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Course Outline:
Matrices: Basic concept, addition of matrices and its multiplication with a scalar number, Partitioning of matrices, Matrix multiplication and its properties, Special matrices, transpose of a matrix, Adjoin and inverse of a square matrix, Row operations Echelon & reduced Echelon form of matrix, rank of matrix, Application of Matrices, Eigen values and Eigenvectors
1st Order Differential Equations: Basic concepts, formation and solution of differential equations by direct integration and by separating the variables. Homogeneous equations and equations reducible to homogeneous form. Linear differential equations of the 1st order and equations reducible to the linear form, Bernoulli’s equations and orthogonal trajectories, engineering application.
2nd and Higher Orders Equations: Special types of 2nd order differential equations with constant coefficients and their solutions. The operator D, Inverse operator 1/ D, Solution of differential equations by operator D methods, Special cases, Cauchy’s differential equations, Simultaneous differential equations, Simple application of differential equations in Engineering.
Partial Differential Equations: Basic concepts and formation of partial differential equations, Linear homogeneous partial differential equations and relations to ordinary differential equations, Solution of first order linear and special types of second and higher order differential equations, D’Alembert’s solution of the wave equation and two dimensional wave equations, Lagrange’s solution, Various standard forms.
Fourier Series: Periodic functions and expansion of periodic functions in Fourier series and Fourier coefficients. Expansion of functions with arbitrary periods, Odd and even functions and their Fourier series, Half range expansions of Fourier series.
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