This textbook on elementary stochastic calculus is designed for senior undergraduate students in math, economics, and business. Although the material is presented at an introductory level, students sh
The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author aims to capture as much as possible the spirit of elementary det
A masterful, inviting telling of the Christian story Christian faith, says Martin Copenhaver, is not a subject to be mastered like calculus or Shakespeare—it is a story to be told and a life to be liv
This text forms a bridge between courses in calculus and real analysis. It focuses on the construction of mathematical proofs as well as their final content. Suitable for upper-level undergraduates an
Exceptionally clear exposition of an important mathematical discipline and its applications to sociology, economics, and psychology. Logical, easy-to-follow coverage of calculus of finite differences,
The book begins at the level of an undergraduate student assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, Lebesgue in
This textbook presents an understanding of how basic physical descriptions can be translated into mathematical analogues that provide an opportunity to investigate environmental processes. Examples come from a range of hydrologic, atmospheric, and geophysical problems. The emphasis is on simple examples and calculations that add to understanding. The book provides a sense for the meaning of mathematical expressions, a physical feel for their relations to processes, and confidence in working with mathematical solutions. The goal of this book, in essence, is to present the timeless basic physical and mathematical principles and philosophy of environmental modeling, often to students who need to be taught how to think in a different way than they would for more narrowly-defined engineering or physics problems. Minimum prerequisites for the student reader include a knowledge of calculus through differential equations, but the book provides the mathematical and physical tools needed as the
Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite.
Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite.
A thorough and logically fluent textbook on elementary dynamics, primarily intended for first-year Mathematics undergraduates. A basic knowledge of calculus and elementary statics is required, though no previous knowledge of dynamics is assumed. Pars, a former lecturer in Mathematics at Cambridge, also provides an introductory grounding in ideas that will recur throughout the book, such as vectors and the fundamentals of Newtonian mechanics. Included in the text are a number of worked examples to illustrate the application of the theory to concrete problems, and exercises for practice at the ends of the chapters.
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
This introductory 2004 textbook describes the nature of the Earth's environment and its physical processes so as to highlight environmental concerns arising from human use and misuse of soil and water resources. The author provides a thorough introduction to the basic issues regarding the sustainable, productive use of land resources that is vital in maintaining healthy rivers and good groundwater qualities. He develops a quantitative approach to studying these growing environmental concerns in a way that does not require prior knowledge of the physical sciences or calculus. The straightforward writing style, lack of prerequisite knowledge and copious illustrations make this textbook suitable for introductory university courses, as well as being a useful primer for research and management staff in environmental and resources management organisations. Each chapter ends with a set of student exercises for which solutions are available from solutions@cambridge.org.
This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.
This introductory 2004 textbook describes the nature of the Earth's environment and its physical processes so as to highlight environmental concerns arising from human use and misuse of soil and water resources. The author provides a thorough introduction to the basic issues regarding the sustainable, productive use of land resources that is vital in maintaining healthy rivers and good groundwater qualities. He develops a quantitative approach to studying these growing environmental concerns in a way that does not require prior knowledge of the physical sciences or calculus. The straightforward writing style, lack of prerequisite knowledge and copious illustrations make this textbook suitable for introductory university courses, as well as being a useful primer for research and management staff in environmental and resources management organisations. Each chapter ends with a set of student exercises for which solutions are available from solutions@cambridge.org.
This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to defor
This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, in
