Calicut University Syllabus IT: Difference between revisions

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  The syllabus for Information Technology at University of Calicut.
  The syllabus for Information Technology at University of Calicut.


COMBINED FIRST AND SECOND SEMESTER
= COMBINED FIRST AND SECOND SEMESTER =


== ENO4- 101 : MATHEMATICS I ==
== ENO4- 101 : MATHEMATICS I ==
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  Module I: Differential Calculus (15 hours)
  Module I: Differential Calculus (15 hours)
Indeterminate forms-L' hospital's rule- radius of curvature-centre of curvature - evolute -functions of more than one variable-idea of partial differentiation-Euler's Theorem for homogeneous functions-chain rule of partial differentiation-applications in errors and approximations-change of variables-Jacobians-maxima and minima of functions of two -method of Litgrange multipliers.
Indeterminate forms-L' hospital's rule- radius of curvature-centre of curvature - evolute -functions of more than one variable-idea of partial differentiation-Euler's Theorem for homogeneous functions-chain rule of partial differentiation-applications in errors and approximations-change of variables-Jacobians-maxima and minima of functions of two -method of Litgrange multipliers.
  Module II: Infinite series (15 hours)
  Module II: Infinite series (15 hours)
Notion of convergence and divergence of infinite series-ratio test -comparison test-Raabe's test- root test-series of positive and negative terms-absolute convergence-test for alternating series-power series -interval of convergence-Taylors and Maclaaurins series expansion of functions-Leibnitz formula for the nth derivative of the product of two functions-use of Leibnitz formula in the Taylor and Maclaurin expansions.
Notion of convergence and divergence of infinite series-ratio test -comparison test-Raabe's test- root test-series of positive and negative terms-absolute convergence-test for alternating series-power series -interval of convergence-Taylors and Maclaaurins series expansion of functions-Leibnitz formula for the nth derivative of the product of two functions-use of Leibnitz formula in the Taylor and Maclaurin expansions.
  Module III: Matrices (21 hours)
  Module III: Matrices (21 hours)
Rank of a matrix- reduction of a matrix to echelon and normal forms- system of linear equations- consistency of linear equations-Gauss elimination- homogeneous linear equations-fundamental system of solutions- solution of a system of equations using matrix inversion -Eigen values and eigen vectors - Cayley-Hamilton theorem- Eigen value of Hermitian, skew-hermitian and unitary matrices- Digitalization of matrix using Eigen values and Eigen vectors-quadratic forms-matrix associated with a quadratic form -definite, semidefinite and indefinite forms.
Rank of a matrix- reduction of a matrix to echelon and normal forms- system of linear equations- consistency of linear equations-Gauss elimination- homogeneous linear equations-fundamental system of solutions- solution of a system of equations using matrix inversion -Eigen values and eigen vectors - Cayley-Hamilton theorem- Eigen value of Hermitian, skew-hermitian and unitary matrices- Digitalization of matrix using Eigen values and Eigen vectors-quadratic forms-matrix associated with a quadratic form -definite, semidefinite and indefinite forms.
  Module IV: Fourier series and harmonic analysis (15 hours)
  Module IV: Fourier series and harmonic analysis (15 hours)
Periodic functions-trigonometric series-Fourier series-Euler formulae-even and odd functions-functions having arbitrary period -half page expansions-approximation by trigonometric polynomials- minimum square error- numerical method for determining Fourier Coefficients- harmonic analysis
Periodic functions-trigonometric series-Fourier series-Euler formulae-even and odd functions-functions having arbitrary period -half page expansions-approximation by trigonometric polynomials- minimum square error- numerical method for determining Fourier Coefficients- harmonic analysis