Mathematics for Chemistry. Instructor: Prof. Madhav Ranganathan, Department of Chemistry, IIT Kanpur. This course will introduce the students to various basic mathematical methods for chemists. The methods involve error analysis, probability and statistics, linear algebra, vectors and matrices, first and second order differential equations and their solution. Students in 3rd year B.Sc or 1st year M.Sc are encouraged to take this course. The problem will be mathematical and hence the format of assignments and exams will be subjective problem solving which will be graded offline.
(from nptel.ac.in)
| Error Analysis, Probability and Distributions |
| Lecture 01 - Errors, Precision of Measurement, Accuracy, Significant Figures |
| Lecture 02 - Probability, Probability Distributions, Binomial and Poisson Distributions |
| Lecture 03 - Gaussian Distribution, Integrals, Averages |
| Lecture 04 - Estimation of Parameters, Errors, Least Square Fit |
| Lecture 05 - Practice Problems 1 |
| Vectors, Vector Spaces and Vector Functions |
| Lecture 06 - Vectors and Scalars, Vector Space, Vector Products |
| Lecture 07 - Linear Independence, Basis, Dimensionality |
| Lecture 08 - Vector Functions, Scalar and Vector Fields, Vector Differentiation |
| Lecture 09 - Vector Differentiation: Gradient, Divergence, Curl |
| Lecture 10 - Practice Problems 2 |
| Vector Integration, Matrices, Determinants, Linear Systems, Cramer's Rule |
| Lecture 11 - Line Integrals and Potential Theory |
| Lecture 12 - Surface and Volume Integrals |
| Lecture 13 - Matrices, Matrix Operations and Determinants |
| Lecture 14 - Cramer's Rule |
| Lecture 15 - Practice Problems 3 |
| Matrix Rank, Inverse, Eigenvalues, Eigenvectors, Special Matrices, Normal Modes |
| Lecture 16 - Rank of Matrix, Inverse of a Matrix |
| Lecture 17 - Eigenvalues and Eigenvectors for a Matrix |
| Lecture 18 - Special Matrices: Symmetric, Orthogonal, Hermitian, Unitary |
| Lecture 19 - Spectral Decomposition: Normal Modes, Sparse Matrices, Ill-conditioned Systems |
| Lecture 20 - Practice Problems 4 |
| First Order Ordinary Differential Equations |
| Lecture 21 - Differential Equations, Order, 1st Order ODEs, Separation of Variables |
| Lecture 22 - Exact Differentials |
| Lecture 23 - Integrating Factors |
| Lecture 24 - System of 1st Order ODES, Matrix Method |
| Lecture 25 - Practice Problems 5 |
| Second Order ODEs, Homogeneous/Nonhomogeneous Equations |
| Lecture 26 - Types of 2nd Order ODEs, Nature of Solutions |
| Lecture 27 - Homogeneous 2nd Order ODEs, Solution using Basis Functions |
| Lecture 28 - Homogeneous and Nonhomogeneous Equations |
| Lecture 29 - Nonhomogeneous Equations - Variation of Parameters |
| Lecture 30 - Practice Problems 6 |
| Power Series Method for Solving 2nd Order ODEs |
| Lecture 31 - Power Series Method for Solving Legendre Differential Equation |
| Lecture 32 - Properties of Legendre Differential Equation |
| Lecture 33 - Associated Legendre Polynomials, Spherical Harmonics |
| Lecture 34 - Hermite Polynomials, Solutions of Quantum Harmonic Oscillator |
| Lecture 35 - Practice Problems 7 |
| Modified Power Series Method, Frobenius Method |
| Lecture 36 - Conditions for Power Series Solution |
| Lecture 37 - Frobenius Method, Bessel Functions |
| Lecture 38 - Prosperities of Bessel Functions, Circular Boundary Problems |
| Lecture 39 - Laguerre Polynomials, Solution to Radial Part of H-atom |
| Lecture 40 - Practice Problems 8 |