Mathematical Analysis Differentiation And Integration
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Mathematical Analysis
Mathematical Analysis: Differentiation and Integration is devoted to two basic operations of mathematical analysis, differentiation and integration. The problems directly connected with the operations of differentiation and integration of functions of one or several variables are discussed, together with elementary generalizations of these operations. This volume is comprised of seven chapters and begins by considering the differentiation of functions of one variable and of n variables, paying particular attention to derivatives and differentials as well as their properties. The next chapter deals with composite and implicit functions of n variables in connection with differentiation, along with the representation of functions in the form of superpositions. Subsequent chapters offer detailed accounts of systems of functions and curvilinear coordinates in a plane and in space; the integration of functions; and improper integrals. The final chapter examines the transformation of differential and integral expressions. This book will be a useful resource for mathematicians and mathematics students.
Mathematical Analysis, Differential Equations And Applications
This comprehensive volume presents essential mathematical results devoted to topics of mathematical analysis, differential equations and their various applications. It focuses on differential operators, Wardowski maps, low-oscillation functions, Galois and Pataki connections, Hardy-type inequalities, to name just a few.Effort has been made for this unique title to have an interdisciplinary flavor and features several applications such as in tomography, elastic scattering, fluid mechanics, etc.This work could serve as a useful reference text to benefit professionals, academics and graduate students working in theoretical computer science, computer mathematics, and general applied mathematics.
A Course of Mathematical Analysis
A Course of Mathematical Analysis, Part I is a textbook that shows the procedure for carrying out the various operations of mathematical analysis. Propositions are given with a precise statement of the conditions in which they hold, along with complete proofs. Topics covered include the concept of function and methods of specifying functions, as well as limits, derivatives, and differentials. Definite and indefinite integrals, curves, and numerical, functional, and power series are also discussed. This book is comprised of nine chapters and begins with an overview of mathematical analysis and its meaning, together with some historical notes and the geometrical interpretation of numbers. The reader is then introduced to functions and methods of specifying them; notation for and classification of functions; and elementary investigation of functions. Subsequent chapters focus on limits and rules for passage to the limit; the concepts of derivatives and differentials in differential calculus; definite and indefinite integrals and applications of integrals; and numerical, functional, and power series. This monograph will be a valuable resource for engineers, mathematicians, and students of engineering and mathematics.