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Claudia Prevot – A Concise Course on Stochastic Partial Differential Equations

Claudia Prevot – A Concise Course on Stochastic Partial Differential Equations

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These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. There are three approaches to analyze SPDE: the “martingale measure approach”, the “mild solution approach” and the “variational approach”. The purpose of these notes is to give a concise and as self-contained as possible an introduction to the “variational approach”. A large part of necessary background material is included in appendices.

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Medicine is the science and practice of establishing the diagnosis, prognosis, treatment, and prevention of disease.
Medicine encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness.
Contemporary medicine applies biomedical sciences, biomedical research, genetics, and medical technology to diagnose, treat, and prevent injury and disease,
typically through pharmaceuticals or surgery, but also through therapies as diverse as psychotherapy, external splints and traction, medical devices, biologics, and ionizing radiation, amongst others.

Medicine has been around for thousands of years, during most of which it was an art (an area of skill and knowledge) frequently having connections to the religious and
philosophical beliefs of local culture. For example, a medicine man would apply herbs and say prayers for healing, or an ancient philosopher and physician would apply bloodletting according to the theories of humorism.
In recent centuries, since the advent of modern science, most medicine has become a combination of art and science (both basic and applied, under the umbrella of medical science).
While stitching technique for sutures is an art learned through practice, the knowledge of what happens at the cellular and molecular level in the tissues being stitched arises through science.

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