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Professional PGD in Environmental Engineering
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 Euclidean spaces, Vector spaces, Subspaces, Linear independence and dependence, Basis and
dimensions, Normed spaces, Inner product spaces, Angle and orthogonality in Inner product
spaces, Orthogonal basis; Linear transformations, Kernel and range, Inverse linear
transformation, Rank and nullity of linear transformation, Eigenvalues and eigenvectors,
Applications to relevant problems.
 Formation of differential equations; Solution of various types of first order differential equations;
orthogonal trajectories, Application in physical problems. Linear differential equations of second
order, Complementary function and particular integral. Solution of non-homogeneous linear
differential equations of second order and higher by (i) the method of undetermined coefficients
(ii) the method of variation of parameters. Laplace transform, Solution of initial value
problems by Laplace transform.
 Formation of partial differential equations; Equations reducible to ordinary differential
 Periodic functions. Even and odd functions. Fourier series of functions of period 2 and arbitrary
period; Half range series.

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Linear Algebra and Differential Equation.pdf
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