Algebra Vector Analysis Geometry
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ALGEBRA, VECTOR ANALYSIS & GEOMETRY
Unit-I 1.1 Historical background : 1.1.1 Development of Indian Mathematics Later Classical Period (500-1250) 1.1.2 A brief biography of Varahamihira and Aryabhatta 1.2 Rank of Matrix 1.3 Echelon and normal form of matrix 1.4 Characteristic equations of a matrix 1.4.1 Eigen-values 1.4.2 Eigen-vectors Unit-II 2.1 Cayley Hamilton theorem 2.2 Application of Cayley Hamilton theorem to find the inverse of a matrix 2.3 Application of matrix to solve a system of linear equations 2.4 Theorems on consistency and inconsistency of a system of linear equations 2.5 Solving linear equations up to three unknowns Unit-III 3.1 Scalar and Vector products of three and four vectors 3.2 Reciprocal vectors 3.3 Vector differentiation 3.3.1 Rules of differentiation 3.3.2 Derivatives of Triple Products 3.4 Gradient, Divergence and Curl 3.5 Directional derivatives 3.6 Vector Identities 3.7 Vector Equations Unit-IV 4.1 Vector Integration 4.2 Gauss theorem (without proof) and problems based on it 4.3 Green theorem (without proof) and problems based on it 4.4 Stoke theorem (without prof) and problems based on it Unit-V 5.1 General equation of second degree 5.2 Tracing of conics 5.3 System of conics 5.4 Cone 5.4.1 Equation of cone with given base 5.4.2 Generators of cone 5.4.3 Condition for three mutually perpendicular gerators 5.4.5 Right circular cone 5.5 Cylinder 5.5.1 Equation of cylinder and its properties 5.5.2 Right Circular Cylinder 5.5.3 Enveloping Cylinder
Tensor and Vector Analysis
Reflecting the significant contributions of Russian mathematicians to the field, this book contains a selection of papers on tensor and vector analysis. It is divided into three parts, covering Hamiltonian systems, Riemannian geometry and calculus of variations, and topology. The range of applications of these topics is very broad, as many modern geometrical problems recur across a wide range of fields, including mechanics and physics as well as mathematics. Many of the approaches to problems presented in this volume will be novel to the Western reader, although questions are of global interest. The main achievements of the Russian school are placed in the context of the development of each individual subject.