ADVANCED MATHEMATICAL PHYSICS-I
₹
59
Inclusive of taxes
Share this
![](https://www.facebook.com/dialog/feed?app_id=1767574003460647&link=https://bsc-physics-notes-online.myinstamojo.com/product/advanced-mathematical-physics-i&picture=https://storeassets.im-cdn.com/media-manager/bsc-physics-notes-online/rFXSuK9KSUiaWcmnmBNA_AMP1.png&name=ADVANCED MATHEMATICAL PHYSICS-I&caption=undefined&description=<p><br></p><h4 class="ql-align-center">Topics Covered in Notes</h4><h4><br></h4><h4>Linear Vector Spaces : Abstract Systems , Binary Operations and Relations. Introduction to Groups and Fields. Vector Spaces and Subspaces. Linear Independence and Dependence of Vectors. Basis and Dimensions of a Vector Space. Change of basis. Homomorphism and Isomorphism of Vector Spaces. Linear Transformations. Algebra of Linear Transformations. Nonsingular Transformations. Representation of Linear Transformations by Matrices. (12 Lectures)</h4><h4><br></h4><h4>Matrices: Addition and Multiplication of Matrices. Null Matrices. Diagonal, Scalar and Unit Matrices. Upper-Triangular and Lower-Triangular Matrices. Transpose of a Matrix. Symmetric and Skew-Symmetric Matrices. Conjugate of a Matrix. Hermitian and Skew- Hermitian Matrices. Singular and Non-Singular matrices. Orthogonal and Unitary Matrices. Trace of a Matrix. Inner Product. (8 Lectures)</h4><h4><br></h4><h4><br></h4><h4>Eigen-values and Eigenvectors. Cayley- Hamiliton Theorem. Diagonalization of Matrices. Solutions of Coupled Linear Ordinary Differential Equations. Functions of a Matrix. (10 Lectures)</h4><h4><br></h4><h4>Cartesian Tensors: Transformation of Co-ordinates. Einstein’s Summation Convention. Relation between Direction Cosines. Tensors. Algebra of Tensors. Sum, Difference and Product of Two Tensors. Contraction. Quotient Law of Tensors. Symmetric and Anti-symmetric Tensors. Invariant Tensors : Kronecker and Alternating Tensors. Association of Antisymmetric Tensor of Order Two and Vectors. Vector Algebra and Calculus using Cartesian Tensors : Scalar and Vector Products, Scalar and Vector Triple Products. Differentiation. Gradient, Divergence and Curl of Tensor Fields. Vector Identities.Tensorial Formulation of Analytical Solid Geometry : Equation of a Line. Angle Between Lines. Projection of a Line on another Line. Condition for Two Lines to be Coplanar. Foot of the Perpendicular from a Point on a Line. Rotation Tensor (No Derivation). Isotropic Tensors. Tensorial Character of Physical Quantities. Moment of Inertia Tensor. Stress and Strain Tensors : Symmetric Nature. Elasticity Tensor. Generalized Hooke’s Law. </h4><h4> (20 lectures)</h4><h4><br></h4><h4>General Tensor:Transformation of Co-ordinates. Minkowski Space. Contravariant & Covariant Vectors. Contravariant, Covariant and Mixed Tensors. Kronecker Delta and Permutation Tensors. Algebra of Tensors. Sum, Difference & Product of Two Tensors. Contraction. Quotient Law of Tensors. Symmetric and Anti-symmetric Tensors. Metric Tensor. (10 Lectures)</h4><h4><br></h4><h4><br></h4><h4>Suggested Books in Syllabus:</h4><ul><li><strong style="color: rgb(204, 0, 0);">Mathematical Tools for Physics, James Nearing, 2010, Dover Publications</strong></li><li><strong style="color: rgb(204, 0, 0);">Mathematical Methods for Physicists, G.B. Arfken, H.J. Weber and F.E.Harris,1970, Elsevier.</strong></li><li><strong style="color: rgb(204, 0, 0);">Modern Mathematical Methods for Physicists and Engineers, C.D. Cantrell, 2011</strong></li><li><strong style="color: rgb(204, 0, 0);">Introduction to Matrices & Linear Transformations, D.T.Finkbeiner,1978, Dover Pub.</strong></li><li><strong style="color: rgb(204, 0, 0);">Mathematics for Physicists, Susan M. Lea, 2004, Thomson Brooks/Cole</strong></li></ul><p><br></p>&redirect_uri=http://www.facebook.com)
ADVANCED MATHEMATICAL PHYSICS-I
₹
59
Inclusive of taxes
Share this
Quantity
1
Product Description
Topics Covered in Notes
Linear Vector Spaces : Abstract Systems , Binary Operations and Relations. Introduction to Groups and Fields. Vector Spaces and Subspaces. Linear Independence and Dependence of Vectors. Basis and Dimen
View more
©bsc-physics-notes-online.myinstamojo.com2024All rights reserved