An Introduction to Vectors, Vector Operators and Vector Analysis – Pramod S. Joag

Conceived as s a supplementary text and reference book for undergraduate and graduate students of science and engineering, this book intends communicating the fundamental concepts of vectors and their applications. It is divided into three units. The first unit deals with basic formulation: both conceptual and theoretical. It discusses applications of algebraic operations, Levi-Civita notation and curvilinear coordinate systems like spherical polar and parabolic systems. Structures and analytical geometry of curves and surfaces is covered in detail.

The second unit discusses algebra of operators and their types. It explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigenvectors and eigenvalues of a linear vector operator are discussed using vector algebra. Topics including Mohr’s algorithm, Hamilton’s theorem and Euler’s theorem are discussed in detail. The unit ends with a discussion on transformation groups, rotation group, group of isometries and the Euclidean group, with applications to rigid displacements.

The third unit deals with vector analysis. It discusses important topics including vector valued functions of a scalar variable, functions of vector argument (both scalar valued and vector valued): thus covering both the scalar and vector fields and vector integration

Pramod S. Joag is presently working as CSIR Emeritus Scientist at the Savitribai Phule University of Pune, India. For over 30 years he has been teaching classical mechanics, quantum mechanics, electrodynamics, solid state physics, thermodynamics and statistical mechanics at undergraduate and graduate levels. His research interests include quantum information, and more specifically measures of quantum entanglement and quantum discord, production of multipartite entangled states, entangled Fermion systems, models of quantum nonlocality etc.

Contents:

Figures
Tables
Preface
Nomenclature
I. Basic Formulation
1. Getting Concepts and Gathering Tools
2. Vectors and Analytic Geometry
3. Planar Vectors and Complex Numbers
II. Vector Operators
4. Linear Operators
5. Eigenvalues and Eigenvectors
6. Rotations and Reflections
7. Transformation Groups
III. Vector Analysis
8. Preliminaries
9. Vector Valued Functions of a Scalar Variable
10. Functions with Vector Arguments
11. Vector Integration
12. Odds and Ends
Appendices
A. Matrices and Determinants

Formato:  pdf Comprimido:  rar Peso:  4.84 MB Lenguaje:  Inglés

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