الصفحة 1
الصفحة 1
Nonsmooth Vector Functions and Continuous Optimization
A recent significant innovation in mathematical sciences has been the progressive use of nonsmooth calculus, an extension of the differential calculus, as a key tool of modern analysis in many areas of mathematics, operations research, and engineering. Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems and variational inequalities in finite dimensions.
Mathématiques de base pour économistes = Basic Mathematics for Economists
This book contains fundamental elements of mathematics and includes the following elements: notion of logic, propositions, theorems, sets, relations and functions; graphical representations of functions, economic applications of lines and functions, sequences, limits and first derivative, differential economic applications of derivatives; integrals: undefined and defined with economic applications; mathematical series; functions of several variables, partial derivatives, Lagrange multiplier with economic applications; linear algebra: matrix calculus, system of linear equations, vectors, differential calculus in matrix form.
Hypoelliptic estimates and spectral theory for Fokker-Planck operators and witten Laplacians
There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart; the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators.
Math for business and economics : Compedium of essential formulas
This mathematical formulary is presented in a practice-oriented, clear, and understandable manner, as it is needed for meaningful and relevant application in global business, as well as in the academic setting and economic practice. The topics presented include but are not limited to mathematical signs and symbols, logic, arithmetic, algebra, linear algebra, combinatorics, and financial mathematics, including an international comparison between different national methods used in the calculation of interest, optimization of linear models, functions, differential calculus, integral calculus, elasticities, annuity calculation, economic functions, and the Peren Theorem.
Lacroix and the Calculus
Lacroix and the Calculus is the first major study of Lacroix’s large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18th-century calculus, and the way it is reflected in Lacroix’s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions).
Basic Probability Theory with Applications
This book presents elementary probability theory with interesting and well-chosen applications that illustrate the theory. An introductory chapter reviews the basic elements of differential calculus which are used in the material to follow. The theory is presented systematically, beginning with the main results in elementary probability theory. This is followed by material on random variables. Random vectors, including the all important central limit theorem, are treated next. The last three chapters concentrate on applications of this theory in the areas of reliability theory, basic queuing models, and time series. Examples are elegantly woven into the text and over 400 exercises reinforce the material and provide students with ample practice.
