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Mathematical Methods for Statistics: Home

Course Outline

  • Review of Matrices and Vectors
  • Matrix Differentiation
  • Eigenvalues 
  • Eigenvectors and their Properties 
  • Positive definite matrix
  • Semi positive definite matrix 
  • Introduction to quadratic forms 
  • Maximization of Quadratic Forms 
  • Variance-Covariance matrix
  • Partitioned Matrices 
  • Rank of Matrix
  • Gamma and Beta functions with their applications 
  • Line integrals
  • transformation of coordinates (Cartesian & Polar) 
  • Change of variables in multiple integrals
  • Extrema of functions of two variables
  • Orthogonal polynomials
  • Complex exponential
  • Fourier series and Fourier Transforms
  • Laplace Transforms and their  applications 
  • Geometrical interpretation of multiple integrals

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