Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Auditya Sharma
NPTEL Co-ordinating Institute : IISER Bhopal
NPTEL Lecture Count : 90
NPTEL Course Size : 4.0 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Vectors
Lecture 2 - Linear vector spaces
Lecture 3 - Linear vector spaces: immediate consequences
Lecture 4 - Dot product of Euclidean vectors
Lecture 5 - Inner product on a Linear vector space
Lecture 6 - Cauchy-Schwartz inequality for Euclidean vectors
Lecture 7 - Cauchy-Schwartz inequality for vectors from LVS
Lecture 8 - Applications of the Cauchy-Schwartz inequality
Lecture 9 - Triangle inequality
Lecture 10 - Linear dependence and independence of vectors
Lecture 11 - Row reduction of matrices
Lecture 12 - Rank of a matrix
Lecture 13 - Rank of a matrix: consequences
Lecture 14 - Determinants and their properties
Lecture 15 - The rank of a matrix using determinants
Lecture 16 - Cramer's rule
Lecture 17 - Square system of equations
Lecture 18 - Homogeneous equations
Lecture 19 - The rank of a matrix and linear dependence
Lecture 20 - Span, basis, and dimension of a LVS
Lecture 21 - Gram-Schmidt orthogonalization
Lecture 22 - Vector subspaces
Lecture 23 - Linear operators
Lecture 24 - Inverse of an operator
Lecture 25 - Adjoint of an operator
Lecture 26 - Projection operators
Lecture 27 - Eigenvalues and Eigenvectors
Lecture 28 - Hermitian operators
Lecture 29 - Unitary operators
Lecture 30 - Normal operators
Lecture 31 - Similarity and Unitary transformations
Lecture 32 - Matrix representations
Lecture 33 - Eigenvalues and Eigenvectors of matrices
Lecture 34 - Defective matrices
Lecture 35 - Eigenvalues and eigenvectors: useful results
Lecture 36 - Transformation of Basis
Lecture 37 - A class of invertible matrices
Lecture 38 - Diagonalization of matrices
Lecture 39 - Diagonalizability of matrices
Lecture 40 - Functions of matrices
Lecture 41 - SHM and waves
Lecture 42 - Periodic functions
Lecture 43 - Average value of a function
Lecture 44 - Piecewise continuous functions
Lecture 45 - Orthogonal basis: Fourier series
Lecture 46 - Fourier coefficients
Lecture 47 - Dirichlet Conditions
Lecture 48 - Complex Form of Fourier Series
Lecture 49 - Other intervals: arbitrary period
Lecture 50 - Even and Odd Functions
Lecture 51 - Differentiating Fourier series
Lecture 52 - Parseval's theorem
Lecture 53 - Fourier series to Fourier transforms
Lecture 54 - Fourier Sine and Cosine transforms
Lecture 55 - Parseval's theorem for Fourier series
Lecture 56 - Ordinary Differential equations
Lecture 57 - First order ODEs
Lecture 58 - Linear first order ODEs
Lecture 59 - Orthogonal Trajectories
Lecture 60 - Exact differential equations
Lecture 61 - Special first order ODEs
Lecture 62 - Solutions of linear first-order ODEs
Lecture 63 - Revisit linear first-order ODEs
Lecture 64 - ODEs in disguise
Lecture 65 - 2nd order Homogeneous linear equations with constant coefficients
Lecture 66 - The use of a known solution to find another
Lecture 67 - An alternate approach to auxiliary equation
Lecture 68 - Inhomogeneous second order equations
Lecture 69 - Methods to find a Particular solution
Lecture 70 - Successive Integration of two first order equations
Lecture 71 - Illustrative examples
Lecture 72 - Variation of Parameters
Lecture 73 - Vibrations in mechanical systems
Lecture 74 - Forced Vibrations
Lecture 75 - Resonance
Lecture 76 - Linear Superposition
Lecture 77 - Laplace Transform (LT)
Lecture 78 - Basic Properties of Laplace Transforms
Lecture 79 - Step functions, Translations, and Periodic functions
Lecture 80 - The Inverse Laplace Transform
Lecture 81 - Convolution of functions
Lecture 82 - Solving ODEs using Laplace transforms
Lecture 83 - The Dirac Delta function
Lecture 84 - Properties of the Dirac Delta function
Lecture 85 - Green's function method
Lecture 86 - Green's function method: Boundary value problem
Lecture 87 - Power series method
Lecture 88 - Power series solutions about an ordinary point
Lecture 89 - Initial value problem: power series solution
Lecture 90 - Frobenius method for regular singular points