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The exhaustive list of topics in Mathematical Physics in which we provide Help with Homework Assignment and Help with Project is as follows:

  • Vector calculus, Gradient, Divergence and Curl in curvilinear coordinates applications to Classical mechanics and Electrodynamics.
  • Linear independence, bases, orthogonality and completeness, Gram-Schmidt orthogonalization, Hilbert space, linear operators, change of basis, similarity transformation, dual spaces, applications to quantum mechanics.
  • Matrix diagonalization, eigenvalues and eigenvectors, orthogonal and unitary matrices, Pauli matrices.
  • Dirac delta function, definitions and different representations of delta functions, applications to Electrodynamics.
  • Tensors in index notation, Kronecker and Levi Civita tensors, inner and outer products, contraction, symmetric and antisymmetric tensors, quotient law.
  • Metric tensors, covariant and contravariant tensors, simple applications to general theory of relativity and Klein Gordon and Dirac equations in relativistic quantum mechanics
  • Cauchy-Riemann conditions, analyticity, Cauchy-Goursat theorem Cauchy’s integral formula, branch points and branch cuts, multivalued functions, residue theorem.