear transforms, and systems of linear differential equations.
In 1982, professors Hildebrando Rodrigues, Paulo Porto and Plácido Táboas organized a Cálculo book called "Differential and integral A Cálculo" as teaching material to support the discipline with the same name. This book was published by the then Instituto de Ciências Matemáticas de São Carlos (ICMSC) of the University of São Paulo, today under the name of Instituto de Ciências Matemáticas e de Computação (ICMC).
This textbook was intended to be a reference book for junior undergraduate students of the discipline named Partial Differential Equations. Besides the Dirichlet problem and the boundary value problem, it covers an introduction to Bessel functions, Fourier-Bessel series, Legendre polynomial and Fourier-Legendre series, Fourier integral and Fourier transform, ending with applications of the Fourier integral.
This textbook entitled "Retarded differential equations" by professor Nelson Onuchic has the collaboration of professors Hildebrando Rodrigues, Lourdes Onuchic and Plácido Táboas. Its target audience is graduate students and senior undergraduate students. Besides basic facts of this type of equations, the book also covers stability (definitions and second Lyapunov method), invariant sets and Lyapunov functionals for autonomous systems, stability and asymptotic behavior for perturbed systems of linear systems. This text appears in the annals of the Colloquio Brasileiro de Matemática (8. 1971 Poços de Caldas).
This book is a joint publication of the Mathematical Research Institute of the University of São Paulo and the Faculty of Philosophy, Sciences and Letters of Rio Claro, dated 1965. The title of the book, authored by professor Nelson Onuchic, in collaboration with professors Lourdes Onuchic and Odelar Leite Linhares, is "Functional Differential Equations". Its content includes results on the existence and uniqueness of solutions, stability and Lyapunov functionals, invariant sets and implications for stability, and perturbed systems of a linear system (boundedness and stability).
The content of this textbook on "Ordinary Differential Equations", presented at the Third Brazilian Mathematical Colloquium, held in Fortaleza, Ceará, in 1961, includes stability of linear systems, asymptotic equivalence and the topological method of T. Wazewski. Professor Nelson Onuchic is the author of this book which was published by the Faculty of Philosophy, Sciences and Letters of Rio Claro, State of São Paulo, Brazil.
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