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Physics
Mathematical Physics - 1 (Web)
Syllabus
Co-ordinated by :
IIT Guwahati
Available from :
2014-11-21
Lec :
1
Modules / Lectures
Quantities
Definition
Gradient
Physical examples of divergence
Curl in Curvilinear Coordinates
Gauss Divergence Theorem
Stoke's Theorem
Vector Spaces
Linear Vector Spaces
Bases
Linear Independence , Change of Basis
Similarity Transformation
Orthogonality and Completeness
Gram-Schmidt Orthogonalization (GSO)
Hilbert Space
Linear Algebra in Quantum Mechanics
Matrices
Inverse of a Matrix
Symmetric, Skew Symmetric and Orthogonal Matrices
Basis of Eigenvectors
Matrix Eigenvalue
Eigenvalues Equation
Tutorials
Delta Function
Dirac Delta Function
Different representations of Delta Functions
Definitions and different representations of Delta Functions
Tensors
Introduction
Transformation Properties of Vectors
Covariant and Contravariant Vectors
Tensors with multiple indices – cross product
Algelraic Properties of Tensors
Metric Tensor
Dynamics of Particle :Usage of Tensors
Complex Analysis
Complex Numbers
Algebraic Properties Complex Numbers
Cauchy-Riemann Conditions
Analyticity
Branch points and Branch cuts
Cauchy's Integral Formula
Residue Theorem
Jordan's Lemma
Taylor and Laurent Series
Summary
Conformal Mapping
Jacobian of a transformation
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