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Methods of Mathematical Physics-I: Course Outline

A course on methods of mathematical physics. The course aims to demonstrate the utility and limitations of a variety of powerful calculational techniques and to provide a deeper understanding of the mathematics underpinning theoretical physics.

Course Outline

  • Mathematical preliminaries.
  • Infinite series.
  • Series of functions.
  • Binomial theorem.
  • Mathematical induction.
  • Operation of series expansion of functions.
  • Some important series.
  • Vectors.
  • Complex number and functions.
  • Derivative and extrema.
  • Evaluations of integrals. 
  • Dirac delta functions.
  • Determinants and matrices.
  • Determinants, Matrices.
  • Vector analysis.
  • Review of basics properties.
  • Vector in 3-D spaces.
  • Coordinates transformations.
  • Rotations in R3.
  • Differential vectors operators.
  • Vector integrations.
  • Integral theorem.
  • Potential theory. 
  • Curvilinear coordinates.
  • Tensor and differential forms.
  • Tensor analysis.
  • Pseudo-tensors. 
  • Dual tensors, and Tensors in general coordinates. 
  • Jacobians.
  • Differential forms. 
  • Integrating forms. 
  • Vector Spaces.
  • Vector in function spaces. 
  • Gram Schmidt orthogonalization. 
  • Operators.
  • Self adjoint operators. 
  • Unitary operators.
  • Transformations of operators, and Invariants.

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