Calicut University Syllabus IT: Difference between revisions
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= IT: INFORMATION TECHNOLOGY = | |||
== COMBINED FIRST AND SECOND SEMESTER == | == COMBINED FIRST AND SECOND SEMESTER == | ||
= ENO4- 101 : MATHEMATICS I = | == ENO4- 101 : MATHEMATICS I == | ||
(Common for all B. Tech. Programmes) | (Common for all B. Tech. Programmes) | ||
3 hours lecture per week | 3 hours lecture per week | ||
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) | |||
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) | |||
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) | |||
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 | ||
Reference Books | Reference Books | ||
Michael D. Greenberg, Advanced Engineering Mathematics (second edition),Pearson Education Asia. | Michael D. Greenberg, Advanced Engineering Mathematics (second edition),Pearson Education Asia. | ||
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QV - 2 questions A and B of 15 marks from module IV with choice to answer anyone | QV - 2 questions A and B of 15 marks from module IV with choice to answer anyone | ||
EN04-102 : MATHEMATICS II | == EN04-102 : MATHEMATICS II == | ||
(Common for all B.Tech. Programmes) | |||
3 hours lecture per week | (Common for all B.Tech. Programmes) | ||
3 hours lecture per week | |||
Module I: Ordinary diferential equations (21 hours) | Module I: Ordinary diferential equations (21 hours) | ||
Equations of first order-seperable, homogeneous and linear types-exact equations -orthogonal trajectories-linear second order equations-homogeneous linear equation of the second order with constant coefficients-fundamental system of solutions-Solutions of the general linear equations of second order with constant coefficients- method of variation of parameters-Cauchy's equation-simple applications of differential equations in engineering problems, including problems in mechanical vibrations, electric circuits and bending of beams | Equations of first order-seperable, homogeneous and linear types-exact equations -orthogonal trajectories-linear second order equations-homogeneous linear equation of the second order with constant coefficients-fundamental system of solutions-Solutions of the general linear equations of second order with constant coefficients- method of variation of parameters-Cauchy's equation-simple applications of differential equations in engineering problems, including problems in mechanical vibrations, electric circuits and bending of beams | ||