Concise Vector Analysis
The Commonwealth and International Library of Science, Technology, Engineering and Liberal Studies: Mathematics Division
Published on 16. May 2014
164 pages
978-1-4831-4193-0 (ISBN)
Description
Concise Vector Analysis is a five-chapter introductory account of the methods and techniques of vector analysis. These methods are indispensable tools in mathematics, physics, and engineering. The book is based on lectures given by the author in the University of Ceylon. The first two chapters deal with vector algebra. These chapters particularly present the addition, representation, and resolution of vectors. The next two chapters examine the various aspects and specificities of vector calculus. The last chapter looks into some standard applications of vector algebra and calculus. This book will prove useful to applied mathematicians, students, and researchers.
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Content
PrefaceChapter 1. Vectors and Vector Addition 1.1 Vectors 1.2 Representation of Vectors 1.3 Vector Addition 1.4 -a, O, ¿a 1.5 Resolution of a Vector 1.6 Point Dividing AB in the Ratio m:n 1.7 Centroid or Mean Centre of n Points ExercisesChapter 2. Products of Vectors 2.1 Scalar Product 2.2 Vector Product 2.3 Triple Products 2.4 Mutual Moment of Two Lines 2.5 Positive and Negative Triads ExercisesChapter 3. Vector Calculus 3.1 Vector Function of a Scalar 3.2 Unit Tangent Vector ¿ 3.3 Functions of a Vector 3.4 Map of a Field 3.5 Directional Derivative 3.6 Gradient Vector ExercisesChapter 4. Vector Calculus 4.1 Line Integrals 4.2 Line Integral of Grad f 4.3 Surface Integrals 4.4 Volume Integrals 4.5 Divergence 4.6 Gauss's Transformation 4.7 Curl A 4.8 Stokes' Theorem 4.9 The Operator ¿ 4.10 The Laplacian Operator 4.11 Orthogonal Curvilinear Coordinates ExercisesChapter 5. Some Applications 5.1 Equivalence of Force Systems 5.2 Poinsot's Central Axis 5.3 Space-Curve 5.4 Infinitesimal Rotations. Angular Velocity 5.5 Angular Velocity of a Rigid Body 5.6 Gauss's Theorem 5.7 Gravitational Potential 5.8 Equipotential Surfaces 5.9 Green's Theorems ExercisesIndex
