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Last updated:

September 23, 2023

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

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)

Course Curriculum

    • Lecture 01 – Errors, Precision of Measurement, Accuracy, Significant Figures Unlimited
    • Lecture 02 – Probability, Probability Distributions, Binomial and Poisson Distributions Unlimited
    • Lecture 03 – Gaussian Distribution, Integrals, Averages Unlimited
    • Lecture 04 – Estimation of Parameters, Errors, Least Square Fit Unlimited
    • Lecture 05 – Practice Problems 1 Unlimited
    • Lecture 06 – Vectors and Scalars, Vector Space, Vector Products Unlimited
    • Lecture 07 – Linear Independence, Basis, Dimensionality Unlimited
    • Lecture 08 – Vector Functions, Scalar and Vector Fields, Vector Differentiation Unlimited
    • Lecture 09 – Vector Differentiation: Gradient, Divergence, Curl Unlimited
    • Lecture 10 – Practice Problems 2 Unlimited
    • Lecture 11 – Line Integrals and Potential Theory Unlimited
    • Lecture 12 – Surface and Volume Integrals Unlimited
    • Lecture 13 – Matrices, Matrix Operations and Determinants Unlimited
    • Lecture 14 – Cramer’s Rule Unlimited
    • Lecture 15 – Practice Problems 3 Unlimited
    • Lecture 16 – Rank of Matrix, Inverse of a Matrix Unlimited
    • Lecture 17 – Eigenvalues and Eigenvectors for a Matrix Unlimited
    • Lecture 18 – Special Matrices: Symmetric, Orthogonal, Hermitian, Unitary Unlimited
    • Lecture 19 – Spectral Decomposition: Normal Modes, Sparse Matrices, Ill-conditioned Systems Unlimited
    • Lecture 20 – Practice Problems 4 Unlimited
    • Lecture 21 – Differential Equations, Order, 1st Order ODEs, Separation of Variables Unlimited
    • Lecture 22 – Exact Differentials Unlimited
    • Lecture 23 – Integrating Factors Unlimited
    • Lecture 24 – System of 1st Order ODES, Matrix Method Unlimited
    • Lecture 25 – Practice Problems 5 Unlimited
    • Lecture 26 – Types of 2nd Order ODEs, Nature of Solutions Unlimited
    • Lecture 27 – Homogeneous 2nd Order ODEs, Solution using Basis Functions Unlimited
    • Lecture 28 – Homogeneous and Nonhomogeneous Equations Unlimited
    • Lecture 29 – Nonhomogeneous Equations – Variation of Parameters Unlimited
    • Lecture 30 – Practice Problems 6 Unlimited
    • Lecture 31 – Power Series Method for Solving Legendre Differential Equation Unlimited
    • Lecture 32 – Properties of Legendre Differential Equation Unlimited
    • Lecture 33 – Associated Legendre Polynomials, Spherical Harmonics Unlimited
    • Lecture 34 – Hermite Polynomials, Solutions of Quantum Harmonic Oscillator Unlimited
    • Lecture 35 – Practice Problems 7 Unlimited
    • Lecture 36 – Conditions for Power Series Solution Unlimited
    • Lecture 37 – Frobenius Method, Bessel Functions Unlimited
    • Lecture 38 – Prosperities of Bessel Functions, Circular Boundary Problems Unlimited
    • Lecture 39 – Laguerre Polynomials, Solution to Radial Part of H-atom Unlimited
    • Lecture 40 – Practice Problems 8 Unlimited

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