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Complex Numbers lie at the heart of most technical and scientific subjects. This book can be used to teach complex numbers as a course text,a revision or remedial guide, or as a self-teaching work. The author has designed the book to be a flexiblelearning tool, suitable for A-Level students as well as other students in higher and further education whose courses include a substantial maths component (e.g. BTEC or GNVQ science and engineering courses). Verity Carr has accumulated nearly thirty years of experience teaching mathematics at all levels and has a rare gift for making mathematics simple and enjoyable. At Brooklands College, she has taken a leading role in the development of a highly successful Mathematics Workshop. This series of Made Simple Maths books widens her audience but continues to provide the kind of straightforward and logical approach she has developed over her years of teaching.
Presents the Dirichlet problem for harmonic functions twice: once using the Poisson integral for the unit disk and again in an informal section on Brownian motion, where the reader can understand intuitively how the Dirichlet problem works for general domains. This book is suitable for a first-year course in complex analysis
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Set in the genre of a children's book, John and Betty trace the evolution of complex numbers and explore their operations. From integers, to fractions, to surds, complex numbers are made to seem like an obvious extension. Incorporating graphing on the complex number plane and culminating in De Moivre's Theorem, the logic of complex numbers is made to seem intuitive and simple. John and Betty delight in their journey, as will senior mathematics students.
* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory
A clear guide to the key concepts and mathematical techniques underlying the Schrödinger equation, including homework problems and fully worked solutions.
Math, Better Explained is an intuitive guide to the math fundamentals. Learn math the way your teachers always wanted.
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
This book is a sequel to the volume of selected papers of Dyson up to 1990 that was published by the American Mathematical Society in 1996. The present edition comprises a collection of the most interesting writings of Freeman Dyson, all personally selected by the author, from the period 1990–2014. The five sections start off with an Introduction, followed by Talks about Science, Memoirs, Politics and History, and some Technical Papers. The most noteworthy is a lecture entitled Birds and Frogs to the American Mathematical Society that describes two kinds of mathematicians with examples from real life. Other invaluable contributions include an important tribute to C. N. Yang written for his retirement banquet at Stony Brook University, as well as a historical account of the Operational Research at RAF Bomber Command in World War II provocatively titled A Failure of Intelligence. The final section carries the open-ended question of whether any conceivable experiment could detect single gravitons to provide direct evidence of the quantization of gravity — Is a Graviton Detectable? Various possible graviton-detectors are examined. This invaluable compilation contains unpublished lectures, and surveys many topics in science, mathematics, history and politics, in which Freeman Dyson has been so active and well respected around the world.
For decades, Alan Siegel and Irene Etzkorn have championed simplicity as a competitive advantage and a consumer right. Consulting with businesses and organizations around the world to streamline products, services, processes and communications, they have achieved dramatic results. In Simple, the culmination of their work together, Siegel and Etzkorn show us how having empathy, striving for clarity, and distilling your message can reduce the distance between company and customer, hospital and patient, government and citizen-and increase your bottom line. Examining the best and worst practices of an array of organizations big and small-including the IRS, Google, Philips, Trader Joe's, Chubb Insurance, and ING Direct, and many more-Siegel and Etzkorn recast simplicity as a mindset, a design aesthetic, and a writing technique. In these illuminating pages you will discover, among other things: Why the Flip camera became roadkill in the wake of the iPhone What SIMPLE idea allowed the Cleveland Clinic to improve care and increase revenue How OXO designed a measuring cup that sold a million units in its first 18 months on the market Where Target got the idea for their "ClearRX" prescription system How New York City simplified its unwieldy bureaucracy with three simple numbers By exposing the overly complex things we encounter every day, SIMPLE reveals the reasons we allow confusion to persist, inspires us to seek clarity, and explores how social media is empowering consumers to demand simplicity. The next big idea in business is Simple.