Methods of Mathematical Physics-I: 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 R^3.
• 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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