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Elementary Fluid Dynamics
This textbook provides a clear and concise introduction to both theory and application of fluid dynamics. It has a wide scope, frequent references to experiments, and numerous exercises (with hints and answers).
Elementary Fluid Dynamics
The study of the dynamics of fluids is a central theme of modern applied mathematics. It is used to model a vast range of physical phenomena and plays a vital role in science and engineering. This textbook provides a clear introduction to both the theory and application of fluid dynamics, and will be suitable for all undergraduates coming to the subject for the first time. Prerequisites are few: a basic knowledge of vector calculus, complex analysis, and simple methods for solving differential equations are all that is needed. Throughout, numerous exercises (with hints and answers) illustrate the main ideas and serve to consolidate the reader's understanding of the subject. The book's wide scope (including inviscid and viscous flows, waves in fluids, boundary layer flow, and instability in flow) and frequent references to experiments and the history of the subject, ensures that this book provides a comprehensive and absorbing introduction to the mathematical study of fluid behaviour.
The Wonder Book of Geometry
David Acheson transports us into the world of geometry, one of the oldest branches of mathematics. He describes its history, from ancient Greece to the present day, and its emphasis on proofs. With its elegant deduction and practical applications, he demonstrates how geometry offers the quickest route to the spirit of mathematics at its best.
The Calculus Story
"[Acheson] introduces the fundamental ideas of calculus through the story of how the subject developed, from approximating π to imaginary numbers, and from Newton's falling apple to the vibrations of an electric guitar."--Back cover
1089 and All that
This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famouscartoonists. This unusual book is one of the most readable explanations of mathematics available.
Mathematical Models in Applied Mechanics
This textbook demonstrates the power of mathematics in solving practical, scientific, and technical problems through mathematical modelling techniques. It has been designed specifically for final year undergraduate and graduate students, and springs from the author's extensive teachingexperience. The text is combined with twenty-one carefully ordered problems taken from real situations, and students are encouraged to develop the skill of constructing their own models of new situations.
Solitons
This textbook is an introduction to the theory of solitons in the physical sciences.
Introduction to Hydrodynamic Stability
Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.
From Calculus to Chaos
What is calculus really for? This book is a highly readable introduction to applications of calculus, from Newton's time to the present day. These often involve questions of dynamics, i.e., of how--and why--things change with time. Problems of this kind lie at the heart of much of applied mathematics, physics, and engineering. From Calculus to Chaos takes a fresh approach to the subject as a whole, by moving from first steps to the frontiers, and by focusing on the many important and interesting ideas which can get lost amid a snowstorm of detail in conventional texts. The book is aimed at a wide readership, and assumes only some knowledge of elementary calculus. There are exercises (with full solutions) and simple but powerful computer programs which are suitable even for readers with no previous computing experience. David Acheson's book will inspire new students by providing a foretaste of more advanced mathematics and some of its liveliest applications.
