Higher mathematics / Madan Pal.

Includes bibliographical references and index.

Linear algebra -- Discrete mathematics -- Mathematical physics -- Vector algebra -- Differentiation calculus -- Order of partial differential equation -- Geometrical representation -- Laplace transforms -- Logical Boolean algebra.

"This book is designed to provide accessible knowledge of higher-level mathematics demanded in contemporary physics and engineering. Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in computer algorithms and programming languages. Mathematical physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. In mathematics, the Laplace transform is a technique for analyzing linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behaviour of the system, or in synthesizing a new system based on a set of specifications. Today, all our computers use Boole's logic system - using microchips that contain thous ands of tiny electronic switches arranged into logical 'gates' that produce predictable and reliable conclusions. The basic logic gates are AND, OR and NOT. It is these gates, used in different combinations, that allow the computer to execute its operations using binary language. Each gate assesses information (consisting of high or low voltages) in accordance with predetermined rules, and produces a single high or low voltage logical conclusion. This book is a valuable resource for mathematicians and readers who are embarking on the study of functional analysis"-- Back cover.