A quadratic differential on aRiemann surface is locally represented by a ho lomorphic function element wh ich transforms like the square of a derivative under a conformal change of the parameter. More generally, one also allows for meromorphic function elements; however, in many considerations it is con venient to puncture the surface at the poles of the differential. One is then back at the holomorphic case. A quadratic differential defines, in a natural way, a field of line elements on the surface, with singularities at the critical points, i.e. the zeros and poles of the differential. The integral curves of this field are called the trajectories of the differential. A large part of this book is about the trajectory structure of quadratic differentials. There are of course local and global aspects to this structure. Be sides, there is the behaviour of an individual trajectory and the structure deter mined by entire subfamilies of trajectories. An Abelian or first order differential has an integral or primitive function is in general not single-valued. In the case of a quadratic on the surface, which differential, one first has to take the square root and then integrate. The local integrals are only determined up to their sign and arbitrary additive constants. However, it is this multivalued function which plays an important role in the theory; the trajectories are the images of the horizontals by single valued branches of its inverse.

The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community.

Small Animal Medical Differential Diagnosis, 2nd Edition is a practical, concise guide to the differential diagnosis, etiology, laboratory abnormalities, and classification of clinical signs and medical disorders in dogs and cats. By covering nearly every possible sign and clinical disorder relevant to small animal medical practice, this pocket-sized, rapid reference helps you make more reliable on-the-scene decisions. More than 400 lists bring the most important medical diagnostic information from multiple resources into a single rapid reference. An organized presentation of differential diagnoses by sign and symptom, disorder, and body system, facilitates quick and flexible access to information at many stages of the diagnostic work-up. Alphabetical listing of all relevant laboratory tests makes information easy to find for students and experienced practitioners alike. Easily identify the likeliest diagnosis by reviewing the possibilities listed in order of incidence. Pocket-sized for portability, practicality, and quick reference. NEW! Coverage of new disorders and syndromes expands the span of differential diagnoses to help you effectively evaluate more signs and symptoms. NEW! Addition of new and more widely used diagnostic and laboratory tests keeps you up-to-date as lab tests become more specialized and sophisticated.

Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

First-rate introduction for undergraduates examines first order equations, complex-valued solutions, linear differential operators, the Laplace transform, Picard's existence theorem, and much more. Includes problems and solutions.

Graduate-level text surveys games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, games with restricted phase coordinates, and N-person games. 1971 edition.