ISBN: 978-1-84265-360-9
Publication Year: 2006
Pages: 368
Binding: Hard Back
Dimension: 185mm x 240mm
Weight: 1000
About the book
Based on many years of experience of the author Complex Analysis with Vector Calculus provides clear and condensed treatment of the subject. It is primarily intended to be used by undergraduate students of engineering and science as a part of a course in engineering mathematics, where they are introduced to complex variable theory, through conceptual development of analysis. The book also introduces vector algebra, step by step, with due emphasis on various operations on vector field and scalar fields. Especially, it introduces proof of vector identities by use of a new approach and includes many examples to clarify the ideas and familiarize students with various techniques of problem solving.
Table of content
Complex Numbers: Introduction / Manipulation Rules / Quadratic Equations / Argand Diagram / Polar Co-ordinates / De Movire’s Theorem / Polynomials / Complex Analysis: Introduction / Function of Complex Variables / Derivatives of Complex Variable Function / Power Series and Analyticity / Differentiation of Complex Variable Function / Harmonic Functions / Complex Integration: Introduction / Cauchy’s Integral Formulae / Taylor and Laurent Series / Singularities and Residue / Indefinite Integrals: Evaluation of Real Integrals / Improper Integrals / Integration Along Indented Contours / Conformal Mappings: Mapping / Conformal Mapping / Bilinear Transformation / Exponential Transformation / Trigonometric Transformations / The Map / Vectors: Basic Concepts / Vectors in xyz-space / The Scalar Product of Vectors / The Vector Product / Systems of Forces: Representation of Force by a Vector / Study of Forces with Vectors / Reduction of a System of Forces / Reduction of a System Consisting of Two Parallel Forces / Reduction to Three Forces / Condition For Equilibrium / Couples / Equivalent Couples / Reduction of Systems of Forces to Single Force with Couple / Vector Valued Functions and Scalar Functions: Introduction / Limit of a Vector Function / Derivative / Geometry of Space Curves / Partial Differentiation of Vectors / Integration of a Vector Function / Vector Equations: Introduction / The Equation of a Straight Line / Normal Form of Vector Equation of a Plane / Equation of a Sphere / Gradient, Divergence and Curl: Scalar Fields and Vector Fields / Gradient of a Scalar Field / Divergence and Curl of a Vector Field / Multiple Operations / Rules of Vector Differentiation / Divergence and Curl of Products / Orthogonal Curvilinear Co-ordinates: Introduction / Orthogonal Curvilinear co-ordinates / Differential Operators in Terms of Orthogonal Curvilinear Co-ordinates / Special Curvilinear Systems / Line Integrals Surface Integrals and Volume Integrals: Line Integrals / Conservative Vector Fields and Independent of Paths / Double Integrals / Change of Order of Integration / Double Integrals in Polar Coordinates / Surface Integrals with Vector Function / Triple Integrals / Change of Variables / Green’s, Stokes’ and Gauss’s Divergence Theorems.
ISBN: 978-1-84265-339-5
Publication Year: 2006
Pages: 282
Binding: Hard Back
Dimension: 160mm x 240mm
Weight: 660
Price: GBP 39.95 / USD 74.95
Textbook
About the book
Functional Analysis, written in a clear and entertaining style for senior and postgraduate students discusses Hilbert spaces, Banach algebras, Operator theory and Topological vector spaces. The book covers many standard results including the Hahn-Banach, open mapping and closed graph theorems; the Banach-Steinhaus and the Banach-Alaoglu theorems; Riesz-Fischer and Riesz representation theorems; Gelfand-Mazur and Gelfand-Neumark theorems; Bipolar theorem; and the Kolmogoroff criterion for normability. The book is designed for senior undergraduate and postgraduate students of mathematics and mathematical physics.
Key Features
New to the Second Edition ? Chapter on Lp-spaces Salient Features: ? Complete proofs delineated with meticulous details ? Solved problems and extensive exercises ? Excellent motivation displayed in each chapter
Table of content
Preliminaries / Normed Spaces / Hilbert Spaces / Banach Algebras / Operator Theory / Topological Vector Spaces / Lp-spaces / Bibliography / Index.
ISBN: 978-1-84265-322-7
Publication Year: 2006
Pages: 410
Binding: Hard Back
Dimension: 180mm x 240mm
Weight: 800
About the book
A First Course in Functional Analysis lucidly covers Banach spaces, continuous linear functionals, the basic theorems of bounded linear operators, Hilbert spaces, operators on Hilbert spaces, spectral theory and Banach algebras usually taught as a core course to post-graduate students in mathematics. The special distinguishing features of the book includes the establishment of the spectral theorem for the compact normal operators in the infinite dimensional case exactly in the same form as in the finite dimensional case and a detailed treatment of the theory of Banach algebras leading to the proof of the Gelfond ? Neumark structure theorem for Banach algebras.
Key Features
Examples at the End of Each Chapter Elementary Problems to Illustrate Theory Challenging Exercises as Theorems
Table of content
Preface / Banach Spaces / Continuous Linear Functionals / The Basic Theorems of Bounded Linear Operators / Hilbert Spaces / Operators on Hilbert Spaces / Spectral Theory / Banach Algebras / References / Index.
ISBN: 978-1-84265-308-1
Publication Year: 2006
Pages: 230
Binding: Hard Back
Dimension: 185mm x 240mm
Weight: 700
Textbook
About the book
Two Versions of Wavelets and Applications presents an accessible treatment and description of discrete and generalized wavelet analysis and how they can be applied to fundamental data analysis problems. This book provides a complete study of transmutation operators, the harmonic analysis, generalized wavelets, and generalized wavelet packets associated with differential and differential-difference operators. Many applications of these theories have been given by way of a rich collection of references. The results and methods presented should be of interest to graduate students and researchers working in wavelets, Fourier analysis, operator theories, differential equations and Mathematical Physics because they allow a greatly flexibility and are easy to implement.
Table of content
Preface / Introduction to wavelet theory / Multiresolution analyses on the interval [0, 1] and commutation properties / Segmented biorthogonal multiresolution analyses on the interval [0, 1] and applications / Wavelets on manifolds and applications to Sobolev spaces / Orthogonal and biorthogonal multiresolution analyses on the L-shaped domain / Harmonic Analysis associated with a singular differential operator on ]0, + 8 [ / Generalized wavelet packets associated with a singular differential operator on ]0, + 8[ / Generalized Daubechies wavelet packets and inversion of the dual of J. L. Lions transmutation operator / Generalized two-scale equation and application / Harmonic Analysis Associated with the Dunkl operator on R / Dunkl wavelets and applications / Bibliography / Index.
ISBN: 978-1-84265-298-5
Publication Year: 2007
Pages: 554
Binding: Hard Back
Dimension: 185mm x 240mm
Weight:
Price: GBP 39.95 / USD 74.95
Textbook
About the book
Discrete Mathematical Structures describes the basic ideas involved along with the mathematical theory of computation. Importance has been given to problem solving with the understanding of basic theory with stress on the mathematical rigour. Every topic is illustrated with a large number of solved problem of increasing complexities which will help both the beginner and the professional understand the fundamentals involved and enable them to solve various problems given as exercises. This book will also greatly help readers understand the advanced ideas involved in data structure and algorithms, mathematical theory of languages and computation etc.
Table of content
Preface / Acknowledgements / Elements of Set Theory / Mathematical Logic / Relations / Functions / Partial Order and Structures / Combinatorics and Algebraic Systems / Elements of Graph Theory / Trees / Finite State Machine and Automata / Languages, Grammar, Push Down Automata & Turing Machine / References / Index