Learn · Advanced Mathematical Methods for Chemistry

Lecture 2 of 55Week 1: Vectors, linear independence, vector differentiation and transfomation

Lecture 2: Vector Operations, Generalization of Vectors

Prof. Madhav Ranganathan · IIT Kanpur

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From
Advanced Mathematical Methods for Chemistry, IIT Kanpur (at NPTEL)
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CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures

  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
  6. Lecture 6: Matrix as a vector transformation, linear system Video
  7. Lecture 7: Special Matrices: Symmetric, Orthogonal, Complex Video
  8. Lecture 8: Rotational Matrices, Eigenvalues and Eigenvectors Video
  9. Lecture 9: Determinants, Matrix Inverse Video
  10. Lecture 10: Practice Problems Video
  11. Lecture 11: Step Function, Delta Function Video
  12. Lecture 12 : Gamma Function, Error Function Video
  13. Lecture 13: Spherical Polar Coordinates Video
  14. Lecture 14: Cylindrical Polar Coordinates, Integrals Video
  15. Lecture 15: Recap of Module 3, Practice Problems Video
  16. Lecture 16: ODEs and PDEs, First order ODEs, system of 1st order ODEs Video
  17. Lecture 17: First order ODEs, exact integrals, integrating factors Video
  18. Lecture 18: System of first order ODEs, Linear first order ODEs Video
  19. Lecture 19: General solution of a system of linear first order ODEs with constant coefficients Video
  20. Lecture 20: Recap of Module 4, Practice problems Video
  21. Lecture 21: Homogeneous 2nd Order ODE, Basis Functions Video
  22. Lecture 22: Nonhomogeneous 2nd Order ODE Video
  23. Lecture 23: Power Series Method of Solving ODEs Video
  24. Lecture 24: Frobenius Method / Power Series Method Video
  25. Lecture 25: Time-independent Schrodinger Equation for H-atom Video
  26. Lecture 26: Maxima and Minima, Taylor Series Video
  27. Lecture 27: Taylor Series for functions of several variables Video
  28. Lecture 28: Critical Points of Functions Video
  29. Lecture 29: Lagranges Method of Undetermined Multipliers Video
  30. Lecture 30: Recap of Module 6, Practice Problems Video
  31. Lecture 31: Nonlinear Differential Equations Video
  32. Lecture 32: Phase Plane of A Pendulum Video
  33. Lecture 33: Stability of Critical Points Video
  34. Lecture 34: Population Dynamics Models Video
  35. Lecture 35: Recap of Module 7, Practice Problems Video
  36. Lecture 36: Fourier Series, Fourier Expansion of Periodic Functions Video
  37. Lecture 37 (Part A): Fourier Expansions and Differential Equations Video
  38. Lecture 37 (Part B): Fourier Expansions and Differential Equations Video
  39. Lecture 38: Orthogonal Eigenfunctions, Sturm-Liouville Theory Video
  40. Lecture 39: Recap of Module 8, Practice Problems Video
  41. Lecture 40: Fourier Transforms Video
  42. Lecture 41: Properties of Fourier Transforms Video
  43. Lecture 42: Fourier Transforms and Partial Differential Equations Video
  44. Lecture 43: Laplace Transforms Video
  45. Lecture 44: Recap of Module 9, Practice Problems Video
  46. Lecture 45: Partial Differential Equations, Boundary Conditions Video
  47. Lecture 46: Separation of Variables Video
  48. Lecture 47 (Part A): Two-dimensional Wave Equation, Bessel Functions Video
  49. Lecture 47 (Part B): Two-dimensional Wave Equation, Bessel Functions Video
  50. Lecture 48: Recap of Module 10, Practice Problems Video
  51. Lecture 49: Discrete and Continuous Random Variables Video
  52. Lecture 50: Probability Distribution Functions Video
  53. Lecture 51: Poisson Distribution, Gaussain Distribution Video
  54. Lecture 52: Error Estimates, Least Square Fit, Correlation Functions Video
  55. Lecture 53: Recap of Module 11, Practice Problems Video