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Mathematical Methods in Physics 1

Prof. Auditya Sharma · IISER Bhopal

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Vectors Video
  2. Linear vector spaces Video
  3. Linear vector spaces: immediate consequences Video
  4. Dot product of Euclidean vectors Video
  5. Inner product on a Linear vector space Video
  6. Cauchy-Schwartz inequality for Euclidean vectors Video
  7. Cauchy-Schwartz inequality for vectors from LVS Video
  8. Applications of the Cauchy-Schwartz inequality Video
  9. Triangle inequality Video
  10. Linear dependence and independence of vectors Video
  11. Row reduction of matrices Video
  12. Rank of a matrix Video

Week 2

  1. Rank of a matrix: consequences Video
  2. Determinants and their properties Video
  3. The rank of a matrix using determinants Video
  4. Cramer's rule Video
  5. Square system of equations Video
  6. Homogeneous equations Video
  7. The rank of a matrix and linear dependence Video
  8. Span, basis, and dimension of a LVS Video
  9. Gram-Schmidt orthogonalization Video
  10. Vector subspaces Video
  11. Linear operators Video
  12. Inverse of an operator Video
  13. Adjoint of an operator Video

Week 3

  1. Projection operators Video
  2. Eigenvalues and Eigenvectors Video
  3. Hermitian operators Video
  4. Unitary operators Video
  5. Normal operators Video
  6. Similarity and Unitary transformations Video
  7. Matrix representations Video
  8. Eigenvalues and Eigenvectors of matrices Video
  9. Defective matrices Video
  10. Eigenvalues and eigenvectors: useful results Video
  11. A class of invertible matrices Video
  12. Diagonalization of matrices Video
  13. Diagonalizability of matrices Video
  14. Functions of matrices Video

Week 4

  1. SHM and waves Video
  2. Periodic functions Video
  3. Average value of a function Video
  4. Piecewise continuous functions Video
  5. Orthogonal basis: Fourier series Video
  6. Fourier coefficients Video
  7. Dirichlet Conditions Video
  8. Complex Form of Fourier Series Video
  9. Other intervals: arbitrary period Video
  10. Even and Odd Functions Video
  11. Differentiating Fourier series Video
  12. Parseval's theorem Video
  13. Fourier series to Fourier transforms Video
  14. Fourier Sine and Cosine transforms Video
  15. Parseval's theorem for Fourier series Video

Week 5

  1. Ordinary Differential equations Video
  2. First order ODEs Video
  3. Linear first order ODEs Video
  4. Orthogonal Trajectories Video
  5. Exact differential equations Video
  6. Special first order ODEs Video
  7. Solutions of linear first-order ODEs Video
  8. Revisit linear first-order ODEs Video
  9. ODEs in disguise Video
  10. 2nd order Homogeneous linear equations with constant coefficients Video
  11. The use of a known solution to find another Video
  12. An alternate approach to auxiliary equation Video

Week 6

  1. Inhomogeneous second order equations Video
  2. Methods to find a Particular solution Video
  3. Successive Integration of two first order equations Video
  4. Illustrative examples. Video
  5. Variation of Parameters Video
  6. Vibrations in mechanical systems. Video
  7. Forced Vibrations. Video
  8. Resonance Video
  9. Linear Superposition Video

Week 7

  1. Laplace Transform (LT) Video
  2. Basic Properties of Laplace Transforms Video
  3. Step functions, Translations, and Periodic functions Video
  4. The Inverse Laplace Transform Video
  5. Convolution of functions Video
  6. Solving ODEs using Laplace transforms Video
  7. The Dirac Delta function Video
  8. Properties of the Dirac Delta function Video

Week 8

  1. Green's function method Video
  2. Green's function method: Boundary value problem Video
  3. Power series method Video
  4. Power series solutions about an ordinary point Video
  5. Initial value problem: power series solution Video
  6. Frobenius method for regular singular points Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISER Bhopal
Department
Mathematics
Teacher
Prof. Auditya Sharma
Level
Undergraduate
Language
English
Subjects
Mathematics
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. Coordinated by IIT Madras.
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