Mathematics for Chemistry

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

Lecture 26 - Types of 2nd Order ODEs, Nature of Solutions

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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