NOC:Advanced Mathematical Methods for Chemistry


Lecture 1 - Vectors, Vector Operations and Linear Independence


Lecture 2 - Vector Operations, Generalization of Vectors


Lecture 3 - Vector Differentiation, Vector Transformations


Lecture 4 - Vector Integration, Line, Surface and Volume Integrals


Lecture 5 - Practice Problems


Lecture 6 - Matrix as a vector transformation, linear system


Lecture 7 - Special Matrices: Symmetric, Orthogonal, Complex


Lecture 8 - Rotational Matrices, Eigenvalues and Eigenvectors


Lecture 9 - Determinants, Matrix Inverse


Lecture 10 - Practice Problems


Lecture 11 - Step Function, Delta Function


Lecture 12 - Gamma Function, Error Function


Lecture 13 - Spherical Polar Coordinates


Lecture 14 - Cylindrical Polar Coordinates, Integrals


Lecture 15 - Recap of Module 3, Practice Problems


Lecture 16 - ODEs and PDEs, First order ODEs, system of 1st order ODEs


Lecture 17 - First order ODEs, exact integrals, integrating factors


Lecture 18 - System of first order ODEs, Linear first order ODEs


Lecture 19 - General solution of a system of linear first order ODEs with constant coefficients


Lecture 20 - Recap of Module 4, Practice problems


Lecture 21 - Homogeneous 2nd Order ODE, Basis Functions


Lecture 22 - Nonhomogeneous 2nd Order ODE


Lecture 23 - Power Series Method of Solving ODEs


Lecture 24 - Frobenius Method / Power Series Method


Lecture 25 - Time-independent Schrodinger Equation for H-atom


Lecture 26 - Maxima and Minima, Taylor Series


Lecture 27 - Taylor Series for functions of several variables


Lecture 28 - Critical Points of Functions


Lecture 29 - Lagranges Method of Undetermined Multipliers


Lecture 30 - Recap of Module 6, Practice Problems


Lecture 31 - Nonlinear Differential Equations


Lecture 32 - Phase Plane of A Pendulum


Lecture 33 - Stability of Critical Points


Lecture 34 - Population Dynamics Models


Lecture 35 - Recap of Module 7, Practice Problems


Lecture 36 - Fourier Series, Fourier Expansion of Periodic Functions


Lecture 37 - (Part A): Fourier Expansions and Differential Equations


Lecture 38 - (Part B): Fourier Expansions and Differential Equations


Lecture 39 - Orthogonal Eigenfunctions, Sturm-Liouville Theory


Lecture 40 - Recap of Module 8, Practice Problems


Lecture 41 - Fourier Transforms


Lecture 42 - Properties of Fourier Transforms


Lecture 43 - Fourier Transforms and Partial Differential Equations


Lecture 44 - Laplace Transforms


Lecture 45 - Recap of Module 9, Practice Problems


Lecture 46 - Partial Differential Equations, Boundary Conditions


Lecture 47 - Separation of Variables


Lecture 48 - (Part A): Two-dimensional Wave Equation, Bessel Functions


Lecture 49 - (Part B): Two-dimensional Wave Equation, Bessel Functions


Lecture 50 - Recap of Module 10, Practice Problems


Lecture 51 - Discrete and Continuous Random Variables


Lecture 52 - Probability Distribution Functions


Lecture 53 - Poisson Distribution, Gaussain Distribution


Lecture 54 - Error Estimates, Least Square Fit, Correlation Functions


Lecture 55 - Recap of Module 11, Practice Problems