Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Significant digits, precision, accuracy, number representation, errors (roundoff errors, experimental errors, truncation, error propagation).
- Introduction to numerical libraries,Fortran, Matlab and Mathematica.
- Linear algebra: Matrices and determinants, eigenvalues and eigenvectors, simultaneous equations (Gauss elimination, LU factorization), diagonalization methods (Jacobi, Hausholder and Davidson), matrix exponential. (Connectivity matrices, Hückel matrices, charge density bond order matrix, Normal modes of polyatomic molecules, standard orientations of molecules, Orthogonalization of nonorthogonal basis sets, Rotation matrices, Euler angles, symmetry operations of point groups, coordinate transformations).
- Numerical interpolation and extrapolation,splines, 2D plotting. (The problems will be chosen from experimental data, involving spectra, potential energy curves of diatomic molecules, heat capacities of etc.)
- Numerical differentiation and integration. (Integration of spectra.)
- Infinite series, power series, convergence, L’Hospital’s rule.
- Complex numbers.
- Vector analysis and multivariate calculus, plotting in 3D.
- Calculus of variations and optimization methods. (Least squares fitting, nonlinear least squares optimization).
- Fourier transform and fast Fourier transform methods, convolution. (analysis of spectral data).
- Differential equations: First-Order ODE, Second-Order Linear ODEs,Higher Order Linear ODEs,Systems of ODEs,Phase Plane, Series Solutions of ODEs, Special Functions,Laplace Transforms. (Kinetics of chemical reactions, diffusion equation).
- Difference methods, discrete variable representation (DVR). (Vibrational and rovibrational states of diatomic molecules from a numerical potential) Probability and statistics.
- Erwin Kreyzig, Advanced Engineering Mathematics
- Numerical Recipes in Fortran 90 (second edition)., Numerical Recipes in C
- Mary L. Boas, Mathematical Methods In the Physical sciences
- M. P. Hobson & K. F. Riley, Essential Mathematical Methods for the Physical Sciences
- George B. Arfken, Hans J. Weber & Frank E. Harris, Mathematical methods for physicists
