In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods.
Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding.
This book is a survey of abstract algebra with emphasis on algebra tinh.Do is online
for students in mathematics, computer science, and physical sciences.
The rst three or four chapters can stand alone as a one semester course in abstract
algebra. However, they are structured to provide the foundation for the program
linear algebra. Chapter 2 is the most di cult part of the book for group
written in additive notation and multiplication, and the concept of coset is confusing
at rst. Chapter 2 After the book was much easier as you go along....
There are many books on linear algebra, in which many people are really great
ones (see for example the list of recommended literature). One might think that one does
no books on this subject. Choose a person's words more carefully, it
can deduce that this book contains everything needed and the best
possible, and so any new book, just repeat the old ones.
This idea is evident wrong, but almost everywhere.
New results in linear algebra and are constantly appearing so refreshing, simple and
neater proof of the famous theorem.
You can teach a course that will give their students exposure to linear algebra. In their first brush with the topic, your students can work with the Euclidean space and the matrix. In contrast, this course will emphasize the abstract vector spaces and linear maps. Bold title of this book deserves an explanation. Almost all linear algebra books use determinants to prove that each linear op-erator on a finite dimensional vector space has a complex eigenvalue.
Linear algebra is the language of chemometrics. One cannot expect to truly understand most
chemometric techniques without a basic understanding of linear algebra. This article
reviews the basics of linear algebra and provides the reader with the foundation required for
understanding most chemometrics literature. It is presented in a rather dense fashion: no
proofs are given and there is little discussion of the theoretical implications of the theorems
and results presented.
The goal of this book is to develop robust, accurate and efficient numerical methods to price a
number of derivative products in quantitative finance.We focus on one-factor and multi-factor
models for a wide range of derivative products such as options, fixed income products, interest
rate products and ‘real’ options. Due to the complexity of these products it is very difficult to
find exact or closed solutions for the pricing functions. Even if a closed solution can be found
it may be very difficult to compute. For this and other reasons we need to resort to approximate
Here are my online notes for my Linear Algebra course that I teach here at Lamar University. Despite the fact that these are my “class notes” they should be accessible to anyone wanting to learn Linear Algebra or needing a refresher. These notes do assume that the reader has a good working knowledge of basic Algebra.
Regression models form the core of the discipline of econometrics. Although econometricians routinely estimate a wide variety of statistical models, using many diﬀerent types of data, the vast majority of these are either regression models or close relatives of them. In this chapter, we introduce the concept of a regression model, discuss several varieties of them, and introduce the estimation method that is most commonly used with regression models, namely, least squares.
This work is intended to survey the basic theory that underlies the multitude of
parameter-rich models that dominate the hydrological literature today. It is concerned
with the application of the equation of continuity (which is the fundamental theorem of
hydrology) in its complete form combined with a simplified representation of the
principle of conservation of momentum. Since the equation of continuity can be
expressed in linear form by a suitable choice of state variables and is also parameterfree,
it can be readily formulated at all scales of interest.
In Chapter 11, Linear Programming was applied to those investments satisfying the following assumptions:Additivity within activities: resource consumption is constant per unit of output; there are no economies of scale.
This paper proposes a new method for approximate string search, speciﬁcally candidate generation in spelling error correction, which is a task as follows. Given a misspelled word, the system ﬁnds words in a dictionary, which are most “similar” to the misspelled word. The paper proposes a probabilistic approach to the task, which is both accurate and efﬁcient. The approach includes the use of a log linear model, a method for training the model, and an algorithm for ﬁnding the top k candidates. ...
Linear algebra occupies a central place in modern mathematics. Also, it is a beautiful and mature field of mathematics, and mathematicians have developed highly effective methods for solving its problems. It is a subject well worth studying for its own sake. This book contains selected topics in linear algebra, which represent the recent contributions in the most famous and widely problems. It includes a wide range of theorems and applications in different branches of linear algebra, such as linear systems, matrices, operators, inequalities, etc.
The present volume, compiled in honor of an outstanding historian of science,
physicist and exceptional human being, Sam Schweber, is unique in assembling
a broad spectrum of positions on the history of science by some of its leading
representatives. Readers will find it illuminating to learn how prominent authors
judge the current status and the future perspectives of their field. Students will find
this volume helpful as a guide in a fragmented field that continues to be dominated
by idiosyncratic expertise and still lacks a methodical canon.
This note deals with two fully parallel methods for solving linear partial differentialalgebraic equations (PDAEs) of the form: Aut + B∆u = f(x, t) where A is a singular, symmetric and nonnegative matrix, while B is a symmetric positive define matrix. The stability and convergence of proposed methods are discussed. Some numerical experiments on high-performance computers are also reported.
Recent work has seen the emergence of a common framework for parsing categorial grammar (CG) formalisms that fall within the 'type-logical' tradition (such as the Lambek calculus and related systems), whereby some method of linear logic theorem proving is used in combination with a system of labelling that ensures only deductions appropriate to the relevant grammatical logic are allowed. The approaches realising this framework, however, have not so far addressed the task of incremental parsing - - a key issue in earlier work with 'flexible' categorial grammars.
Lecture Quantiative methods for bussiness - Chapter 7 introduction to linear programming. This chapter presents the following content: Linear programming problem, problem formulation, a simple maximization problem, graphical solution procedure, extreme points and the optimal solution, computer solutions, a simple minimization problem, special cases.
Lecture "Advanced Econometrics (Part II) - Chapter 13: Generalized method of moments (GMM)" presentation of content: Orthogonality condition, method of moments, generalized method of moments, GMM and other estimators in the linear models, the advantages of GMM estimator, GMM estimation procedure.
After studying this chapter you will be able to: Formulate linear programming models, including an objective function and constraints, graphically solve an LP problem with the iso-profit line method, graphically solve an LP problem with the corner-point method, interpret sensitivity analysis and shadow prices, construct and solve a minimization problem.