CHM600A - Mathematics For Chemistry

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)