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Course10410408140 lectures

Mathematics for Chemistry

Prof. Madhav Ranganathan · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

Week 1: Error Analysis, Probability and Distributions

  1. Lecture 1: Errors, precision and accuracy Video
  2. Lecture 2: Probability and distributions Video
  3. Lecture 3: Gaussian distribution and integrals Video
  4. Lecture4:Gaussian distribution, integrals, averages Video
  5. Lecture 5: Practice problems 1 Video

Week 2: Vectors, Vector Spaces and Vector Functions

  1. Lecture 6: Vectors and Vector Spaces Video
  2. Lecture 7: Linear Independence Video
  3. Lecture 8: Scalar and vector fields Video
  4. Lecture 9: Gradient, divergence and curl Video
  5. Lecture 10: Practice problems 2 Video

Week 3: Vector Integration, Matrices, Determinants, Linear Systems, Cramers Rule

  1. Lecture 11: Line integrals, Potential Theory Video
  2. Lecture 12: Surface and Volume Integrals Video
  3. Lecture 13: Matrices Video
  4. Lecture 14: Linear Systems, Cramer's Rule Video
  5. Lecture 15: Practice Problems 3 Video

Week 4: Matrix Rank, Inverse, Eigenvalues, Eigenvectors, Special Matrices, Normal modes

  1. Lecture 16: Rank and Inverse of a Matrix Video
  2. Lecture 17: Eigenvalues and Eigenvectors Video
  3. Lecture 18: Special matrices Video
  4. Lecture 19: Spectral decomposition and Normal modes Video
  5. Lecture 20: Practice Problems 4 Video

Week 5: First Order Differential Equations

  1. Lecture 21: Differential equations, Order Video
  2. Lecture 22: Exact and Inexact differentials Video
  3. Lecture 23: Integrating Factors Video
  4. Lecture 24: System of 1st order ODEs, matrix methods Video
  5. Lecture 25: Practice Problems 5 Video

Week 6: Second Order ODEs, Homogeneous/Nonhomogeneous equations

  1. Lecture 26: Types of 2nd order ODEs, nature of solutions Video
  2. Lecture 27: Homogeneous 2nd order ODEs Video
  3. Lecture 28: Homogeneous and nonhomogeneous equations Video
  4. Lecture 29: Nonhomogeneous equations – Variation of parameters Video
  5. Lecture 30: Practice Problems 6 Video

Week 7: Power Series Method for Solving 2nd Order ODEs

  1. Lecture 31: Power series method for solving Legendre DE Video
  2. Lecture 32: Properties of Legendre Polynomials Video
  3. Lecture 33: Associated Legendre Polynomials, Spherical Harmonics Video
  4. Lecture 34: Hermite Polynomials, Solution of Quantum Harmonic Oscillator Video
  5. Lecture 35: Practice Problems 7 Video

Week 8: Modified Power Series Method, Frobenius Method

  1. Lecture 36: Conditions for power series solution Video
  2. Lecture 37: Frobenius Method, Bessel Functions Video
  3. Lecture 38: Properties of Bessel Functions, circular boundary problems Video
  4. Lecture 39: Leguerre Polynomials, solution to radial part of H-atom Video
  5. Lecture 40: Practice Problems 8 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
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