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Contents: Adapting Courant-Friedrichs-Levy to the 1980's; Parametrization Methods for Approximation of Solutions of Elliptic Boundary Value Problems; Two Mixed Finite Element Methods for the Simply Supported Plat Problem; Approximation of Non-linear Problems; Two-dimensional Approximations of Three-dimensional Models in Nonlinear Plate Theory; Changing Meshes in Time-dependent Problems; Alternating-direction Galerkin Methods for Parabolic Hyperbolic and Sobolev Partial Differential Equations; Galerkin Methods for Miscible Displacement Problems with Point Sources and Sinks-Unit Mobility Ratio Case; Overtaking of Shock Waves in Steady Two-dimensional Supersonic Flows; Homogenization, Convex Analysis, and the Geometry Optimization of Engineering Structures; Stability and Error Bounds for a Fractional Step Scheme to Compute Weak Solutions of the Nonlinear Waterhammer Problem; Schauder Estimates for Finite Element Approximations of Second Order Elliptic Boundary Value Problems; Analysis of Some Contact Problems in Nonlinear Elasticity; Single Step Methods for Linear Differential Equations in Banach Spaces; The Quasi-optimality in the Maximum Norm of the H1 Projection into Piecewise Linear Functions in the Plane: a Complete Proof (Second lecture); A Brief Survey of Parabolic Smoothing and How It Affects a Numerical Solution: Finite Differences and Finite Elements (Third lecture); Integral Equation Methods for Mixed Boundary Value Problems (Second lecture).

This effort studied a proposed numerical method for finding elliptic solutions of the Monge-Ampere equations, in the context of hydrodynamic and antenna design applications. Some computational experiments were performed on representative model problems. A theoretical estimate for the convergence rate of one part of the scheme was obtained. For the problem of reflector antenna design, the solvability of the corresponding linearized problem was demonstrated. A geometric interpretation of the solution was obtained which helps in understanding the problem.

Journal of Research of the National Bureau of Standards

Journal of Research of the National Bureau of Standards

Journal of Research of the National Bureau of Standards

We study a scalable, parallel mechanism for stochastic identification/control for problems constrained by PDEs with random input data. Several identification objectives are discussed that either minimize the expectation of a tracking cost functional or minimize the difference of desired statistical quantities in the appropriate $Lp$ norm, and the distributed parameters/control can both deterministic or stochastic. The modeling process may describe the solution in terms of high dimensional spaces, particularly in the case when the input data (coefficients, forcing terms, boundary conditions, geometry, etc) are affected by a large amount of uncertainty. For higher accuracy, the computer simulation must increase the number of random variables (dimensions), and expend more effort approximating the QoI in each individual dimension. We introduce a novel stochastic parameter identification algorithm that integrates an adjoint-based deterministic algorithm with the sparse grid stochastic collocation FEM approach. This allows for decoupled, moderately high dimensional, parameterized computations of the stochastic optimality system and optimal identification of statistical moments (mean value, variance, covariance, etc.) or even the whole probability distribution of system responses

We study a scalable, parallel mechanism for stochastic identification/control for problems constrained by PDEs with random input data. Several identification objectives are discussed that either minimize the expectation of a tracking cost functional or minimize the difference of desired statistical quantities in the appropriate $Lp$ norm, and the distributed parameters/control can both deterministic or stochastic. The modeling process may describe the solution in terms of high dimensional spaces, particularly in the case when the input data (coefficients, forcing terms, boundary conditions, geometry, etc) are affected by a large amount of uncertainty. For higher accuracy, the computer simulation must increase the number of random variables (dimensions), and expend more effort approximating the QoI in each individual dimension. We introduce a novel stochastic parameter identification algorithm that integrates an adjoint-based deterministic algorithm with the sparse grid stochastic collocation FEM approach. This allows for decoupled, moderately high dimensional, parameterized computations of the stochastic optimality system and optimal identification of statistical moments (mean value, variance, covariance, etc.) or even the whole probability distribution of system responses

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

The work in progress has included the result that, for a certain class of partial differential equations, nonlinearization will often not aid in stabilization. Partial results have been obtaining on the following two types of questions: (1) What sort of estimates can one obtain for solutions of nonlinear parabolic problems backward in time at a given time in terms of the solution at alter times? Also: (2) If a solution of a certain parabolic bundary value problem is known to exist for positive time, what are the possible behaviors as the time tends to zero? Other topics addressed include coefficient determination in hyperbolic-equations, quenching for wave equations, and positive solutions of a nonlinear elliptic equation in all of space. Two presentations will be given this summer on results to date. (Author)

The authors have studied a novel numerical solution approach to Monge Ampere type equations. The equations have important applications. In particular, the leading term in the balance equation in dynamic meteorology has the form (1) . In a more complicated form, an equation of this type appears in the von Karman system of equations for elasticity and also in inverse problems of geometric optics. It also turned out that recent progress in the study of fully nonlinear equations became possible after important properties of the equation (1) were discovered.

The authors have studied a novel numerical solution approach to Monge Ampere type equations. The equations have important applications. In particular, the leading term in the balance equation in dynamic meteorology has the form (1) . In a more complicated form, an equation of this type appears in the von Karman system of equations for elasticity and also in inverse problems of geometric optics. It also turned out that recent progress in the study of fully nonlinear equations became possible after important properties of the equation (1) were discovered.

This study involved investigation of numerical methods for the approximate solution of partial differential equations. Specifically, the following two topics were investigated: Spatial meshes that change with time; and Space-time finite elements. The work involved both theoretical investigations and computational experiments.

General differentiation formulas for successive derivatives of a function are obtained in terms of the values of the function at unequally spaced arguments and the corresponding distances between the successive arguments using Lagrangian polynomials of various degrees. The remainder term is also obtained. Tables of coefficients in the formulas for the first four derivatives are given in intervals of 0.01 for the special case where only one spacing at either and is different from the others, as is often encountered near a curved boundary, for different ratios of this spacing to the others.

Mathematical modeling and computer simulations are nowadays widely used tools to predict the behavior of problems in engineering and in the natural and social sciences. All such predictions are obtained by formulating mathematical models and then using computational methods to solve the corresponding problems. We use a probability theory approach for uncertainty quantification (UQ) since it is particularly well suited for SPDE models, and focus on the broad research areas of algorithmic development and numerical analysis for the discretization of systems of linear or nonlinear SPDEs, building upon and significantly extending our previous successful work. We conduct comprehensive theoretical and computational comparison of the efficiency, accuracy, and range of applicability of non-intrusive methods, such as stochastic collocation methods, and intrusive techniques, such as stochastic Galerkin methods, for solving SPDEs and for UQ applications. We extend the algorithmic and analysis advances wrought by these efforts to the even more challenging settings of optimal control and parameter identification problems for SPDEs. The parameter identification problem is especially important in the SPDE setting since it provides a very useful mechanism for determining statistical information about the input parameters from, e.g., measurements of output quantities. This effort builds on our previous work on adjoint and sensitivity-based methods for deterministic optimal control and parameter identification problems to develop similar methods for tracking statistical quantities of interest from the computational solutions of linear and nonlinear SPDEs driven by high-dimensional random inputs.

Mathematical modeling and computer simulations are nowadays widely used tools to predict the behavior of problems in engineering and in the natural and social sciences. All such predictions are obtained by formulating mathematical models and then using computational methods to solve the corresponding problems. We use a probability theory approach for uncertainty quantification (UQ) since it is particularly well suited for SPDE models, and focus on the broad research areas of algorithmic development and numerical analysis for the discretization of systems of linear or nonlinear SPDEs, building upon and significantly extending our previous successful work. We conduct comprehensive theoretical and computational comparison of the efficiency, accuracy, and range of applicability of non-intrusive methods, such as stochastic collocation methods, and intrusive techniques, such as stochastic Galerkin methods, for solving SPDEs and for UQ applications. We extend the algorithmic and analysis advances wrought by these efforts to the even more challenging settings of optimal control and parameter identification problems for SPDEs. The parameter identification problem is especially important in the SPDE setting since it provides a very useful mechanism for determining statistical information about the input parameters from, e.g., measurements of output quantities. This effort builds on our previous work on adjoint and sensitivity-based methods for deterministic optimal control and parameter identification problems to develop similar methods for tracking statistical quantities of interest from the computational solutions of linear and nonlinear SPDEs driven by high-dimensional random inputs.

Mathematical modeling and computer simulations are nowadays widely used tools to predict the behavior of problems in engineering and in the natural and social sciences. All such predictions are obtained by formulating mathematical models and then using computational methods to solve the corresponding problems. We use a probability theory approach for uncertainty quantification (UQ) since it is particularly well suited for SPDE models, and focus on the broad research areas of algorithmic development and numerical analysis for the discretization of systems of linear or nonlinear SPDEs, building upon and significantly extending our previous successful work. We conduct comprehensive theoretical and computational comparison of the efficiency, accuracy, and range of applicability of non-intrusive methods, such as stochastic collocation methods, and intrusive techniques, such as stochastic Galerkin methods, for solving SPDEs and for UQ applications. We extend the algorithmic and analysis advances wrought by these efforts to the even more challenging settings of optimal control and parameter identification problems for SPDEs. The parameter identification problem is especially important in the SPDE setting since it provides a very useful mechanism for determining statistical information about the input parameters from, e.g., measurements of output quantities. This effort builds on our previous work on adjoint and sensitivity-based methods for deterministic optimal control and parameter identification problems to develop similar methods for tracking statistical quantities of interest from the computational solutions of linear and nonlinear SPDEs driven by high-dimensional random inputs.

Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.

In the method of lines for solving certain kinds of boundary value problems in rectangular or trapezoidal regions one of the variables, say y, is discretized while the other variable x is left continuous. When suitable finite difference approximations are substituted for the partial derivatives with respect to y the differential equation is changed into a simultaneous system of ordinary differential equations in the variable x. The method used very little in the USA is used extensively in the Soviet Union and nearly all the literature on this subject is in Russian. The method has been tried in BRL and it seems to be a very useful one. This report does not pretend to be a monograph on the subject. It intends to be a practical guide to computations.

This text discusses the importance of boundary value problems for partial differential equations in modern technological theory. Although analytical methods are theoretically well-developed, they are often impractical due to complex computations and the lack of suitable formulas for real-world problems. Hence, engineers and scientists increasingly turn to approximate methods, which are divided into two groups: (a) methods yielding approximate analytical expressions (like the Ritz and Galerkin methods), and (b) numerical or graphical methods (like the method of differences), which provide numerical solutions but no analytical form. The second group, especially the method of differences, is more broadly applicable and less restricted by problem conditions, making it highly valuable in practice despite being relatively recent and not widely known among engineers. This volume aims to bridge that gap by presenting a structured account of these numerical methods, with explanations and examples, making it both a reference and a practical textbook. The primary focus is on solving boundary value problems for the Laplace equation, due to their significance, computational complexity, and the clarity with which they demonstrate the method of differences. The third edition includes updates, particularly on solving hyperbolic equations using the method of characteristics. Translated by Charles M. Stern

The numerical solution of stochastic partial differential equations (SPDE) presents challenges not encountered in the simulation of PDEs or SDEs. Indeed, the roughness of the noise in conjunction with nonlinearities in the drift typically make these equations particularly stiff. In practice, this means that it is tricky to construct, operate, and validate numerical methods for SPDEs. This is especially true if one is interested in path-dependent expected values, long-time simulations, or in the simulation of SPDEs whose solutions have constraints on their domains. To address these numerical issues, this paper introduces a Markov jump process approximation for SPDEs, which we refer to as the spectral random walk method (SPECTRWM). The accuracy and ergodicity of SPECTRWM are verified in the context of a heat and overdamped Langevin SPDE, respectively. We also apply the method to Burgers and KPZ SPDEs.

Research was undertaken on questions concerning the existence, uniqueness, continuous data dependence and numerical computations of solutions of various ill posed problems in partial differential equations. It was shown that a potential well theory is possible for certain hyperbolic problems in which a nonlinear boundary condition is prescribed and not possible in certain cases when the forcing term in the differential equation is singular. Several papers were accepted or submitted during this period. Examples of titles are: Inequalities between Dirichlet and Neumann eigenvalues, and A potential well theory for the heat equation with a nonlinear boundary condition. Keywords: Partial differential equations; Hyperbolic problems; Continuous data. (Author)

Research was undertaken on questions concerning the existence, uniqueness, continuous data dependence and numerical computations of solutions of various ill posed problems in partial differential equations. It was shown that a potential well theory is possible for certain hyperbolic problems in which a nonlinear boundary condition is prescribed and not possible in certain cases when the forcing term in the differential equation is singular. Several papers were accepted or submitted during this period. Examples of titles are: Inequalities between Dirichlet and Neumann eigenvalues, and A potential well theory for the heat equation with a nonlinear boundary condition. Keywords: Partial differential equations; Hyperbolic problems; Continuous data. (Author)

Research was undertaken on questions concerning the existence, uniqueness, continuous data dependence and numerical computations of solutions of various ill posed problems in partial differential equations. It was shown that a potential well theory is possible for certain hyperbolic problems in which a nonlinear boundary condition is prescribed and not possible in certain cases when the forcing term in the differential equation is singular. Several papers were accepted or submitted during this period. Examples of titles are: Inequalities between Dirichlet and Neumann eigenvalues, and A potential well theory for the heat equation with a nonlinear boundary condition. Keywords: Partial differential equations; Hyperbolic problems; Continuous data. (Author)

Research was undertaken on questions concerning the existence, uniqueness, continuous data dependence and numerical computations of solutions of various ill posed problems in partial differential equations. It was shown that a potential well theory is possible for certain hyperbolic problems in which a nonlinear boundary condition is prescribed and not possible in certain cases when the forcing term in the differential equation is singular. Several papers were accepted or submitted during this period. Examples of titles are: Inequalities between Dirichlet and Neumann eigenvalues, and A potential well theory for the heat equation with a nonlinear boundary condition. Keywords: Partial differential equations; Hyperbolic problems; Continuous data. (Author)

Research was undertaken on questions concerning the existence, uniqueness, continuous data dependence and numerical computations of solutions of various ill posed problems in partial differential equations. It was shown that a potential well theory is possible for certain hyperbolic problems in which a nonlinear boundary condition is prescribed and not possible in certain cases when the forcing term in the differential equation is singular. Several papers were accepted or submitted during this period. Examples of titles are: Inequalities between Dirichlet and Neumann eigenvalues, and A potential well theory for the heat equation with a nonlinear boundary condition. Keywords: Partial differential equations; Hyperbolic problems; Continuous data. (Author)

Research was undertaken on questions concerning the existence, uniqueness, continuous data dependence and numerical computations of solutions of various ill posed problems in partial differential equations. It was shown that a potential well theory is possible for certain hyperbolic problems in which a nonlinear boundary condition is prescribed and not possible in certain cases when the forcing term in the differential equation is singular. Several papers were accepted or submitted during this period. Examples of titles are: Inequalities between Dirichlet and Neumann eigenvalues, and A potential well theory for the heat equation with a nonlinear boundary condition. Keywords: Partial differential equations; Hyperbolic problems; Continuous data. (Author)

In this study, wave equations with initial boundary conditions have been studied. The general form of the wave equation has been derived. The first order and second order difference schemes were established for the presented IBVP. The stability of the difference schemes has been guaranteed. The approximation solution of the problem was achieved by using finite difference methods. Two different examples are provided. A comparison between the exact and approximation solution has been carried out. Absolute errors of the problem have been presented by using MATLAB software. Moreover, the comparison shows that the second order difference scheme is a more accurate result than the first order. It is shown that the results of the comparison guaranty the reliability and accuracy of the presented method.

The physical phenomena described by nonlinear partial differential equations have become at present the central theme of investigation by many researchers. A good understanding of most physical processes requires accounting for nonlinear effects and, consequently, methods for studying nonlinear equations have to be developed. Among nonlinear equations the Dirichlet problem for the Monge-Ampere equation is the model case for fully nonlinear equations.

This project is concerned with several questions conern ing the existence, uniqueness, continuous data dependence and numerical computation of solutions of various ill posed problems in partial differential equations. Several problems involving reaction diffusion equations with and without convection terms present were studied. In the latter case the ability of finite element approximate solutions to reproduce the continuous time dynamics was investigated. In the former case, a convective diffusion equation with a semilinear source in the boundary conditions was analyzed. A fairly complete picture of the dynamics was obtained. With the source term in the equation, computations revealed a rich structure which has been partially analyzed theoretically. Several problems for reaction diffusion equations in unbounded regimes were also investigated. It was shown that under certain conditions in the rate law all nonzero solutions blow up in finite time, while for other conditions in the rate law, solutions damp out. It was shown that a potential well theory is possible for certain hyperbolic problems in which a nonlinear boundary condition is prescribed and not possible in certain cases when forcing term in the differential equation is singular. Numerical experiments performed on the wave equation with a singular forcing term have down that when quenching occurs, the time and exact derivatives blow up in finite time. The nature of the blowup was studied computationally.

This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted linear combinations of the function values at discrete grid points on problem domain with the weights calculated via using three types of radial basis functions (RBFs) as test functions. The method in presence is robust, straight forward to apply, and highly accurate under the condition that the shape parameters of RBFs are well chosen. Numerical tests are provided to illustrate its validity and capability.

Synspade 1970. proc. 2nd Symp. on the Numerical Solution of Partial Differential Equations, Synspade 1970, at Univ Maryland, May 11-15, 1970

Synspade 1970. proc. 2nd Symp. on the Numerical Solution of Partial Differential Equations, Synspade 1970, at Univ Maryland, May 11-15, 1970

Synspade 1970. proc. 2nd Symp. on the Numerical Solution of Partial Differential Equations, Synspade 1970, at Univ Maryland, May 11-15, 1970

The report summarizes progress made in several, areas, including: estimates for finite element methods, numerical simulation of nonlinear dispersive waves, numerical models for plasticity, numerical methods for the transport equation, and computation of fluid-flow problems. (Author)

This Memorandum shows how to approximate a nonlinear partial differential integral equation by a system of ordinary differential equations. A table of necessary constants is provided, and the results of a test calculation on an equation of radiative transfer in a spherical shell are described.

This Memorandum shows how to approximate a nonlinear partial differential integral equation by a system of ordinary differential equations. A table of necessary constants is provided, and the results of a test calculation on an equation of radiative transfer in a spherical shell are described.

This Memorandum shows how to approximate a nonlinear partial differential integral equation by a system of ordinary differential equations. A table of necessary constants is provided, and the results of a test calculation on an equation of radiative transfer in a spherical shell are described.

This Memorandum shows how to approximate a nonlinear partial differential integral equation by a system of ordinary differential equations. A table of necessary constants is provided, and the results of a test calculation on an equation of radiative transfer in a spherical shell are described.

This project is concerned with several questions concerning the existence, uniqueness continuous data dependence and numerical computation of solutions of various ill posed problems in partial differential equations. Several problems involving reaction diffusion equations with and without convection terms present were studied. In the latter case the ability of finite element approximate solutions to reproduce the continuous time dynamics was investigated. In the former case a convective diffusion equation with a similar source in the boundary condition was analyzed. A fairly complete picture of the dynamics was obtained. With the source term in the equation, computations revealed a rich structure which has been partially analyzed theoretically. Several problems for reaction diffusion equations in unbounded regimes were also investigated. It was shown that under certain conditions in the rate law all nonzero solutions blow up in finite time, while for other conditions in the rate law, solutions damp out.

The physical phenomena described by nonlinear partial differential equations have become at present the central theme of investigations by many researchers. A good understanding of most physical processes requires accounting for nonlinear effects and, consequently, methods for studying nonlinear equations have to be developed. Among nonlinear equations the Dirichlet problem for the Monge-Ampere equation is the model case for fully nonlinear equations.

The physical phenomena described by nonlinear partial differential equations have become at present the central theme of investigations by many researchers. A good understanding of most physical processes requires accounting for nonlinear effects and, consequently, methods for studying nonlinear equations have to be developed. Among nonlinear equations the Dirichlet problem for the Monge-Ampere equation is the model case for fully nonlinear equations.

The physical phenomena described by nonlinear partial differential equations have become at present the central theme of investigations by many researchers. A good understanding of most physical processes requires accounting for nonlinear effects and, consequently, methods for studying nonlinear equations have to be developed. Among nonlinear equations the Dirichlet problem for the Monge-Ampere equation is the model case for fully nonlinear equations.

The basic ideas of the construction and use of numerically-generated boundary-fitted coordinate systems for the numerical solution of partial computation can be done on a fixed square grid in the rectangular transformed region regardless of the shape of movement of the physical boundaries. A number of different types of configurations for the transformed region and the basic transformation relations from a cartesian system to a general curvilinear system are given. The material of this paper is applicable to all types of coordinate system generation.

A new approach for the generation of flow-adaptive grids for numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numerical evaluation of any partial differential equation. The dynamic coupling of the grid with the flow solution is accomplished through a grid-optimization technique. The optimization is based on the minimization of the finite difference truncation error in the transformed plane. The method is tested on the one-dimensional Burgers' equation which is representative of typical fluid dynamics problems. Burgers' equation is solved with an optimized SOR (Successive Over Relaxation) method using upwind difference for the convective term. Results are presented for various Reynolds numbers and are compared to results from a similar adaptive grid method and to results for a static grid. They show the ability of the method to concentrate grid points high in gradient regions where large truncation errors occur. (Author)

Several problems relevant in the application of mechanics to real-world problems were treated. The work included theoretical analysis of solutions of partial differential equations, detailed studies of numerical techniques for approximately solving differential equations arising in mechanics, as well as actual numerical computations using such numerical schemes to model experimental phenomena. Application areas impacted by this research include heat conduction and fluid mechanics. Also closely related are problems arising in the study of controlled fusion. In addition, the work has added significantly to theoretical understanding of numerical methods for solving various partial differential equations. (Author)

Charlotte Turner Smith (1749 – 1806) was an English poet and novelist. She initiated a revival of the English sonnet, helped establish the conventions of Gothic fiction, and wrote political novels of sensibility.<br /><br />It was in 1784, in debtor's prison with her husband Benjamin, that she wrote and published her first work, Elegiac Sonnets. The work achieved instant success, allowing Charlotte to pay for their release from prison. Smith's sonnets helped initiate a revival of the form and granted an aura of respectability to her later novels.<br /><br />Stuart Curran, the editor of Smith's poems, has written that Smith is "the first poet in England whom in retrospect we would call Romantic". She helped shape the "patterns of thought and conventions of style" for the period. Romantic poet William Wordsworth was the most affected by her works. He said of Smith in the 1830s that she was "a lady to whom English verse is under greater obligations than are likely to be either acknowledged or remembered". By the second half of the nineteenth century, however, Smith was largely forgotten.

2Wealth of Nations, Book 1

By Adam Smith

An Inquiry into the Nature and Causes of the Wealth of Nations is the magnum opus of the Scottish economist Adam Smith, published on March 9, 1776 during the Scottish Enlightenment. It is a clearly written account of political economy at the dawn of the Industrial Revolution, and is widely considered to be the first modern work in the field of economics. (Summary from Wikipedia)

"How selfish soever man may be supposed, there are evidently some principles in his nature, which interest him in the fortunes of others, and render their happiness necessary to him, though he derives nothing from it, except the pleasure of seeing it." (from The Theory of Moral Sentiments)<br><br>Adam Smith considered his first major book, The Theory of Moral Sentiments, his most important work. Indeed, the tome was a wild success upon its publication, selling out immediately. It has not lost popularity since. In this legendary work, Smith discusses the nature of morality, and the motives behind and origins of these "sentiments." Originally published in 1759, this work provides the philosophical underpinnings for his later works, as well as elucidating the psychological and moral foundations of the workings of a complex society. Smith parses many important concepts in this book, with the central questions perhaps being: Where do our moral principles come from? Are they divine and inborn, reflection of man-made laws, or rational, based on their usefulness to society? Smith's answers to these questions and more, and his explanation of how such sentiments, however derived, influence society's self-coordination, have interested lay and scholar alike for hundreds of years. (summary written by Nikki Sullivan)<br /><br /> note: This is the First edition, the 6th edition was revised and extra material added.

A story for children about a little bear with no name, “there were not enough names to go round,” and his adventures in finding one. (Summary by Carolyn Frances)

<i>The Fairy Ring</i>, originally published in 1910, is a collection of 63 fairy tales from around the globe. It includes such well-known favorites as "History of Jack the Giant-Killer", "The Frog Prince","Rumpel-stilts-ken", and "Snow-white and Rose-red", among many others. Children of all ages will enjoy these stories. (Summary by Paul Williams)

6Wealth of Nations, Book 2 and 3

By Adam Smith

An Inquiry into the Nature and Causes of the Wealth of Nations is the magnum opus of the Scottish economist Adam Smith, published on March 9, 1776 during the Scottish Enlightenment. It is a clearly written account of political economy at the dawn of the Industrial Revolution, and is widely considered to be the first modern work in the field of economics. (from Wikipedia)

7Masters of Space

By Edward Everett Evans and E. E. Smith

The Masters had ruled all space with an unconquerable iron fist. But the Masters were gone. And this new, young race who came now to take their place--could they hope to defeat the ancient Enemy of All? (Summary by Gutenberg)

8Wealth of Nations, Book 4

By Adam Smith

An Inquiry into the Nature and Causes of the Wealth of Nations is the magnum opus of the Scottish economist Adam Smith, published on March 9, 1776 during the Scottish Enlightenment. It is a clearly written account of political economy at the dawn of the Industrial Revolution, and is widely considered to be the first modern work in the field of economics. (from Wikipedia)

9Triplanetary

By E. E. Smith

“Doc” E.E. Smith pretty much invented the space opera genre, and Triplanetary is a good and well-known example. Physics, time, and politics never stand in the way of a plot that gallops ahead without letup. Having earned a PhD in chemical engineering, it’s understandable that the heroes of Smith’s story are all scientists. He didn’t want to be constrained by the limits of known science, however, so in his hands the electromagnetic spectrum becomes a raw material to be molded into ever-more amazing and lethal forms, and the speed of light is no bar to traveling through the interstellar void. Come enjoy this story of yesteryear, set in tomorrow, where real women ignite love at a glance, real men achieve in days what governments manage in decades, and aliens are an ever-present threat to Life-As-We-Know-It! (Summary by Mark F. Smith)

10Spacehounds of IPC

By E. E. Smith

When the Inter-Planetary Corporation's (IPC) crack liner “IPV Arcturus” took off on a routine flight to Mars, it turned out to be the beginning of a unexpected and long voyage. There had been too many reports of errors in ship's flight positions from the Check Stations and brilliant physicist Dr. Percival (“Steve”) Stevens is aboard the Arcturus on a fact-finding mission to find out what's really happening, and hopefully save the honor of the brave pilots of the space-liner Arcturus from the desk-jockeys' in the Check Stations implications of imprecision - the nastiest insult you could cast at a ships pilot. He and the pilots are right, it was the Check Stations that were out of position, not the ships. But that's cold consolation because before the Arcturus reaches Mars it's attacked by a small, mysterious, globe shaped spaceship. (Summary from Wikipedia)

11Wealth of Nations, Book 5

By Adam Smith

An Inquiry into the Nature and Causes of the Wealth of Nations is the magnum opus of the Scottish economist Adam Smith, published on March 9, 1776 during the Scottish Enlightenment. It is a clearly written account of political economy at the dawn of the Industrial Revolution, and is widely considered to be the first modern work in the field of economics. (Introduction from Wikipedia)<br /><br />This project was proof listened by mim@can, Betty M., and Barry Eads.

This book is written to Christians who profess to believe the Bible as God's revelation, but whose "lives are filled with discomfort and unrest." Smith aims to show that the Bible's claim that God is the "the God of all comfort" is not an over-advertisement or misunderstanding, but that it is possible to avail ourselves of the doubts and heavy anxieties that plague so many Christians. <br><br> By explaining God's part and man's part, Smith aims to show her readers that it is possible to overcome feelings of defeat and despair and find rest and peace in Christ. Abundant life and genuine enduring joy are available to all believers - even you. Deep and lasting peace, beyond all Earthly circumstances, is possible. (Introduction by Rachel Craig)

LibriVox volunteers bring you 5 recordings of America by Samuel Francis Smith. This was the Weekly Poetry project for July 4th, 2010.

14Skylark of Space

By Lee Hawkins Garby and E. E. Smith

The novel begins with the accidental discovery, in a Government laboratory in Washington D. C., of a form of clean nuclear power. Our hero, Dr. Richard Seaton, uses this power to build first a flying belt and then an interstellar spaceship. He later discovers that the process operates by generation and manipulation of gravity fields.<br /><br /> When his government coworkers do not believe him, Seaton acquires rights to his discovery from the government and commercializes it with the aid of his friend, millionaire inventor Martin Crane. A former colleague, Dr. Marc DuQuesne, joins with the unscrupulous World Steel Corporation to try to steal Seaton's invention. The resulting conflict escalates, as Seaton and Duquesne develop greater and greater technical capabilities and enlist more and more powerful alien races as allies.. (Summary by Wikipedia)

15Skylark of Space (version 2)

By Lee Hawkins Garby and E. E. Smith

The Skylark of Space is one of the earliest novels of interstellar travel and is considered a classic of pulp science fiction. Originally serialized in 1928 in the magazine Amazing Stories it is often categorized as the first literary space opera, complete with protagonists perfect in mind, body, and spirit, who fight against villains of absolute evil. (Introduction from Wikipedia)

16Skylark Three

By E. E. Smith

This is a sequel to The Skylark of Space. The novel concerns Richard Seaton and his allies who have encounters with aliens while fighting DuQuesne and the Fenachrone..(Introduction by Wikipedia)

Captain John Smith (c. January 1580 – June 21, 1631) Admiral of New England was an English soldier, explorer, and author. He was knighted for his services to Sigismund Bathory, Prince of Transylvania. He is remembered for his role in establishing the first permanent English settlement in North America at Jamestown, Virginia, and his brief association with the Virginia Indian girl Pocahontas during an altercation with the Powhatan Confederacy and her father, Chief Powhatan. He was a leader of the Virginia Colony (based at Jamestown) between September 1608 and August 1609, and led an exploration along the rivers of Virginia and the Chesapeake Bay.<br /><br />His books and maps may have been as important as his deeds, as they encouraged more Englishmen and women to follow the trail he had blazed and to colonize the New World. He gave the name New England to that region, and encouraged people with the comment, "Here every man may be master and owner of his owne labour and land...If he have nothing but his hands, he may...by industrie quickly grow rich."<br /><br />In 1614, Smith returned to the Americas in a voyage to the coasts of Maine and Massachusetts Bay. He named the region "New England". He made two attempts in 1614 and 1615 to return to the same coast. First a storm dismasted his ship. In the second attempt, he was captured by French pirates off the Azores. Smith escaped after weeks of captivity and made his way back to England, where he published an account of his two voyages as A Description of New England. He never left England again. He died in the year 1631 in London at the age of 51. (Introduction by Wikipedia)

The proud, cruel and arrogant Mrs. Rayland never married. Therefore, "Rayland Hall", the old Manor House of the title, had to pass to their heir, Somerive, whom they never treated kindly. According to the British laws at the time, the heir must be the oldest son. But what is to be done when the second son is more worthy of it - and is more beloved by Miss Rayland herself? And must the fact that he is in love with a servant and dependent of Miss Rayland take its toll? (Summary by Stav Nisser)

Articles by numerous authors, compiled into a single collection for use by first year divinity students. This book is intended to be a guide to the study of the Christian religion for Protestants. It was prepared to aid students to understand various aspects of education for the Christian ministry, including basic textual studies, theology, Christian history, denominations, Christian ethics and pastoral duties. (Summary by JoeD)

20Triplanetary, First in the Lensman Series

By E. E. Smith

Triplanetary was first serialized in Amazing Stories in 1934. After the Lensman series became popular, Smith took his Triplanetary story and turned it into the first of the Lensman series, using it as a prequel to give the back story for the protaganists in the Lensmen series. He added 6 new chapters, doubling it in size and it's really a different book from the serialized novel, being published 14 years after the first. It was put into Gutenberg just last year.<br /><br /> The novel covers several episodes in an eons-long eugenics project of the super-intelligences of the Arisia. This alien race is breeding two genetic lines to become the ultimate weapon in Arisia's cosmic war with their arch enemy, the Eddore. The initial chapters cover the Kinnison genetic line during the fall of Atlantis and Nero's (Gharlane of Eddore) reign in Rome. These tales were inserted into the novel following the serialized release, along with chapters covering members of the Kinnison line in World Wars One, Two and Three. The final chapter of Triplanetary tells of the discovery of the inertialess drive that allows faster than light travel. Patrolman Conway Costigan and his friends engage in a space battle with Gray Roger the pirate gangster. This conflict is complicated by the arrival of the technologically superior, extra-Solar, amphibian-like Nevians, resulting in the first interstellar war involving humans. In this story Virgil Samms and Roderick Kinnison, two very important members of the eugenics project, are introduced. They will play the leading roles in the next story, First Lensman. (Summary by Wikipedia and Phil Chenevert)

In 1822, Aaron Smith, a young English seaman, was taken captive by Cuban pirates when his ship was boarded en route from Jamaica to England. Forced to work as a navigator and as a member of pirate boarding parties, he witnessed unspeakable acts of murder and torture. Befriended by a young Cuban woman, he managed to escape with his life, but was arrested as a pirate in Havana and sent back to England in chains. There, he found himself on trial for his life at the Old Bailey courthouse—with the attorney general himself leading the prosecution. Smith's dramatic account of his personal experience is a brutally honest, unromanticized [sic] look at piracy in the 19th century. (Summary by Google Books)

22Vortex Blaster

By E. E. Smith

Uncontrolled, terribly violent Atomic Vortices are slowly destroying civilization on every human planet throughout the galaxy. Nothing can contain or stop them despite the lensmen's best efforts until one destroys the home and family of "Storm" Cloud, brilliant atomic physicist. The tragedy triggers actions on his part that pit him one-on-one against the horrible vortices. Introducing "storm" Cloud as THE Vortex Blaster (Summary by book cover and Phil Chenevert)

23On The Seashore

By R. Cadwallader Smith

This gifted nature writer who is so good at describing animals and their habitat and habits here gives us a look at many of the fascinating creatures that can be found on the seashore. Starfish, the many types of crabs, shrimp, sea weed and finally something called the Precious Wentletrap which I will allow your imagination to think about for a while. His writing is clear and, as always, easy to read. Note that these are presented as educational 'lessons' on the various animals found near the sea and each lesson or chapter ends with a few questions called 'Exercises' which the student is asked to see if the main points of the chapter are retained. These questions have been include in the audiobook at the end of each chapter (Summary by Phil Chenevert)

Peggy Raymond and her friends, Amy, Priscilla and Ruth, encounter a new neighbour, Elaine, and her family. While Peggy, in her usual cheerful and practical manner, welcomes them into the neighbourhood of Friendly Terrace, a variety of mysteries slowly unfold about them and why they ended up moving there. (Harriet Lummis Smith later went on to write four sequels to Eleanor H. Porter's "Pollyanna" books.) (Summary by Daryl Wor)

25Within the Deep

By R. Cadwallader Smith

Presented in the form of lessons, R. Cadwallader Smith vividly portrays life in the ocean. Learn about the common and not so common that swim about in the deep, how they hunt for food and hide from enemies, visit a nursery and find out about the babies that live there, or take a stroll in an underwater garden. (Summary by Laura Victoria)

26Peggy Raymond's Vacation (or Friendly Terrace Transplanted)

By Harriet Lummis Smith

Sequel to The Girls of Friendly Terrace (or Peggy Raymond's Success). As the summer opens the girls fan themselves on the porch, wishing for a get away. As it happens, opportunity knocks, leading them into a country vacation along with a few more members to the party. (Summary by Daryl Wor)

Published in 1916, this third installment with The Friendly Terrace girls places them in The Girl’s High School, with an array of new characters, and a few peripherally known from the first book. A heavier edge of drama comes through via a new student with a superiority complex, another student whose diligent scholastic achievements mar her socially, and an odd tradition of affectionate favouritism between Freshman and Seniors which proves to be awkward and disruptive to more than just the students. Peggy, Amy, Priscilla and Ruth are again faced with new challenges, and complicated scenarios to help resolve. (Summary by Daryl Wor)