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Course10410408655 lectures

Advanced Mathematical Methods for Chemistry

Prof. Madhav Ranganathan · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

Week 1: Vectors, linear independence, vector differentiation and transfomation

  1. Lecture 1: Vectors, Vector Operations and Linear Independence Video
  2. Lecture 2: Vector Operations, Generalization of Vectors Video
  3. Lecture 3: Vector Differentiation, Vector Transformations Video
  4. Lecture 4: Vector Integration, Line, Surface and Volume Integrals Video
  5. Lecture 5: Practice Problems Video

Week 2: Matrices, Linear Transformations, Special Matrices, Eigenvalues

  1. Lecture 6: Matrix as a vector transformation, linear system Video
  2. Lecture 7: Special Matrices: Symmetric, Orthogonal, Complex Video
  3. Lecture 8: Rotational Matrices, Eigenvalues and Eigenvectors Video
  4. Lecture 9: Determinants, Matrix Inverse Video
  5. Lecture 10: Practice Problems Video

Week 3: Special Functions

  1. Lecture 11: Step Function, Delta Function Video
  2. Lecture 12 : Gamma Function, Error Function Video
  3. Lecture 13: Spherical Polar Coordinates Video
  4. Lecture 14: Cylindrical Polar Coordinates, Integrals Video
  5. Lecture 15: Recap of Module 3, Practice Problems Video

Week 4:1st order ODEs

  1. Lecture 16: ODEs and PDEs, First order ODEs, system of 1st order ODEs Video
  2. Lecture 17: First order ODEs, exact integrals, integrating factors Video
  3. Lecture 18: System of first order ODEs, Linear first order ODEs Video
  4. Lecture 19: General solution of a system of linear first order ODEs with constant coefficients Video
  5. Lecture 20: Recap of Module 4, Practice problems Video

Week 5: 2nd Order ODEs, Power Series Method

  1. Lecture 21: Homogeneous 2nd Order ODE, Basis Functions Video
  2. Lecture 22: Nonhomogeneous 2nd Order ODE Video
  3. Lecture 23: Power Series Method of Solving ODEs Video
  4. Lecture 24: Frobenius Method / Power Series Method Video
  5. Lecture 25: Time-independent Schrodinger Equation for H-atom Video

Week 6: Optimization, Constrained Optimization

  1. Lecture 26: Maxima and Minima, Taylor Series Video
  2. Lecture 27: Taylor Series for functions of several variables Video
  3. Lecture 28: Critical Points of Functions Video
  4. Lecture 29: Lagranges Method of Undetermined Multipliers Video
  5. Lecture 30: Recap of Module 6, Practice Problems Video

Week 7: Nonlinear Differential Equations, Phase Plane, Stability Analysis

  1. Lecture 31: Nonlinear Differential Equations Video
  2. Lecture 32: Phase Plane of A Pendulum Video
  3. Lecture 33: Stability of Critical Points Video
  4. Lecture 34: Population Dynamics Models Video
  5. Lecture 35: Recap of Module 7, Practice Problems Video

Week 8: Fourier Series, Orthogonal Eigenfunctions, Sturm-Liouville Theory

  1. Lecture 36: Fourier Series, Fourier Expansion of Periodic Functions Video
  2. Lecture 37 (Part A): Fourier Expansions and Differential Equations Video
  3. Lecture 37 (Part B): Fourier Expansions and Differential Equations Video
  4. Lecture 38: Orthogonal Eigenfunctions, Sturm-Liouville Theory Video
  5. Lecture 39: Recap of Module 8, Practice Problems Video

Week 9: Integral Transforms

  1. Lecture 40: Fourier Transforms Video
  2. Lecture 41: Properties of Fourier Transforms Video
  3. Lecture 42: Fourier Transforms and Partial Differential Equations Video
  4. Lecture 43: Laplace Transforms Video
  5. Lecture 44: Recap of Module 9, Practice Problems Video

Week 10:Partial Differential Equations

  1. Lecture 45: Partial Differential Equations, Boundary Conditions Video
  2. Lecture 46: Separation of Variables Video
  3. Lecture 47 (Part A): Two-dimensional Wave Equation, Bessel Functions Video
  4. Lecture 47 (Part B): Two-dimensional Wave Equation, Bessel Functions Video
  5. Lecture 48: Recap of Module 10, Practice Problems Video

Week 11: Probability, Probability Distributions and Error Analysis

  1. Lecture 49: Discrete and Continuous Random Variables Video
  2. Lecture 50: Probability Distribution Functions Video
  3. Lecture 51: Poisson Distribution, Gaussain Distribution Video
  4. Lecture 52: Error Estimates, Least Square Fit, Correlation Functions Video
  5. Lecture 53: Recap of Module 11, Practice Problems Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Chemistry and Biochemistry
Teacher
Prof. Madhav Ranganathan
Level
Undergraduate
Language
English
Subjects
Chemistry
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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