C. Plumpton – författare

Sixth Form Pure Mathematics, Volume 1, Second Edition, is the first of a series of volumes on Pure Mathematics and Theoretical Mechanics for Sixth Form students whose aim is entrance into British and Commonwealth Universities or Technical Colleges. A knowledge of Pure Mathematics up to G.C.E. O-level is assumed and the subject is developed by a concentric treatment in which each new topic is used to illustrate ideas already treated. The major topics of Algebra, Calculus, Coordinate Geometry, and Trigonometry are developed together. This volume covers most of the Pure Mathematics required for the single subject Mathematics at Advanced Level. Early and rapid progress in calculus is made at the beginning of this volume in order to facilitate the student''s progress along the most satisfactory lines in Pure Mathematics, in Theoretical Mechanics and in Physics. The worked examples are an essential feature of this book and they are followed by routine exercises within the text of each chapter, associated closely with the work on which they are dependent. The exercises at the end of each chapter collectively embody all the topics of that chapter and, where possible, the preceding chapters also.

Steady Electric Fields and Currents, Volume 1 is an introductory text to electromagnetism and potential theory. This book starts with the fields associated with stationary charges and unravels the stationary condition to allow consideration of the flow of steady currents in closed circuits. The opening chapter discusses the experimental results that require mathematical explanation and discussion, particularly those referring to phenomena that question the validity of the simple Newtonian concepts of space and time. The subsequent chapters consider steady-state fields, electrostatics, dielectrics, energy theorems, and uniqueness theorems. The concluding chapter examines the steady flow of electric currents in closed circuits. Undergraduate students with electromagnetism course will greatly benefit from this book.

Theoretical Mechanics for Sixth Forms, Volume 2 deals with mathematics as a double subject for sixth-form pupils. This book is a continuation of the revised edition of the course in Theoretical Mechanics. This volume discusses the principle of virtual work, stability of equilibrium, vector algebra, and the motion of bodies with variable mass—subjects that can help the student prepare for the freshman year in a university or in one of the polytechnic schools. Compared to the earlier edition, this volume discusses in more detail topics such as the motion of a particle in two dimensions and systems of coplanar forces. This book also emphasizes vector algebra and its many applications, explaining the concept of a vector, the Cartesian coordinates and components, the definitions of vectors and scalars, and vector applications to kinetics. This text also contains exercise problems with answers. This volume can be used for sixth-form students in the U.K. and is also suitable for third year students of a sixth form course as preparation for further studies.

Theoretical Mechanics for Sixth Forms, Second Edition is a 14-chapter book that begins by elucidating the nature of theoretical mechanics. The book then describes the statics of a particle in illustration of the techniques of handling vector quantities. Subsequent chapters focus on the principle of moments, parallel forces and centers of gravity; and the application of Newton''s second law to the dynamics of a particle and the ideas of work and energy, impulse and momentum, and power. The concept of friction is also explained. This volume concludes with chapters concerning motion in a circle and simple harmonic motion. This text will serve as a more complete course for pupils taking mathematics as a single or double subject.

Magnetic Fields, Special Relativity and Potential Theory is an introduction to electromagnetism, special relativity, and potential theory, with emphasis on the magnetic field of steady currents (magnetostatics). Topics covered range from the origin of the magnetic field and the magnetostatic scalar potential to magnetization, electromagnetic induction and magnetic energy, and the displacement current and Maxwell''s equations. This volume is comprised of five chapters and begins with an overview of magnetostatics, followed by a chapter on the methods of solving potential problems drawn from electrostatics, magnetism, current flow, and gravitation. Relaxing the constraint of stationary steady currents, the next chapter considers electromagnetic induction when the current strengths in closed circuits vary or when the circuits move. This leads to the necessity of assessing the breakdown of Newtonian ideas and the introduction of special relativity. When the constraint of closed circuits is further relaxed and the motion of charges in open circuits is taken into account, the discussion turns to displacement current because of the relativistic theory already set up, leading to Maxwell''s equations. This book will be a valuable resource for undergraduate students of physics.

Modern Syllabus Algebra presents topics of traditional and modern algebra found in the Teachers Certificate and B.Ed, part I syllabuses of University Institutes of Education. It also contains additional exercises taken from examination papers of the University of London Institute of Education (the Teachers'' Certificate). The book discusses several mathematical concepts such as sets, relations and functions, Boolean algebra, groups, and number systems. It also illustrates linear equations, matrices, and vector spaces and then demonstrates how to solve complex numbers and combine probabilities. Mathematics teachers will find this text a suitable and convenient way of bringing themselves up to date in what is now being taught in schools.

Sixth Form Pure Mathematics, Volume 2, provides an introduction to inverse trigonometric functions, hyperbolic and inverse hyperbolic functions, and a range of mathematical methods including the use of determinants, the manipulation of inequalities, the solution of easy differential equations, and the use of approximate numerical methods. Complex numbers are defined and the various ways of representing and manipulating them are considered. Polar coordinates, curvature, an elementary study of lengths of curves and areas of surfaces of revolution, a more mature discussion of two-dimensional coordinate geometry than was possible in Volume 1, and an elementary introduction to the methods of three dimensional coordinate geometry comprise the geometrical content of the book. Throughout, the authors have tried to preserve the concentric style which they used in Volume 1 and the many worked examples and exercises in each chapter are designed or chosen to provide a continuous reminder of the work of the preceding chapters. Except for Pure Geometry, the two volumes cover almost all of the syllabuses for Advanced Pure Mathematics of the nine Examining Boards. This book provides an adequate course for mathematical pupils at Grammar Schools and a useful introductory course for Science and Engineering students in their first year at University or Technical College or engaged in private study.

Lattice Theory presents an elementary account of a significant branch of contemporary mathematics concerning lattice theory. This book discusses the unusual features, which include the presentation and exploitation of partitions of a finite set. Organized into six chapters, this book begins with an overview of the concept of several topics, including sets in general, the relations and operations, the relation of equivalence, and the relation of congruence. This text then defines the relation of partial order and then partially ordered sets, including chains. Other chapters examine the properties of meet and join and explain dimensional considerations. This book discusses as well certain relations between individual elements of a lattice, between subsets of a lattice, and between lattices themselves. The final chapter deals with distributive lattices and explores the complements in distributive lattices. This book is a valuable resource for college and university students of mathematics, logic, and such technologies as communications engineering.

New Tertiary Mathematics, Volume 2, Part 2: Further Applied Mathematics deals with various topics of theoretical mechanics and probability, from statics and the dynamics of a rigid body to the dynamics of a particle with one and two degrees of freedom. Many examples of varying difficulty are worked in the text and exercises are added after each major topic is covered. This book is comprised of five chapters and opens with a discussion on statics, with particular reference to the analysis of systems of forces in three dimensions, along with virtual work, stability, and the catenary. Complicated equilibrium problems are considered. The reader is then introduced to the dynamics of a particle in one and two dimensions, as well as the implications of the Galilean transformation and the general theorems of motion for a system of particles. These theorems are applied to simple cases of the motion of a rigid body. The final chapter on probability examines normal and Poisson distributions, Markov chains, and miscellaneous problems. This monograph will be a useful resource for mathematical pupils and students engaged in private study.

Mathematics with Understanding: Book 2 is an eight-chapter book that begins with an explanation of the number systems. Fractions, rational numbers, systems of integers, algebraic relations, shape, and measurement are then described. The modular arithmetic and groups as well as probability are also explained. This book will be useful to students and teachers for a deeper understanding of the structure behind many mathematical ideas and processes.

Elementary Electromagnetic Theory Volume 3: Maxwell''s Equations and their Consequences is the third of three volumes that intend to cover electromagnetism and its potential theory. The third volume considers the implications of Maxwell''s equations, such as electromagnetic radiation in simple cases, and its relation between Maxwell''s equation and the Lorenz transformation. Included in this volume are chapters 11-14, which contain an in-depth discussion of the following topics: • Electromagnetic Waves • The Lorentz Invariance of Maxwell''s Equation • Radiation • Motion of Charged Particles Intended to serve as an introduction to electromagnetism and potential theory, the book is for second, third, and fourth year undergraduates of physics and engineering, as they are included in their course of study. Do note that the authors assume that the readers are conversant with the basic ideas of vector analysis, including vector integral theorems.

An Introduction to Real Analysis presents the concepts of real analysis and highlights the problems which necessitate the introduction of these concepts. Topics range from sets, relations, and functions to numbers, sequences, series, derivatives, and the Riemann integral. This volume begins with an introduction to some of the problems which are met in the use of numbers for measuring, and which provide motivation for the creation of real analysis. Attention then turns to real numbers that are built up from natural numbers, with emphasis on integers, rationals, and irrationals. The chapters that follow explore the conditions under which sequences have limits and derive the limits of many important sequences, along with functions of a real variable, Rolle''s theorem and the nature of the derivative, and the theory of infinite series and how the concepts may be applied to decimal representation. The book also discusses some important functions and expansions before concluding with a chapter on the Riemann integral and the problem of area and its measurement. Throughout the text the stress has been upon concepts and interesting results rather than upon techniques. Each chapter contains exercises meant to facilitate understanding of the subject matter. This book is intended for students in colleges of education and others with similar needs.

Elementary Classical Hydrodynamics deals with the fundamental principles of elementary classical hydrodynamics, with emphasis on the mechanics of inviscid fluids. Topics covered by this book include direct use of the equations of hydrodynamics, potential flows, two-dimensional fluid motion, waves in liquids, and compressible flows. Some general theorems such as Bernoulli''s equation are also considered. This book is comprised of six chapters and begins by introducing the reader to the fundamental principles of fluid hydrodynamics, with emphasis on ways of studying the motion of a fluid. Basic concepts and quantities such as viscosity, density, and pressure, are considered, along with hydrostatics and the equation of motion. The discussion then turns to Bernoulli''s equation, the motion of a small element of fluid, velocity potential, and the kinetic energy of a uniform incompressible fluid. The chapters that follow explore two-dimensional fluid motion; a uniform inviscid, incompressible liquid having a free surface and upon which the only body force acting is uniform gravity; and a compressible gas with undisturbed uniform pressure and density, paying particular attention to the propagation and reflection of sound waves. This book is intended as an elementary introduction to the mechanics of inviscid fluids for first and second year undergraduates.

Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.