This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.
Over its two editions, The New Oxford Textbook of Psychiatry has come to be regarded as one of the most popular and trusted standard psychiatry texts among psychiatrists and trainees. Bringing together 146 chapters from the leading figures in the discipline, it presents a comprehensive account of clinical psychiatry, with reference to its scientific basis and to the patient's perspective throughout. The New Oxford Textbook of Psychiatry, Third Edition has been extensively re-structured and streamlined to keep pace with the significant developments that have taken place in the fields of clinical psychiatry and neuroscience since publication of the second edition in 2009. The new edition has been updated throughout to include the most recent versions of the two main classification systems---the DSM-5 and the ICD-11---used throughout the world for the diagnosis of mental disorders. In the years since publication of the first edition, many new and exciting discoveries have occurred in the biological sciences, which are having a major impact on how we study and practise psychiatry. In addition, psychiatry has fostered closer ties with philosophy, and these are leading to healthy discussions about how we should diagnose and treat mental illness. This new edition recognises these and other developments. Throughout, accounts of clinical practice are linked to the underlying science, and to the evidence for the efficacy of treatments. Physical and psychological treatments, including psychodynamic approaches, are covered in depth. The history of psychiatry, ethics, public health aspects, and public attitudes to psychiatry and to patients are all given due attention.
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