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Books in Physical sciences and engineering

A Course of Higher Mathematics
International Series of Monographs In: Pure and Applied Mathematics, Volume 3, Part 1
1st Edition
V. I. Smirnov
I. N. Sneddon + 2 more
English
International Series of Monographs in Pure and Applied Mathematics, Volume 59: A Course of Higher Mathematics, III/I: Linear Algebra focuses on algebraic methods. The book first ponders on the properties of determinants and solution of systems of equations. The text then gives emphasis to linear transformations and quadratic forms. Topics include coordinate transformations in three-dimensional space; covariant and contravariant affine vectors; unitary and orthogonal transformations; and basic matrix calculus. The selection also focuses on basic theory of groups and linear representations of groups. Representation of a group by linear transformations; linear representations of the unitary group in two variables; linear representations of the rotation group; and Abelian groups and representations of the first degree are discussed. Other considerations include integration over groups, Lorentz transformations, permutations, and classes and normal subgroups. The text is a vital source of information for students, mathematicians, and physicists.
A Collection of Problems in Analytical Geometry
Analytical Geometry in the Plane
1st Edition
D. V. Kletenik
W. J. Langford + 1 more
English
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.
Mathematics with Understanding
The Commonwealth and International Library: Mathematical Topics, Volume 1
1st Edition
Harold Fletcher + 1 more
C. Plumtpon
English
Mathematical Topics: Mathematics with Understanding, Book 1 focuses on the approaches in teaching mathematics. The book first offers information on the aims of modern approaches in teaching mathematics. The text discusses the language of sets. Set notation, empty, disjoint, and universal sets; union and intersection of two sets; Venn diagrams; and complements of sets are clarified. The selection also reviews relations and sorting, including equivalence relations, equivalent sets, partitioning sets, and number games. Recording of numbers and use of different bases are also discussed. Topics include multiplication in different bases, decomposition, equal addition, bicimals, and operations using bases other than 10. The text also focuses on open sentences, number facts, and pictorial representations. The number line, collection of data, bar charts, block graphs, pi graphs, tally charts, and line graphs are discussed. The book also takes a look at the processes of addition, subtraction, multiplication, and division. The selection is a reliable reference for readers interested in mathematics.
The Iron Blast Furnace
Theory and Practice
1st Edition
J. G. Peacey + 1 more
D. W. Hopkins
English
The Iron Blast Furnace: Theory and Practice presents theoretical, experimental, and operational evidence about the iron blast furnace as well as a mathematical description of its operation. This book includes a set of equations that accurately describe stoichiometric and enthalpy balances for the process and which are consistent with observed temperatures and compositions in the furnace stack. These equations, which have been devised on the basis of the Rist approach, show the effects of altering any blast-furnace variable on the other operating requirements of the process. This monograph is comprised of 14 chapters and begins with a brief description of the blast-furnace process. The next chapter takes a look inside the furnace, paying particular attention to its behavior in front of the tuyères and the kinetics of the coke gasification reaction. The reader is then introduced to the thermodynamics and stoichiometry of the blast-furnace process; enthalpy balance for the bottom segment of the furnace; the effects of tuyères injectants on blast-furnace operations; and blast-furnace optimization by linear programming. A number of important variables covered by the equations are discussed, including hydrocarbon injection at the tuyères, oxygen enrichment of the blast, moisture, limestone decomposition, coke reactivity, and metalloid reduction. The effects of many of these variables are illustrated numerically in the text while others are demonstrated in sets of problems that follow each chapter. This text will be a valuable resource for metallurgists and materials scientists.
Arithmetic Applied Mathematics
International Series in Nonlinear Mathematics: Theory, Methods and Applications
1st Edition
Donald Greenspan
V. Lakshmikantham + 1 more
English
Arithmetic Applied Mathematics deals with the deterministic theories of particle mechanics using a computer approach. Models of classical physical phenomena are formulated from both Newtonian and special relativistic mechanics with the aid only of arithmetic. The computational power of modern digital computers is highlighted, along with simple models of complex physical phenomena and solvable dynamical equations for both linear and nonlinear behavior. This book is comprised of nine chapters and opens by describing an experiment with gravity, followed by a discussion on the two basic types of forces that are important in classical physical modeling: long range forces and short range forces. Gravitation and molecular attraction and repulsion are considered, along with the basic concepts of position, velocity, and acceleration. The reader is then introduced to the N-body problem; conservative and non-conservative models of complex physical phenomena; foundational concepts of special relativity; and arithmetic special relativistic mechanics in one space dimension and three space dimensions. The final chapter is devoted to Lorentz invariant computations, with emphasis on the arithmetic modeling and analysis of a harmonic oscillator. This monograph will be of interest to mathematicians, physicists, and computer scientists.
Programming in GW-BASIC
1st Edition
P. K. McBride
English
Programming in GW-BASIC provides a reference guide on GW-Basic along with a range of extra commands and functions. The book discusses starting a program, program planning and the essentials of GW-Basic, including the most commonly used commands; how data is stored in memory; how a program fits together; and the use of the keyboard and screen in editing. The text also describes graphics and color and the string-handling functions. The principles and concepts of program structures, such as the Paintbox program and chaining, and the use of the Turtle graphics, such as Logo and DRAW, are also considered. The book covers two of the key techniques for handling data in quantity (sorting into order and searching for specific items), statistical analysis, and display program. The text then tackles PEEK and POKE, which examine sections of memory and serve as alternative to PRINT for creating screen displays, and advanced graphics, which enables one to analyze the screen, develop first a double-size print utility, then a sprite designer and some movement routines. The selection is useful to computer programmers and students taking computer courses.
Introduction to Dynamic Programming
International Series in Modern Applied Mathematics and Computer Science, Volume 1
1st Edition
Leon Cooper + 1 more
E. Y. Rodin
English
Introduction to Dynamic Programming introduces the reader to dynamic programming and presents the underlying mathematical ideas and results, as well as the application of these ideas to various problem areas. A large number of solved practical problems and computational examples are included to clarify the way dynamic programming is used to solve problems. A consistent notation is applied throughout the text for the expression of quantities such as state variables and decision variables. This monograph consists of 10 chapters and opens with an overview of dynamic programming as a particular approach to optimization, along with the basic components of any mathematical optimization model. The following chapters discuss the application of dynamic programming to variational problems; functional equations and the principle of optimality; reduction of state dimensionality and approximations; and stochastic processes and the calculus of variations. The final chapter looks at several actual applications of dynamic programming to practical problems, such as animal feedlot optimization and optimal scheduling of excess cash investment. This book should be suitable for self-study or for use as a text in a one-semester course on dynamic programming at the senior or first-year, graduate level for students of mathematics, statistics, operations research, economics, business, industrial engineering, or other engineering fields.
Programming—ALGOL
1st Edition
D. J. Malcolme-Lawes
English
Programming—ALGOL is an instructional book on how to write programs using the Algol language. The book starts with an introduction to computers. The Algol language, which runs on instructions typed or punched on strips of paper by the flexowriter, is explained. The text also compares the instructions used in Algol with words in the English language. The command instructions, calculation of numbers, and printing the output are discussed. After a brief introduction into what a program is, the book gives other commands to be added and improve the program. A sample program for repeating calculations is shown with different variables inputted to the program, and then arranging these for the output. The text then introduces the label and the block parts of the program, especially in procedures when several similar sets of commands are required. After the Algol syntax is explained, the different techniques used in programming are considered. In getting a problem into a form and making translation to Algol easier, the flow diagram is introduced. The process of actually running the program by compiling it, using data and program tapes, then begins. The text makes for interesting reading for computer programming instructors, students of introductory programing, and for readers who are interested in the history of computer programming.
Computing Methods in Crystallography
1st Edition
J. S. Rollett
English
Computing Methods in Crystallography is a collection of lectures delivered at a Summer School, held in Oxford in August 1962. The book presents the underlying mathematics and computing methods in crystallography. The text covers topics on the algebra required for the fundamental operations of transformation of coordinates, interpolation, approximation of trigonometric and exponential functions, solution of linear equations and derivation of latent roots and vectors; methods for calculation of structure factors, least-squares adjustment, and Fourier series evaluation; the theory and practice of intensity scaling and symmetry determination; and methods of direct phase determination. Crystallographers, physicists, and students in allied fields will find the book very useful.
Cartesian Tensors in Engineering Science
The Commonwealth and International Library: Structures and Solid Body Mechanics Division
1st Edition
L. G. Jaeger
B. G. Neal
English
Cartesian Tensors in Engineering Science provides a comprehensive discussion of Cartesian tensors. The engineer, when working in three dimensions, often comes across quantities which have nine components. Variation of the components in a given plane may be shown graphically by a familiar construction called Mohr's circle. For such quantities it is always possible to find three mutually perpendicular axes, called principal axes, with respect to which the six ""paired up"" components are all zero. Such quantities are called symmetric tensors of the second order. The student may at this stage be struck by the fact that the physical quantities with which he normally deals have either one component, three components or nine components, being respectively scalars, vectors, and what have just been called second order tensors. The family of quantities having 1, 3, 9, 27, … components does exist. It is the tensor family in three dimensions. The book discusses the ""tests"" a given quantity must pass in order to qualify as a member of the family. The products of tensors, elasticity, and second moment of area and moment of inertia are also covered. Although written primarily for engineers, it is hoped that students of various branches of physical science may find this book useful.

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