Complex Analysis with Vector Calculus

T.M.J.A Cooray

368 pages, parution le 18/09/2006

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Résumé

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.

Sommaire

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.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Alpha
Auteur(s)	T.M.J.A Cooray
Parution	18/09/2006
Nb. de pages	368
Format	24 x 18,5
Couverture	Relié
Poids	882g
Intérieur	Noir et Blanc
EAN13	9781842653609
ISBN13	978-1-84265-360-9