Skip to main content

Academic Press

A First Course in Linear Algebra
1st Edition
May 12, 2014
Daniel Zelinsky
Samuel S. Saslaw
English
A First Course in Linear Algebra provides an introduction to the algebra and geometry of vectors, matrices, and linear transformations. This book is designed as a background for second-year courses in calculus of several variables and differential equations where the theory of linear differential equations parallels that of linear algebraic equations. The topics discussed include the multiplication of vectors by scalars, vectors in n-space, planes and lines, and composites of linear mappings. The symmetric matrices and mappings, quadratic forms, change of coordinates, and effect of change of basis on matrices of linear functions are also described. This text likewise considers the computation of determinants, diagonalizable transformations, computation of eigenvalues and eigenvectors, and principal axis theorem. This publication is suitable for college students taking a course in linear algebra.
An Introduction to Numerical Mathematics
1st Edition
May 12, 2014
Eduard L. Stiefel
English
An Introduction to Numerical Mathematics provides information pertinent to the fundamental aspects of numerical mathematics. This book covers a variety of topics, including linear programming, linear and nonlinear algebra, polynomials, numerical differentiation, and approximations. Organized into seven chapters, this book begins with an overview of the solution of linear problems wherein numerical mathematics provides very effective algorithms consisting of finitely many computational steps. This text then examines the method for the direct solution of a definite problem. Other chapters consider the determination of frequencies in freely oscillating mechanical or electrical systems. This book discusses as well eigenvalue problems for oscillatory systems of finitely many degrees of freedom, which can be reduced to algebraic equations. The final chapter deals with the approximate representation of a function f(x) given by I-values as in the form of a table. This book is a valuable resource for physicists, mathematicians, theoreticians, engineers, and research workers.
Paired-Associates Learning
The Role of Meaningfulness, Similarity, and Familiarization
1st Edition
May 12, 2014
Albert E. Goss + 1 more
English
Paired-Associates Learning: The Role of Meaningfulness, Similarity, and Familiarization focuses on the role of meaningfulness, similarity, and familiarization of stimuli in paired-associates (PA) learning. The book illustrates the problems, methods, findings, and theoretical implications of research findings. The book first offers information on scalings of meaningfulness, theoretical analyses, and meaningfulness in PA learning. Discussions focus on rationale and general objectives, designs of experiments, techniques, construction and use of lists, and overview and specific analyses. The text then examines similarity and familiarization, including scalings, effects of similarity on acquisition and backward recall, familiarization and transfer, and effects of familiarization. The manuscript ponders on meaning and association and summary, significance, and suggestions. Topics include theoretical analyses and significance of empirical findings and conclusions, acquired-distinctive... training, number of and associations among elements, induction of meaning and meaningfulness, and response-mediated associations. The publication is a dependable reference for researchers interested in paired-associates learning.
Algebraic Methods of Mathematical Logic
1st Edition
May 12, 2014
Ladislav Rieger
English
Algebraic Methods of Mathematical Logic focuses on the algebraic methods of mathematical logic, including Boolean algebra, mathematical language, and arithmetization. The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-math... parallelism and its natural limits; practical applications of methods of mathematical logic; and principal mathematical tools of mathematical logic. The text then elaborates on the language of mathematics and its symbolization and recursive construction of the relation of consequence. Discussions focus on recursive construction of the relation of consequence, fundamental descriptively-semant... rules, mathematical logic and mathematical language as a material system of signs, and the substance and purpose of symbolization of mathematical language. The publication examines expressive possibilities of symbolization; intuitive and mathematical notions of an idealized axiomatic mathematical theory; and the algebraic theory of elementary predicate logic. Topics include the notion of Boolean algebra based on joins, meets, and complementation, logical frame of a language and mathematical theory, and arithmetization and algebraization. The manuscript is a valuable reference for mathematicians and researchers interested in the algebraic methods of mathematical logic.
Robustness in Statistics
1st Edition
May 12, 2014
Robert L. Launer + 1 more
English
Robustness in Statistics contains the proceedings of a Workshop on Robustness in Statistics held on April 11-12, 1978, at the Army Research Office in Research Triangle Park, North Carolina. The papers review the state of the art in statistical robustness and cover topics ranging from robust estimation to the robustness of residual displays and robust smoothing. The application of robust regression to trajectory data reduction is also discussed. Comprised of 14 chapters, this book begins with an introduction to robust estimation, paying particular attention to iteration schemes and error structure of estimators. Sensitivity and influence curves as well as their connection with jackknife estimates are described. The reader is then introduced to a simple analog of trimmed means that can be used for studying residuals from a robust point-of-view; a class of robust estimators (called P-estimators) based on the location and scale-invariant Pitman estimators of location; and robust estimation in the presence of outliers. Subsequent chapters deal with robust regression and its use to reduce trajectory data; tests for censoring of extreme values, especially when population distributions are incompletely defined; and robust estimation for time series autoregressions. This monograph should be of interest to mathematicians and statisticians.
Elementary Differential Geometry
1st Edition
May 12, 2014
Barrett O'Neill
English
Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.
Protein and Amino Acid Requirements of Mammals
1st Edition
May 12, 2014
Anthony A. Albanese
English
Protein and Amino Acid Requirements of Mammals focuses on the determination of the protein and amino acid requirements of various mammals, including man in particular. The selection first offers information on some species and age differences in amino acid requirements and the methods of measuring the nutritive value of protein hydrolysates and amino acid mixtures. Discussions focus on assay methods based on protein regeneration; specificity of amino acid requirements; amino acid requirements for nitrogen equilibrium in the adult; and composition of tissue proteins and amino acid requirements for growth. The text then examines the laboratory evaluation of amino acid mixtures and protein hydrolysates and dietary proteins and synthesis of tissue proteins. Topics include role of dietary proteins in the hypertrophy of gonads, effect of dietary proteins on repletion of liver proteins, and effect of dietary proteins on the synthesis of plasma proteins. The publication examines the protein and amino acid requirements of man, including qualitative amino acid requirements of various species, growth and protein and amino acid needs, and metabolic interactions of essential and nonessential amino acids. The selection is a dependable reference for researchers interested in the determination of the protein and amino acid requirements of mammals, including man.
Topology
Volume II
1st Edition
May 12, 2014
K. Kuratowski
English
Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the topology of the plane. Comprised of seven chapters, this volume begins with a discussion on the compactness of a topological space, paying particular attention to Borel, Lebesgue, Riesz, Cantor, and Bolzano-Weierstrass conditions. Semi-continuity and topics in dimension theory are also considered. The reader is then introduced to the connectedness of a space, with emphasis on the general properties and monotone mappings of connected spaces; local connectedness of a topological space; absolute retracts and contractible spaces; and general properties of commutative groups. Qualitative problems related to polygonal arcs are also examined, together with cohomotopic multiplication and duality theorems. The final chapter is devoted to the topology of a plane and evaluates the concept of the Janiszewski space. This monograph will be helpful to students and practitioners of algebra and mathematics.
A Second Course in Calculus
1st Edition
May 12, 2014
Harley Flanders + 2 more
English
This text, designed for a second year calculus course, can follow any standard first year course in one-variable calculus. Its purpose is to cover the material most useful at this level, to maintain a balance between theory and practice, and to develop techniques and problem solving skills. The topics fall into several categories: Infinite series and integrals Chapter 1 covers convergence and divergence of series and integrals. It ?ontains proofs of basic convergence tests, relations between series and Integrals, and manipulation with geometric, exponential, and related series. Chapter 2 covers approximation of functions by Taylor polynomials, with emphasis on numerical approximations and estimates of remainders. Chapt~r 3 deals with power series, including intervals of convergence, expanSIOns of functions, and uniform convergence. It features calculations with s~ries by algebraic operations, substitution, and term-by-term differentiation and integration. Vector methods Vector algebra is introduced in Chapter 4 and applied to solid analytic geometry. The calculus of one-variable vector functions and its applications to space curves and particle mechanics comprise Chapter 5. Linear algebra Chapter 7 contains a practical introduction to linear algebra in two and three dimensions. We do not attempt a complete treatment of foundations, but rather limit ourselves to thoRe topics that have immediate application to calculus. The main topics are linear transformations in R2 and R3, their matrix representations, manipulation with matrices, linear systems, quadratic forms, and quadric surfaces. Differential calculus of several variables Chapter 6 contains preliminary material on sets in the plane and space, and the definition and basic properties of continuous functions. This is followed by partial derivatives with applications to maxima and minima. Chapter 8 continues with a careful treatment of differentiability and applications to tangent planes, gradients, directional derivatives, and differentials. Here ideas from linear algebra are used judiciously. Chapter 9 covers higher xii Preface order partial derivatives, Taylor polynomials, and second derivative tests for extrema. Multiple integrals In Chapters 10 and 11 we treat double and triple integrals intuitively, with emphasis on iteration, geometric and physical applications, and coordinate changes. In Chapter 12 we develop the theory of the Riemann integral starting with step functions. We continue with Jacobians and the change of variable formula, surface area, and Green's Theorem. Differential equations Chapter 13 contains an elementary treatment of first order equations, with emphasis on linear equations, approximate solutions, and applications. Chapter 14 covers second order linear equations and first order linear systems, including matrix series solutions. These chapters can be taken up any time after Chapter 7. Complex analysis The final chapter moves quickly through basic complex algebra to complex power series, shortcuts using' the complex exponential function, and applications to integration and differential equations. Features The key points of one-variable calculus are reviewed briefly as needed. Optional topics are scattered throughout, for example Stirling's Formula, characteristic roots and vectors, Lagrange multipliers, and Simpson's Rule for double integrals. Numerous worked examples teach practical skills and demonstrate the utility of the theory. We emphaRize Rimple line drawingR that a student can learn to do himself.
Amino Acids, Proteins and Cancer Biochemistry
1st Edition
May 12, 2014
Jesse P. Greenstein
John T. Edsall
English
Amino Acids, Proteins, and Cancer Biochemistry focuses on the contributions of Jesse P. Greenstein to biological chemistry, including kinetics, protein mixtures, metabolism, tumors, and biosynthesis. The selection first offers information on quantitative nutritional and in vivo metabolic studies with water-soluble, chemically defined diets and internal hydrogen bonding in ribonuclease. Discussions focus on the effects of deuterium on transition temperature, kinetics of deuterium-hydrogen exchange, applications of chemically denned diets, formulation of water-soluble, chemically defined diets, and large-scale preparation of optically pure amino acids. The manuscript then examines the chromatographic evaluation of protein mixtures and observations on the activation of amino acids and biosynthesis of peptide bonds, including synthesis of phenylacetylglutamin... and benzoylglycine, studies on amino acyl adenylates, and synthesis of glutamine. The publication ponders on free amino acids and related substances in normal and neoplastic tissues; nucleic acids of normal tissues and tumors; and carbohydrate metabolism in ascites tumor and HeLa cells. Topics include carbohydrate metabolism of ascites tumor cells, comparative biochemistry of glycolysis, DNA and the genetic concept of cancer, and constancy of free amino acid patterns of tissues. The selection is a valuable source of data for biochemists and researchers interested in amino acids, proteins, and cancer biochemistry.

Browse by Publisher