This 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables.
"This book is appropriate for an applied numerical analysis course for upper-level undergraduate and graduate students as well as computer science students. Actual programming is not covered, but an extensive range of topics includes round-off and function evaluation, real zeros of a function, integration, ordinary differential equations, optimization, orthogonal functions, Fourier series, and much more. 1989 edition"--Provided by publisher.
Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books
This text focuses on the most widely used applications of mathematical methods, including those related to probability and statistics. The 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables.
This monograph is a sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion- driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to a study of equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the text. This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options. Also available by Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag New York, Inc., 1991, 470 pp., ISBN 0-387- 97655-8.
Student-Friendly Coverage of Probability, Statistical Methods, Simulation, and Modeling Tools Incorporating feedback from instructors and researchers who used the previous edition, Probability and Statistics for Computer Scientists, Second Edition helps students understand general methods of stochastic modeling, simulation, and data analysis; make optimal decisions under uncertainty; model and evaluate computer systems and networks; and prepare for advanced probability-based courses. Written in a lively style with simple language, this classroom-tested book can now be used in both one- and two-semester courses. New to the Second Edition Axiomatic introduction of probability Expanded coverage of statistical inference, including standard errors of estimates and their estimation, inference about variances, chi-square tests for independence and goodness of fit, nonparametric statistics, and bootstrap More exercises at the end of each chapter Additional MATLAB® codes, particularly new commands of the Statistics Toolbox In-Depth yet Accessible Treatment of Computer Science-Related Topics Starting with the fundamentals of probability, the text takes students through topics heavily featured in modern computer science, computer engineering, software engineering, and associated fields, such as computer simulations, Monte Carlo methods, stochastic processes, Markov chains, queuing theory, statistical inference, and regression. It also meets the requirements of the Accreditation Board for Engineering and Technology (ABET). Encourages Practical Implementation of Skills Using simple MATLAB commands (easily translatable to other computer languages), the book provides short programs for implementing the methods of probability and statistics as well as for visualizing randomness, the behavior of random variables and stochastic processes, convergence results, and Monte Carlo simulations. Preliminary knowledge of MATLAB is not required. Along with numerous computer science applications and worked examples, the text presents interesting facts and paradoxical statements. Each chapter concludes with a short summary and many exercises.
This invaluable book offers engineers and physicists working knowledge of a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, but nevertheless extremely useful when applied to typical problems in many different fields. It deals principally with linear algebraic equations, quadratic and Hermitian forms, operations with vectors and matrices, the calculus of variations, and the formulations and theory of linear integral equations. Annotated problems and exercises accompany each chapter.
An early but still useful and frequently cited contribution to the science of mathematical economics, this volume is geared toward graduate students in the field. Prerequisites include familiarity with the basic theory of matrices and linear transformations and with elementary calculus. Author Jacob T. Schwartz begins his treatment with an exploration of the Leontief input-output model, which forms a general framework for subsequent material. An introductory treatment of price theory in the Leontief model is followed by an examination of the business-cycle theory, following ideas pioneered by Lloyd Metzler and John Maynard Keynes. In the final section, Schwartz applies the teachings of previous chapters to a critique of the general equilibrium approach devised by Léon Walras as the theory of supply and demand, and he synthesizes the notions of Walras and Keynes. 1961 edition.
Probability and Statistics is a calculus-based treatment of probability concurrent with and integrated with statistics.* Incorporates more than 1,000 engaging problems with answers* Includes more than 300 solved examples* Uses varied problem solving methods