| Module Name | Download |
|---|
| Sl.No | Chapter Name | MP4 Download |
|---|---|---|
| 1 | Vectors | Download |
| 2 | Linear vector spaces | Download |
| 3 | Linear vector spaces: immediate consequences | Download |
| 4 | Dot product of Euclidean vectors | Download |
| 5 | Inner product on a Linear vector space | Download |
| 6 | Cauchy-Schwartz inequality for Euclidean vectors | Download |
| 7 | Cauchy-Schwartz inequality for vectors from LVS | Download |
| 8 | Applications of the Cauchy-Schwartz inequality | Download |
| 9 | Triangle inequality | Download |
| 10 | Linear dependence and independence of vectors | Download |
| 11 | Row reduction of matrices | Download |
| 12 | Rank of a matrix | Download |
| 13 | Rank of a matrix: consequences | Download |
| 14 | Determinants and their properties | Download |
| 15 | The rank of a matrix using determinants | Download |
| 16 | Cramer's rule | Download |
| 17 | Square system of equations | Download |
| 18 | Homogeneous equations | Download |
| 19 | The rank of a matrix and linear dependence | Download |
| 20 | Span, basis, and dimension of a LVS | Download |
| 21 | Gram-Schmidt orthogonalization | Download |
| 22 | Vector subspaces | Download |
| 23 | Linear operators | Download |
| 24 | Inverse of an operator | Download |
| 25 | Adjoint of an operator | Download |
| 26 | Projection operators | Download |
| 27 | Eigenvalues and Eigenvectors | Download |
| 28 | Hermitian operators | Download |
| 29 | Unitary operators | Download |
| 30 | Normal operators | Download |
| 31 | Similarity and Unitary transformations | Download |
| 32 | Matrix representations | Download |
| 33 | Eigenvalues and Eigenvectors of matrices | Download |
| 34 | Defective matrices | Download |
| 35 | Eigenvalues and eigenvectors: useful results | Download |
| 36 | Transformation of Basis | Download |
| 37 | A class of invertible matrices | Download |
| 38 | Diagonalization of matrices | Download |
| 39 | Diagonalizability of matrices | Download |
| 40 | Functions of matrices | Download |
| 41 | SHM and waves | Download |
| 42 | Periodic functions | Download |
| 43 | Average value of a function | Download |
| 44 | Piecewise continuous functions | Download |
| 45 | Orthogonal basis: Fourier series | Download |
| 46 | Fourier coefficients | Download |
| 47 | Dirichlet Conditions | Download |
| 48 | Complex Form of Fourier Series | Download |
| 49 | Other intervals: arbitrary period | Download |
| 50 | Even and Odd Functions | Download |
| 51 | Differentiating Fourier series | Download |
| 52 | Parseval's theorem | Download |
| 53 | Fourier series to Fourier transforms | Download |
| 54 | Fourier Sine and Cosine transforms | Download |
| 55 | Parseval's theorem for Fourier series | Download |
| 56 | Ordinary Differential equations | Download |
| 57 | First order ODEs | Download |
| 58 | Linear first order ODEs | Download |
| 59 | Orthogonal Trajectories | Download |
| 60 | Exact differential equations | Download |
| 61 | Special first order ODEs | Download |
| 62 | Solutions of linear first-order ODEs | Download |
| 63 | Revisit linear first-order ODEs | Download |
| 64 | ODEs in disguise | Download |
| 65 | 2nd order Homogeneous linear equations with constant coefficients | Download |
| 66 | The use of a known solution to find another | Download |
| 67 | An alternate approach to auxiliary equation | Download |
| 68 | Inhomogeneous second order equations | Download |
| 69 | Methods to find a Particular solution | Download |
| 70 | Successive Integration of two first order equations | Download |
| 71 | Illustrative examples. | Download |
| 72 | Variation of Parameters | Download |
| 73 | Vibrations in mechanical systems. | Download |
| 74 | Forced Vibrations. | Download |
| 75 | Resonance | Download |
| 76 | Linear Superposition | Download |
| 77 | Laplace Transform (LT) | Download |
| 78 | Basic Properties of Laplace Transforms | Download |
| 79 | Step functions, Translations, and Periodic functions | Download |
| 80 | The Inverse Laplace Transform | Download |
| 81 | Convolution of functions | Download |
| 82 | Solving ODEs using Laplace transforms | Download |
| 83 | The Dirac Delta function | Download |
| 84 | Properties of the Dirac Delta function | Download |
| 85 | Green's function method | Download |
| 86 | Green's function method: Boundary value problem | Download |
| 87 | Power series method | Download |
| 88 | Power series solutions about an ordinary point | Download |
| 89 | Initial value problem: power series solution | Download |
| 90 | Frobenius method for regular singular points | Download |
| Sl.No | Chapter Name | English |
|---|---|---|
| 1 | Vectors | Download To be verified |
| 2 | Linear vector spaces | Download To be verified |
| 3 | Linear vector spaces: immediate consequences | Download To be verified |
| 4 | Dot product of Euclidean vectors | Download To be verified |
| 5 | Inner product on a Linear vector space | Download To be verified |
| 6 | Cauchy-Schwartz inequality for Euclidean vectors | Download To be verified |
| 7 | Cauchy-Schwartz inequality for vectors from LVS | Download To be verified |
| 8 | Applications of the Cauchy-Schwartz inequality | Download To be verified |
| 9 | Triangle inequality | Download To be verified |
| 10 | Linear dependence and independence of vectors | Download To be verified |
| 11 | Row reduction of matrices | Download To be verified |
| 12 | Rank of a matrix | Download To be verified |
| 13 | Rank of a matrix: consequences | Download To be verified |
| 14 | Determinants and their properties | Download To be verified |
| 15 | The rank of a matrix using determinants | Download To be verified |
| 16 | Cramer's rule | Download To be verified |
| 17 | Square system of equations | Download To be verified |
| 18 | Homogeneous equations | Download To be verified |
| 19 | The rank of a matrix and linear dependence | Download To be verified |
| 20 | Span, basis, and dimension of a LVS | Download To be verified |
| 21 | Gram-Schmidt orthogonalization | Download To be verified |
| 22 | Vector subspaces | Download To be verified |
| 23 | Linear operators | Download To be verified |
| 24 | Inverse of an operator | Download To be verified |
| 25 | Adjoint of an operator | Download To be verified |
| 26 | Projection operators | Download To be verified |
| 27 | Eigenvalues and Eigenvectors | Download To be verified |
| 28 | Hermitian operators | Download To be verified |
| 29 | Unitary operators | Download To be verified |
| 30 | Normal operators | Download To be verified |
| 31 | Similarity and Unitary transformations | Download To be verified |
| 32 | Matrix representations | Download To be verified |
| 33 | Eigenvalues and Eigenvectors of matrices | Download To be verified |
| 34 | Defective matrices | Download To be verified |
| 35 | Eigenvalues and eigenvectors: useful results | Download To be verified |
| 36 | Transformation of Basis | Download To be verified |
| 37 | A class of invertible matrices | Download To be verified |
| 38 | Diagonalization of matrices | Download To be verified |
| 39 | Diagonalizability of matrices | Download To be verified |
| 40 | Functions of matrices | Download To be verified |
| 41 | SHM and waves | Download To be verified |
| 42 | Periodic functions | Download To be verified |
| 43 | Average value of a function | Download To be verified |
| 44 | Piecewise continuous functions | Download To be verified |
| 45 | Orthogonal basis: Fourier series | Download To be verified |
| 46 | Fourier coefficients | Download To be verified |
| 47 | Dirichlet Conditions | Download To be verified |
| 48 | Complex Form of Fourier Series | Download To be verified |
| 49 | Other intervals: arbitrary period | Download To be verified |
| 50 | Even and Odd Functions | Download To be verified |
| 51 | Differentiating Fourier series | Download To be verified |
| 52 | Parseval's theorem | Download To be verified |
| 53 | Fourier series to Fourier transforms | Download To be verified |
| 54 | Fourier Sine and Cosine transforms | Download To be verified |
| 55 | Parseval's theorem for Fourier series | Download To be verified |
| 56 | Ordinary Differential equations | Download To be verified |
| 57 | First order ODEs | Download To be verified |
| 58 | Linear first order ODEs | Download To be verified |
| 59 | Orthogonal Trajectories | Download To be verified |
| 60 | Exact differential equations | Download To be verified |
| 61 | Special first order ODEs | Download To be verified |
| 62 | Solutions of linear first-order ODEs | Download To be verified |
| 63 | Revisit linear first-order ODEs | Download To be verified |
| 64 | ODEs in disguise | Download To be verified |
| 65 | 2nd order Homogeneous linear equations with constant coefficients | Download To be verified |
| 66 | The use of a known solution to find another | Download To be verified |
| 67 | An alternate approach to auxiliary equation | Download To be verified |
| 68 | Inhomogeneous second order equations | Download To be verified |
| 69 | Methods to find a Particular solution | Download To be verified |
| 70 | Successive Integration of two first order equations | Download To be verified |
| 71 | Illustrative examples. | Download To be verified |
| 72 | Variation of Parameters | Download To be verified |
| 73 | Vibrations in mechanical systems. | Download To be verified |
| 74 | Forced Vibrations. | Download To be verified |
| 75 | Resonance | Download To be verified |
| 76 | Linear Superposition | Download To be verified |
| 77 | Laplace Transform (LT) | PDF unavailable |
| 78 | Basic Properties of Laplace Transforms | PDF unavailable |
| 79 | Step functions, Translations, and Periodic functions | PDF unavailable |
| 80 | The Inverse Laplace Transform | PDF unavailable |
| 81 | Convolution of functions | PDF unavailable |
| 82 | Solving ODEs using Laplace transforms | PDF unavailable |
| 83 | The Dirac Delta function | PDF unavailable |
| 84 | Properties of the Dirac Delta function | PDF unavailable |
| 85 | Green's function method | PDF unavailable |
| 86 | Green's function method: Boundary value problem | PDF unavailable |
| 87 | Power series method | PDF unavailable |
| 88 | Power series solutions about an ordinary point | PDF unavailable |
| 89 | Initial value problem: power series solution | PDF unavailable |
| 90 | Frobenius method for regular singular points | PDF unavailable |
| Sl.No | Language | Book link |
|---|---|---|
| 1 | English | Not Available |
| 2 | Bengali | Not Available |
| 3 | Gujarati | Not Available |
| 4 | Hindi | Not Available |
| 5 | Kannada | Not Available |
| 6 | Malayalam | Not Available |
| 7 | Marathi | Not Available |
| 8 | Tamil | Not Available |
| 9 | Telugu | Not Available |