Syllabus
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Course Code: ST-103 Course Name: Linear Algebra and Numerical Analysis |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Vector Spaces: Linear dependence and independence , Basis and dimension of a vector space, examples of vector spaces .Linear transformations , Algebra of matrices , row and column spaces of a matrix , elementary matrices , determinant , rank and inverse of a matrix , null space and nullity ,Hermit canonical form. Solutions of matrixequations. |
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| 2 | Orthogonal Transformations and Orthogonal matrix, Gram-Schmidt orthogonalisation process, characteristic roots and characteristic vectors, diagonalisation of a matrix, triangular form of a matrix .Real quadratic forms, reduction and classification of quadratic forms . |
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| 3 | Difference and shift operators, identities involving separation of symbols and differences of zero, Newton's forward and backward interpolation formulae and estimation of the missing terms . Divided differences, Newton's and Lagrange's interpolation formulae for unequal intervals. Solution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidal methods. |
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| 4 | Numerical Integration : Simpson's one-third and three eighth and Weddle's formulae, The Euler-Meclaurin's summation formula . Numerical solutions of ODEs using Picard, Euler, modified Euler and Runge-Kutta methods. |
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