Books in Mathematics and applied mathematics

The Number Systems and Operations of Arithmetic

1st Edition
May 16, 2014
Orval M. Klose
W. J. Langford + 1 more
English
eBook
9 7 8 1 4 8 3 1 3 7 0 9 4

The Number Systems and Operations of Arithmetic was written for the single purpose of explaining to elementary school teachers (both in-service and in-training) the nature of those basic principles of mathematics which form the foundations and structural framework of arithmetic, and how the familiar formal algorithms of arithmetic stem from these structural principles. The book is organized into two parts. Part I on number systems covers the origin of numerical thinking; natural operations with the natural numbers; natural laws for the natural operations; the inverse operations and convergence and the number systems generated by these operations; and classification of the number systems as abstract systems. Part II on computational algorithms discusses computations with natural numbers, rational numbers, real numbers, and complex numbers. The ""answers"" to all the exercises are also provided in the main body of the text and it is hoped that the student will form the habit of looking there for them.

Lambda-Matrices and Vibrating Systems

1st Edition
July 10, 2014
Peter Lancaster
I. N. Sneddon + 2 more
English
eBook
9 7 8 1 4 8 3 1 5 0 9 6 3

Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with latent vectors in common. The book then expounds on Lambda matrices and on some numerical methods for Lambda matrices. These methods explain developments of known approximations and rates of convergence. The text then addresses general solutions for simultaneous ordinary differential equations with constant coefficients. The results of some of the studies are then applied to the theory of vibration by applying the Lagrange method for formulating equations of motion, after the formula establishing the energies and dissipation functions are completed. The book describes the theory of resonance testing using the stationary phase method, where the test is carried out by applying certain forces to the structure being studied, and the amplitude of response in the structure is measured. The book also discusses other difficult problems. The text can be used by physicists, engineers, mathematicians, and designers of industrial equipment that incorporates motion in the design.

The Theory of Jets in an Ideal Fluid

1st Edition
Volume 93
July 22, 2014
M. I. Gurevich
J. P. Kahane + 2 more
English
eBook
9 7 8 1 4 8 3 1 8 5 8 2 8

Pure and Applied Mathematics, Volume 39: The Theory of Jets in an Ideal Fluid provides a general idea of the theory of jets. This book serves as an introduction to the classical problems in the theory and provides some knowledge of the fundamentals of hydromechanics. Organized into 12 chapters, this volume begins with an overview of the theory of plane, steady flow of an ideal, incompressible fluid. This text then examines the jet flow of an unbounded current about a flat plate, placed perpendicular to the flow. Other chapters consider a number of problems involving the plane flow of fluid out of vessels. This book discusses as well the physical importance of Brillouin's condition and also the problem of cavitational flow. The final chapter deals with the flows of weightless fluid in order to know the effect of surface tension forces. This book is a valuable resource for marine and hydraulic engineers.

Model Answers in Pure Mathematics for A-Level Students

1st Edition
May 23, 2014
G.A. Pratt + 1 more
C. W. Schofield
English
eBook
9 7 8 1 4 8 3 1 5 5 5 6 2

Model Answers in Pure Mathematics for A-Level Students provides a set of solutions that indicate what is required and expected in an Advanced Level examination in Pure Mathematics. This book serves as a guide to the length of answer required, layout of the solution, and methods of selecting the best approach to any particular type of math problem. This compilation intends to supplement, not replace, the normal textbook and provides a varied selection of questions for practice in addition to the worked solutions. The subjects covered in this text include algebra, trigonometry, coordinate geometry, and calculus. This publication is valuable to students; working through and coping with the practice questions will help them face advanced mathematical examinations with confidence.

Problems and Methods in Analysis

1st Edition
May 9, 2014
W. Krysicki + 2 more
W. J. Langford + 1 more
English
eBook
9 7 8 1 4 8 3 2 8 0 6 3 9

Problems and Methods in Analysis, Volume 2 provides information pertinent to the methods of calculus. This book provides solutions to problems in analytical calculus. Organized into five chapters, this volume begins with an overview of the integration of functions that are not defined or are not bounded at a finite number of points, and with integrals in which the interval of integration is infinitely large. This text then defines the radius of curvature and provides the formula for curvature and radius of curvature. Other chapters consider the equation of tangent and normal. This book discusses as well the amplitudes of the harmonic components of a set of oscilloscope time base potentials. The final chapter deals with the Euler–Fourier formula, the Fourier series, and Dirichlet's conditions. This book is intended to be suitable for sixth form students, particularly scholarship students. First year university students who need a systematic course in calculus will also find this book useful.

Elementary Analysis

1st Edition
May 16, 2014
K. S. Snell + 1 more
W. J. Langford + 1 more
English
eBook
9 7 8 1 4 8 3 1 5 8 9 8 3

Elementary Analysis, Volume 2 introduces several of the ideas of modern mathematics in a casual manner and provides the practical experience in algebraic and analytic operations that lays a sound foundation of basic skills. This book focuses on the nature of number, algebraic and logical structure, groups, rings, fields, vector spaces, matrices, sequences, limits, functions and inverse functions, complex numbers, and probability. The logical structure of analysis given through the treatment of differentiation and integration, with applications to the trigonometric and logarithmic functions, is also briefly discussed. This volume begins with a description of the trigonometric functions of the general angle and an introduction to the binomial theorem and series. The rest of the chapters cover the numerical solution of equations, analytical geometry, Argand Diagram, numerical methods, and methods of approximation that form an important section of modern applied mathematics. This publication is valuable to teachers and students in training colleges.

A Collection of Problems in Analytical Geometry

1st Edition
June 6, 2016
D. V. Kletenik
W. J. Langford + 1 more
English
eBook
9 7 8 1 4 8 3 1 5 5 8 4 5

A Collection of Problems in Analytical Geometry, Part I: Analytical Geometry in the Plane is a collection of problems dealing with higher analytical geometry. The book discusses elementary problems dealing with plane analytical geometry. The text presents topics on the axis and intervals on an axis and coordinates on a straight line. The book also defines what a rectangular Cartesian coordinates in a plane is, the division of an interval in a given ratio, and shows how to calculate the area of a triangle. The equation of a curve, the functions of two variables, and the concept of an equation of a curve are explained by the use of examples and problems. The author also addresses the geometrical properties of curves of the second order, the equations of a straight line, a circle, an ellipse, a hyperbola, and a parabola. The text then discusses the general theory of second-order curves and emphasizes the equations of the central curves of the second order. The author cites the simplification of these equations as being applicable to theoretical mechanics. This collection of problems can be used by teachers of analytical geometry and their students.

A Collection of Problems in Analytical Geometry

1st Edition
June 6, 2016
D. V. Kletenik
W. J. Langford + 1 more
English
eBook
9 7 8 1 4 8 3 1 5 5 9 2 0

A Collection of Problems in Analytical Geometry, Part II: Three-Dimensional Analytical Geometry is a collection of problems dealing with analytical geometry in the field of theoretical mechanics. The book discusses rectangular Cartesian coordinates in three-dimensional space and the division of an interval in a given ratio. The sample questions concern problems dealing with isosceles triangles, vertices, and center of gravity of equal masses. The book defines the concept of a vector and then lists problems concerning the triangle law and the scalar product of two vectors. Other problems focus on the equations of a surface and a curve and on questions related to the intersection of three surfaces. The text lists other problems such as the equation of a plane, the direction-vector of a straight line, and miscellaneous problems pertaining to the equations of a plane, of a straight line, and of a sphere in a direction-vector. The selection is useful for professors in analytical geometry and for other courses in physic-mathematics and general engineering.

Introductory Statistics

1st Edition
May 17, 2014
M.H. Quenouille
English
eBook
9 7 8 1 4 8 3 1 4 0 3 8 4

Introductory Statistics is an elementary non-mathematical manual on statistics and provides a connected account of the more common statistical tests. It is divided into two parts: the first part introduces the reader to elementary applications of statistical methods and the line of reasoning involved in their use, and the second part covers elementary parts of statistical theory and more advanced applications. This book consists of nine chapters and opens with a discussion on the presentation of sets of measurements, touching on topics such as sampling, grouping, measures of spread, and standard deviation. The following chapters deal with normal distribution and its applications; comparison of two or several sets of measurements; attributes and comparison of proportions; and interrelations of sets of measurements. Concomitant observations are also considered, along with transformations and non-normal distributions. The final chapter is devoted to sampling methods, including the ratio method and the regression method. This monograph is written primarily for students of statistics and aims to help research workers gain a fuller understanding of the methods used in the analysis of their results.

Resolution of Singularities of Embedded Algebraic Surfaces

1st Edition
Volume 24
January 1, 1966
Shreeram Shankar Abhyankar
English
eBook
9 7 8 0 0 8 0 8 7 3 3 6 7

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Books in Mathematics and applied mathematics

The Number Systems and Operations of Arithmetic

Lambda-Matrices and Vibrating Systems

The Theory of Jets in an Ideal Fluid

Model Answers in Pure Mathematics for A-Level Students

Problems and Methods in Analysis

Elementary Analysis

A Collection of Problems in Analytical Geometry

A Collection of Problems in Analytical Geometry

Introductory Statistics

Resolution of Singularities of Embedded Algebraic Surfaces

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