Real Variables

This textbook provides a rigorous and comprehensive introduction to the functions of real variables. It is designed to bridge the gap between elementary calculus and advanced mathematical analysis, focusing on the fundamental properties of the real number system, limits, continuity, and the theory of differentiation and integration. The authors employ a structured pedagogical approach, using a …

A Second Course in Mathematical Analysis

This classic textbook serves as a systematic continuation for students of mathematics and physics who have already mastered the foundational concepts of limits, continuity, and differentiation. It delves into more sophisticated techniques of real and complex analysis, including detailed treatments of infinite series, trigonometric function expansions, and the deeper properties of metric and top…

Ordinary Differential Equations

This classic textbook provides a rigorous yet accessible introduction to the fundamental theory of ordinary differential equations (ODEs). It balances classical methods with modern mathematical rigor, covering key topics such as linear differential equations, power series solutions, and existence and uniqueness theorems. The text also introduces students to more advanced concepts like stability…

Partial Differential Equations

This foundational textbook is part of the Lectures in Applied Mathematics series and stems from the 1957 Summer Seminar at the University of Colorado. The book is divided into two primary parts: the first, by Fritz John, covers hyperbolic and parabolic equations from a classical viewpoint, while the second, by Lipman Bers and Martin Schechter, provides a readable account of elliptic equations u…

Kernel Functions and Elliptic Differential Equations in Mathematical Physics

This foundational text focuses on the theory of boundary value problems in partial differential equations, a subject central to pure mathematics, engineering, and theoretical physics. Written by two pioneers in the field, the book adopts a unifying point of view by concentrating on specific kernels—particularly the Bergman kernel—to explain the shared mathematical foundations of seemingly d…

The Elements of Integration

This classic textbook provides a concise and highly regarded introduction to the theory of integration and measure. Written by Robert G. Bartle, it was specifically designed to make the abstract concepts of the Lebesgue integral accessible to undergraduate students. The text focuses on the core principles of measure theory, measurable functions, and the convergence theorems (Monotone and Domina…

Modern Analytical Methods

Edition

1

ISBN/ISSN

0 85186 759 6

Collation

-

Series Title

-

Call Number

543 000 B565

Nondifferentiable Optimization

This volume is a collection of contributed papers that explore the solution of mathematical programming problems where the standard assumption of differentiability—the ability to calculate smooth derivatives—is dropped. Nondifferentiable optimization (also known as nonsmooth optimization) addresses problems involving functions with sharp "corners" or discontinuous derivatives, which cause c…

Applied Functional Analysis

This textbook provides a rigorous introduction to functional analysis with a specific focus on Hilbert spaces and their practical applications. Balakrishnan views functional analysis as the essential language for addressing complex problems in system optimization, control systems, and mathematical economics. The text covers foundational topics such as linear operators, spectral theory, and semi…

Trigonometric Series, Volume I

Often referred to simply as "Zygmund," this is the definitive, foundational treatise on Fourier analysis. Volume I covers the core theory of trigonometric series, including convergence and summability, the properties of Fourier coefficients, and the theory of Hardy spaces . Zygmund’s work transformed the field from a collection of isolated results into a unified branch of mathematical analysi…