### CHM600A

3-0-0-9 Courses with significant overlap with this course:

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Date of approval: dd-mmm-yyyy Prerequisites:

Remark: CHM 521: Only for 2 yr Msc Chemistry students

CHM600: Only for Ph.D. Students

Course Contents

Error Analysis: Error, precision, accuracy, significant figures, mean, standard deviation, propagation of errors. (2)

Vectors and Matrices: Dot product, cross product, gradient, divergence, continuity equation, curl. Vector integration: Stokes’ and Gauss’ theorems, vector spaces. Matrices: coordinate transformation, Jacobian, system of linear equations, inverse of a matrix, Cramer’s rule, Gaussian elimination and its variants, eigenvalues and eigenvectors. (10)

Ordinary Differential Equations and Special Functions: General and particular solutions of a differential equation. First order equations and their applications. Separation of variables, equations reducible to separable form. Exact differential equations, non-homogeneous differential equations, integrating factors. Second order linear differential equations: homogeneous with constant coefficients, characteristic equation, general solution, particular solution. Non-homogeneous linear second order equations, Sturm-Liouville theorem, Power series method of solution of differential equations, Special functions such as Legendre and Hermite polynomials, Beta, Gamma and error functions. Non-linear differential equations. (14)

Fourier series and transform, basic theorems, convolution. Laplace transform and its properties, Applications of Fourier and Laplace transforms. (6)

Numerical Methods: Numerical differentiation and interpolation, Numerical quadrature, Newton-Cotes formulae, Simultaneous equations and matrix eigenvalues, Numerical solution of differential equations. (8)

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• G.B. Arfken and H.J. Weber, Mathematical Methods for Physicists, Academic Press (2001).

• M.L. Boas, Mathematical Methods in the Physical Sciences, John Wiley, India (2007).

• E. Kreyszig, Advanced Engineering Mathematics, John Wiley, New York (1999).

• D. McQuarrie, Mathematical methods for scientists and engineers, University Science Books (2003)    