There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study. Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere—Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms.
The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www. Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development. Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour.
This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields.
It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems with very brief hints many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem.
There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process.
The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities. A first course in ordinary differential equations for mathematicians, scientists and engineers. Solutions are provided. A comprehensive survey of all the mathematical methods that should be available to graduate students in physics.
In addition to the usual topics of analysis, such as infinite series, functions of a complex variable and some differential equations as well as linear vector spaces, this book includes a more extensive discussion of group theory than can be found in other current textbooks. The main feature of this textbook is its extensive treatment of geometrical methods as applied to physics.
With its introduction of differentiable manifolds and a discussion of vectors and forms on such manifolds as part of a first-year graduate course in mathematical methods, the text allows students to grasp at an early stage the contemporary literature on dynamical systems, solitons and related topological solutions to field equations, gauge theories, gravitational theory, and even string theory.
Free solutions manual available for lecturers at www. Skip to content. Div Grad Curl and All that. A Student s Guide to Vectors and Tensors. Author : Daniel A. Vector Calculus. Vector Calculus Book Review:. Vector Analysis and Cartesian Tensors. Author : D. Calculus of Several Variables. Calculus of Several Variables Book Review:. Applied Calculus for Scientists and Engineers. Multivariable Calculus with Mathematica. Author : Robert P. Multivariable Calculus with Mathematica Book Review:.
Quick Calculus. Quick Calculus Book Review:. Numbers and Functions. Author : R. Numbers and Functions Book Review:. Advanced Calculus. Author : James J. Advanced Calculus Book Review:. A Student s Guide to Maxwell s Equations. Author : Camilla R. Jordan,David A. Groups Book Review:. Mathematical Analysis.
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