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The laws of nature are written in the language of partial differential equations. Therefore, these equations arise as models in virtually all branches of science and technology. Our goal in this book is to help you to understand what this vast subject is about. The book is an introduction to the field suitable for senior undergraduate and junior graduate students. Introductory courses in partial differential equations (PDEs) are given all over the world in various forms. The traditional approach to the subject is to introduce a number of analytical techniques, enabling the student to derive exact solutions of some simplified problems. Students who learn about computational techniques in other courses subsequently realize the scope of partial differential equations beyond paper and pencil. Our book is significantly different from the existing ones. We introduce both analytical theory, including the theory of classical solutions and that of weak solutions, and introductory techniques of ill-posed problems with reference to weak solutions. Besides, since computational techniques are commonly available and are currently used in all practical applications of partial differential equations, we incorporate classical finite difference methods and finite element methods in our book.
This compilation includes eleven chapters detailing various advances in neuropathology. Chapter One includes a quantitative study concerning the spectrum of temporal lobe pathology in argyrophilic grain disease. Chapter Two discusses the clinical, pathologic, and recent genetic features of pineoblastoma tumours. Chapter Three describes the clinical and histopathological features of spinal ependymomas, focusing on the current approach to treatment. Chapter Four defines the clinical and molecular pathological hallmarks of diffuse intrinsic pontine glioma and explores various therapies for treatment. Chapter Five reviews the clinicopathologic and genetic features of supratentorial ependymomas. Chapter Six reviews various features of astroblastoma. Chapter Seven explores the clinical, pathology, and genetic features of pilocytic astrocytomas. Chapter Eight describes rare, benign brain tumours called craniopharyngiomas. Chapter Nine reviews the clinicopathologic features of primary amoebic meningoencephalitis and how it is impacted by climate change. Chapter Ten deals with a rare cerebral hemispheric tumour with characteristics often resembling grade 4 astrocytoma. Finally, Chapter Eleven details the clinicopathologic features of myxoid glioneuronal tumours.
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