Written in an appealing and informal style, this text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics, operations research, computer science, econometrics and mathematical economics. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a cookbook approach, giving concrete and geometric explanations, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interest is in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.
Written in an appealing and informal style, this text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics, operations research, computer science, econometrics and mathematical economics. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a cookbook approach, giving concrete and geometric explanations, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interest is in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.
When new ideas like chaos first move into the mathematical limelight, the early textbooks tend to be very difficult. The concepts are new and it takes time to find ways to present them in a form digestible to the average student. This process may take a generation, but eventually, what originally seemed far too advanced for all but the most mathematically sophisticated becomes accessible to a much wider readership. This book takes some major steps along that path of generational change. It presents ideas about chaos in discrete time dynamics in a form where they should be accessible to anyone who has taken a first course in undergraduate calculus. More remarkably, it manages to do so without discarding a commitment to mathematical substance and rigour. The book evolved from a very popular one-semester middle level undergraduate course over a period of several years and has therefore been well class-tested.
This book is about some of the areas at the intersection of the key topics that form the foundations for high-school mathematics. Most importantly, the book is about some mathematical ways of thinking
The language of mathematics has proven over centuries of application to be an indispensable tool for the expression and analysis of real problems. Here Kalman explains for an audience of non-mathemati
A. S. Ramsey (1867–1954) was a distinguished Cambridge mathematician and President of Magdalene College. He wrote several textbooks 'for the use of higher divisions in schools and for first-year students at university'. This book on electricity and magnetism, first published in 1937, and based upon his lectures over many years, was 'adapted more particularly to the needs of candidates for Part I of the Mathematical Tripos'. It covers electrostatics, conductors and condensers, dielectrics, electrical images, currents, magnetism and electromagnetism, and magnetic induction. The book is interspersed with examples for solution, for some of which answers are provided.
Mathematical methods are essential tools for all physical scientists. This book provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students across the physical sciences. In contrast to more traditional textbooks, all the material is presented in the form of exercises. Within these exercises, basic mathematical theory and its applications in the physical sciences are well integrated. In this way, the mathematical insights that readers acquire are driven by their physical-science insight. This third edition has been completely revised: new material has been added to most chapters, and two completely new chapters on probability and statistics and on inverse problems have been added. This guided tour of mathematical techniques is instructive, applied, and fun. This book is targeted for all students of the physical sciences. It can serve as a stand-alone text, or as a source of exercises and examples to complement other textbooks.
Mathematical methods are essential tools for all physical scientists. This book provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students across the physical sciences. In contrast to more traditional textbooks, all the material is presented in the form of exercises. Within these exercises, basic mathematical theory and its applications in the physical sciences are well integrated. In this way, the mathematical insights that readers acquire are driven by their physical-science insight. This third edition has been completely revised: new material has been added to most chapters, and two completely new chapters on probability and statistics and on inverse problems have been added. This guided tour of mathematical techniques is instructive, applied, and fun. This book is targeted for all students of the physical sciences. It can serve as a stand-alone text, or as a source of exercises and examples to complement other textbooks.
A classic advanced textbook, containing a cross-section of ideas, techniques and results that give the reader an unparalleled introductory overview of the subject. The author gives an integrated prese
A reissue of Professor Coxeter's classic text on non-Euclidean geometry. It surveys real projective geometry, and elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axi
Developed over a period of many years of working with students at the University of Texas, Austin, this book cultivates mathematical creativity and independence. The book is self contained, and assume
Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors approach in this textbook is to cultivate the
●Introduces central topics, such as vector spaces, linear maps, linear dependence, and eigenvalues, early in the book with the aim of helping students transition from calculus to rigorous mathematics●
A. S. Ramsey (1867–1954) was a distinguished Cambridge mathematician and President of Magdalene College. He wrote several textbooks 'for the use of higher divisions in schools and for first year students at university'. This book on statics, published in 1934, was intended as a companion volume to his Dynamics of 1929 and like the latter was based upon his lectures to students of the mathematical tripos, but it assumes no prior knowledge of the subject, provides an introduction and offers more that 100 example problems with their solutions. Topics include vectors, forces acting at a point, moments, friction, centres of gravity, work and energy, and elasticity.
A. S. Ramsey (1867–1954) was a distinguished Cambridge mathematician and President of Magdalene College. He wrote several textbooks 'for the use of higher divisions in schools and for first year students at university'. This book on dynamics, published in 1929, was based upon his lectures to students of the mathematical tripos, and reflects the way in which this branch of mathematics had expanded in the first three decades of the twentieth century. It assumes some knowledge of elementary dynamics, and contains an extensive collection of examples for solution, taken from scholarship and examination papers of the period. The subjects covered include vectors, rectilinear motion, harmonic motion, motion under constraint, impulsive motion, moments of inertia and motion of a rigid body. Ramsey published a companion volume, Statics, in 1934.
A central figure in Victorian science, William Whewell (1794–1866) held professorships in Mineralogy and Moral Philosophy at Trinity College, Cambridge, before becoming Master of the college in 1841. His mathematical textbooks, such as A Treatise on Dynamics (1823), were instrumental in bringing French analytical methods into British science. This three-volume history, first published in 1837, is one of Whewell's most famous works. Taking the 'acute, but fruitless, essays of Greek philosophy' as a starting point, it provides a history of the physical sciences that culminates with the mechanics, astronomy, and chemistry of 'modern times'. Volume 2 focuses on the rise and development of modern mechanics in the seventeenth century. Whewell shows how Galileo's laws of motion exemplify a paradigmatic shift from 'formal' to 'physical' sciences - a new approach concerned with explaining causes rather than merely observing phenomena. It also discusses the implications for physical astronomy of
A central figure in Victorian science, William Whewell (1794–1866) held professorships in Mineralogy and Moral Philosophy at Trinity College, Cambridge, before becoming Master of the college in 1841. His mathematical textbooks, such as A Treatise on Dynamics (1823), were instrumental in bringing French analytical methods into British science. This three-volume history, first published in 1837, is one of Whewell's most famous works. Taking the 'acute, but fruitless, essays of Greek philosophy' as a starting point, it provides a history of the physical sciences that culminates with the mechanics, astronomy, and chemistry of 'modern times'. Volume 1 studies Greek physics and metaphysics, attributing their failure to a method that derived its principles from the common use of language. It surveys the state of the physical sciences in the middle ages, and deals with the rise of 'formal' astronomy - based on observation rather than calculation - as exemplified by Copernicus.
A central figure in Victorian science, William Whewell (1794–1866) held professorships in Mineralogy and Moral Philosophy at Trinity College, Cambridge, before becoming Master of the college in 1841. His mathematical textbooks, such as A Treatise on Dynamics (1823), were instrumental in bringing French analytical methods into British science. This three-volume history, first published in 1837, is one of Whewell's most famous works. Taking the 'acute, but fruitless, essays of Greek philosophy' as a starting point, it provides a history of the physical sciences that culminates with the mechanics, astronomy, and chemistry of 'modern times'. Volume 3 first covers the mechanico-chemical sciences, emphasizing the convergence of mechanical and chemical theories in discoveries pertaining to electricity, magnetism and thermodynamics. A section on chemistry surveys Becher and Stahl's phlogiston theory, Lavoisier's theory of oxygen, and Faraday's laws of electromagnetic induction. The volume also
A central figure in Victorian science, William Whewell (1794–1866) held professorships in Mineralogy and Moral Philosophy at Trinity College, Cambridge, before becoming Master of the college in 1841. His mathematical textbooks, such as A Treatise on Dynamics (1823), were instrumental in bringing French analytical methods into British science. This three-volume history, first published in 1837, is one of Whewell's most famous works. Taking the 'acute, but fruitless, essays of Greek philosophy' as a starting point, it provides a history of the physical sciences that culminates with the mechanics, astronomy, and chemistry of 'modern times'. Volume 1 focuses on ancient Greek physics and metaphysics and their reception during the middle ages. Volume 2 discusses the rise of modern mechanics and emphasises the paradigmatic shift from mere observation to the explanation of causes. Volume 3 highlights the convergence of mechanical and chemical theories in discoveries about electricity, magnetis
