Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms. Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of algebraic notation and practical manipulative skills such as factoring, using exponents and radicals, and simplifying rational expressions is highlighted, along with the most common mistakes in algebra. The reader is then introduced to the solution of linear, quadratic, and other types of equations and systems of equations, as well as the solution of inequalities. Subsequent chapters deal with the most basic functions of algebra: polynomial, rational, exponential, and logarithm. The book concludes with a review of sequences, permutations and combinations, and the binomial theorem, as well as summation and mathematical induction. This monograph will be a useful resource for undergraduate students of mathematics and algebra.
This is the fifth volume of Dr. Justin Glenn’s comprehensive history that traces the “Presidential line” of the Washingtons. Volume One began with the immigrant John Washington, who settled in Westmoreland Co., Va., in 1657, married Anne Pope, and became the great-grandfather of President George Washington. It continued the record of their descendants for a total of seven generations. Volume Two highlighted notable family members in the next eight generations of John and Anne Washington’s descendants, including such luminaries as General George S. Patton, the author Shelby Foote, and the actor Lee Marvin. Volume Three traced the ancestry of the early Virginia members of this “Presidential Branch” back in time to the aristocracy and nobility of England and continental Europe. Volume Four resumed the family history where Volume One ended, and it contained Generation Eight of the immigrant John Washington’s descendants. Volume Five now presents Generation Nine, including more than 10,000 descendants. Future volumes will trace generations ten through fifteen, making a total of over 63,000 descendants. Although structured in a genealogical format for the sake of clarity, this is no bare bones genealogy but a true family history with over 1,200 detailed biographical narratives. These in turn strive to convey the greatness of the family that produced not only The Father of His Country but many others, great and humble, who struggled to build that country. ADVANCE PRAISE “I am convinced that your work will be of wide interest to historians and academics as well as members of the Washington family itself. Although the surname Washington is perhaps the best known in American history and much has been written about the Washington family for well over a century, it is surprising that no comprehensive family history has been published. Justin M. Glenn’s The Washingtons: A Family History finally fills this void for the branch to which General and President George Washington belonged, identifying some 63,000 descendants. This is truly a family history, not a mere tabulation of names and dates, providing biographical accounts of many of the descendants of John Washington who settled in Westmoreland County, Virginia, in 1657. . . . Each individual section is followed by extensive listings of published and manuscript sources supporting the information presented and errors of identification in previous publications are commented upon as appropriate.” John Frederick Dorman, editor of The Virginia Genealogist (1957-2006) and author of Adventurers of Purse and Person “Decades of reviewing Civil War books have left me surprised and delighted when someone applies exhaustive diligence to a topic not readily accessible. Dr. Glenn surely meets that standard with the meticulous research that unveils the Washington family in gratifying detail—many of them Confederates of interest and importance.” Robert K. Krick, author of The Smoothbore Volley that Doomed the Confederacy and Stonewall Jackson at Cedar Mountain
Calculus with Analytic Geometry presents the essentials of calculus with analytic geometry. The emphasis is on how to set up and solve calculus problems, that is, how to apply calculus. The initial approach to each topic is intuitive, numerical, and motivated by examples, with theory kept to a bare minimum. Later, after much experience in the use of the topic, an appropriate amount of theory is presented. Comprised of 18 chapters, this book begins with a review of some basic pre-calculus algebra and analytic geometry, paying particular attention to functions and graphs. The reader is then introduced to derivatives and applications of differentiation; exponential and trigonometric functions; and techniques and applications of integration. Subsequent chapters deal with inverse functions, plane analytic geometry, and approximation as well as convergence, and power series. In addition, the book considers space geometry and vectors; vector functions and curves; higher partials and applications; and double and multiple integrals. This monograph will be a useful resource for undergraduate students of mathematics and algebra.
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.
Algebra and Trigonometry presents the essentials of algebra and trigonometry with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered. Comprised of 11 chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of algebraic notation and practical manipulative skills such as factoring, using exponents and radicals, and simplifying rational expressions is highlighted, along with the most common mistakes in algebra. The reader is then introduced to the solution of linear, quadratic, and other types of equations and systems of equations, as well as the solution of inequalities. Subsequent chapters deal with the most basic functions: polynomial, rational, exponential, logarithm, and trigonometric. Trigonometry and the inverse trigonometric functions and identities are also presented. The book concludes with a review of progressions, permutations, combinations, and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.
Introductory College Mathematics: With Linear Algebra and Finite Mathematics is an introduction to college mathematics, with emphasis on linear algebra and finite mathematics. It aims to provide a working knowledge of basic functions (polynomial, rational, exponential, logarithmic, and trigonometric); graphing techniques and the numerical aspects and applications of functions; two- and three-dimensional vector methods; the fundamental ideas of linear algebra; and complex numbers, elementary combinatorics, the binomial theorem, and mathematical induction. Comprised of 15 chapters, this book begins with a discussion on functions and graphs, paying particular attention to quantities measured in the real number system. The next chapter deals with linear and quadratic functions as well as some of their applications. Tips on graphing are offered. Subsequent chapters focus on polynomial functions, along with graphs of factored polynomials; rational functions; exponential and logarithm functions; and trigonometric functions. Identities and inverse functions, vectors and matrices, and trigonometry are also explored, together with complex numbers, linear transformations, and the geometry of space. The book concludes by considering finite mathematics, with particular reference to mathematical induction and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.
John Murtagh’s General Practice is the gold standard reference for established doctors and new graduates and students in the fields of general practice and primary health care.This new edition is completely revised and expanded, including •New diagnostic strategies for common presenting problems •Significant updates on sexual health and cervical cancer screening •Updated information on mental health diagnosis and treatment This seventh edition builds on its influential legacy and has been thoroughly updated by the experienced author team, including new authors who bring a new generation of knowledge and diagnostic expertise to this authoritative title.
This book is the definitive and most comprehensive guide to modeling derivatives in C++ today. Providing readers with not only the theory and math behind the models, as well as the fundamental concepts of financial engineering, but also actual robust object-oriented C++ code, this is a practical introduction to the most important derivative models used in practice today, including equity (standard and exotics including barrier, lookback, and Asian) and fixed income (bonds, caps, swaptions, swaps, credit) derivatives. The book provides complete C++ implementations for many of the most important derivatives and interest rate pricing models used on Wall Street including Hull-White, BDT, CIR, HJM, and LIBOR Market Model. London illustrates the practical and efficient implementations of these models in real-world situations and discusses the mathematical underpinnings and derivation of the models in a detailed yet accessible manner illustrated by many examples with numerical data as well as real market data. A companion CD contains quantitative libraries, tools, applications, and resources that will be of value to those doing quantitative programming and analysis in C++. Filled with practical advice and helpful tools, Modeling Derivatives in C++ will help readers succeed in understanding and implementing C++ when modeling all types of derivatives.
This is the fifth volume of Dr. Justin Glenn’s comprehensive history that traces the “Presidential line” of the Washingtons. Volume One began with the immigrant John Washington, who settled in Westmoreland Co., Va., in 1657, married Anne Pope, and became the great-grandfather of President George Washington. It continued the record of their descendants for a total of seven generations. Volume Two highlighted notable family members in the next eight generations of John and Anne Washington’s descendants, including such luminaries as General George S. Patton, the author Shelby Foote, and the actor Lee Marvin. Volume Three traced the ancestry of the early Virginia members of this “Presidential Branch” back in time to the aristocracy and nobility of England and continental Europe. Volume Four resumed the family history where Volume One ended, and it contained Generation Eight of the immigrant John Washington’s descendants. Volume Five now presents Generation Nine, including more than 10,000 descendants. Future volumes will trace generations ten through fifteen, making a total of over 63,000 descendants. Although structured in a genealogical format for the sake of clarity, this is no bare bones genealogy but a true family history with over 1,200 detailed biographical narratives. These in turn strive to convey the greatness of the family that produced not only The Father of His Country but many others, great and humble, who struggled to build that country. ADVANCE PRAISE “I am convinced that your work will be of wide interest to historians and academics as well as members of the Washington family itself. Although the surname Washington is perhaps the best known in American history and much has been written about the Washington family for well over a century, it is surprising that no comprehensive family history has been published. Justin M. Glenn’s The Washingtons: A Family History finally fills this void for the branch to which General and President George Washington belonged, identifying some 63,000 descendants. This is truly a family history, not a mere tabulation of names and dates, providing biographical accounts of many of the descendants of John Washington who settled in Westmoreland County, Virginia, in 1657. . . . Each individual section is followed by extensive listings of published and manuscript sources supporting the information presented and errors of identification in previous publications are commented upon as appropriate.” John Frederick Dorman, editor of The Virginia Genealogist (1957-2006) and author of Adventurers of Purse and Person “Decades of reviewing Civil War books have left me surprised and delighted when someone applies exhaustive diligence to a topic not readily accessible. Dr. Glenn surely meets that standard with the meticulous research that unveils the Washington family in gratifying detail—many of them Confederates of interest and importance.” Robert K. Krick, author of The Smoothbore Volley that Doomed the Confederacy and Stonewall Jackson at Cedar Mountain
Ligand binding by macromolecules represents a core event of broad relevance to a range of systems, including catalytic systems alongside noncatalytic systems such as nucleic acid binding by transcription factors or extracellular ligand binding by proteins involved in signaling pathways. The scope of this primer is constrained to introduce only foundational models without significant discussion of more advanced topics such as allosteric or linkage effects. Linkage occurs when the binding of a ligand is influenced by the binding of another molecule of the same ligand (homotropic linkage), the binding of a different ligand (heterotropic linkage), physical variables such as temperature or pressure (physical linkage), or changes in macromolecular assembly state (polysteric linkage). Taking this into account, the foundational themes presented in this primer can be used to describe any macromolecule–ligand interaction either by direct use of the models and techniques described here or by applying them to develop more advanced models to explain additional complexities such as those allosteric or linkage effects just mentioned. The target audience of this primer is the senior undergraduate or junior graduate student who lacks a foundation in ligand-binding thermodynamics. As such, we have focused primarily on foundational thermodynamic treatments and presented only general discussions of relevant experimental designs. Readers of this primer will learn how to build a working understanding of common factors that promote energetic favorability for ligand binding; develop a functional toolbox to understand ligand binding from the perspective of collecting, plotting, and interpreting ligand-binding data; enhance proficiency in deriving thermodynamic mechanisms for ligand binding; and become comfortable in interpreting binding data reported in the literature and independently expanding knowledge beyond the scope introduced in this primer.
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