Description
Book SynopsisIdeal for undergraduate and graduate students of science and engineering, this book covers fundamental concepts of vectors and their applications in a single volume. 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 and structures, and analytical geometry of curves and surfaces. The second unit delves into the algebra of operators and their types and also explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigen vectors and eigen values of a linear vector operator are elaborated using vector algebra. The third unit deals with vector analysis, discussing vector valued functions of a scalar variable and functions of vector argument (both scalar valued and vector valued), thus covering both the scalar vector fields and vector integration.
Table of ContentsList of figures; List of tables; Preface; Nomenclature; 1. Getting concepts and gathering tools; 2. Vectors and analytic geometry; 3. Planar vectors and complex numbers; 4. Linear operators; 5. Eigenvalues and eigenvectors; 6. Rotations and reflections; 7. Transformation groups; 8. Preliminaries; 9. Vector valued functions of a scalar variable; 10. Functions with vector arguments; 11. Vector integration; 12. Odds and ends; Appendices; Bibliography.
