Mod-02 Lec-13 Harmonic Functions

Course Lectures

• Mod-01 Lec-01 Review Groups, Fields and Matrices

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-01 Lec-02 Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-01 Lec-03 Basis, Dimension, Rank and Matrix Inverse

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-01 Lec-04 Linear Transformation, Isomorphism and Matrix Representation

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-01 Lec-05 System of Linear Equations, Eigenvalues and Eigenvectors

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-01 Lec-06 Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-01 Lec-07 Jordan Canonical Form, Cayley Hamilton Theorem

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-01 Lec-08 Inner Product Spaces, Cauchy-Schwarz Inequality

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-01 Lec-09 Orthogonality, Gram-Schmidt Orthogonalization Process

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-01 Lec-10 Spectrum of special matrices,positive/negative definite matrices

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-02 Lec-11 Concept of Domain, Limit, Continuity and Differentiability

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-02 Lec-12 Analytic Functions, C-R Equations

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-02 Lec-13 Harmonic Functions

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-02 Lec-14 Line Integral in the Complex

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-02 Lec-15 Cauchy Integral Theorem

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-02 Lec-16 Cauchy Integral Theorem (Contd.)

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-02 Lec-17 Cauchy Integral Formula

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-02 Lec-18 Power and Taylor's Series of Complex Numbers

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-02 Lec-19 Power and Taylor's Series of Complex Numbers (Contd.)

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-02 Lec-20 Taylor's, Laurent Series of f(z) and Singularities

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-02 Lec-21 Classification of Singularities, Residue and Residue Theorem

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-03 Lec-22 Laplace Transform and its Existence

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-03 Lec-23 Properties of Laplace Transform

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-03 Lec-25 Applications of Laplace Transform to Integral Equations and ODEs

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-03 Lec-26 Applications of Laplace Transform to PDEs

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-03 Lec-27 Fourier Series

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-03 Lec-28 Fourier Series (Contd.)

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-03 Lec-29 Fourier Integral Representation of a Function

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-03 Lec-30 Introduction to Fourier Transform

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-03 Lec-31 Applications of Fourier Transform to PDEs

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-04 Lec-32 Laws of Probability - I

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-04 Lec-33 Laws of Probability - II

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-04 Lec-34 Problems in Probability

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-04 Lec-35 Random Variables

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-04 Lec-36 Special Discrete Distributions

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-04 Lec-37 Special Continuous Distributions

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-04 Lec-38 Joint Distributions and Sampling Distributions

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-04 Lec-39 Point Estimation

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-04 Lec-40 Interval Estimation

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-04 Lec-41 Basic Concepts of Testing of Hypothesis

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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• Mod-04 Lec-42 Tests for Normal Populations

  Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar

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