Modules / Lectures

Sl.No Chapter Name English
1VectorsDownload
Verified
2Linear vector spacesDownload
Verified
3Linear vector spaces: immediate consequencesDownload
Verified
4Dot product of Euclidean vectorsDownload
Verified
5Inner product on a Linear vector spaceDownload
Verified
6Cauchy-Schwartz inequality for Euclidean vectorsDownload
Verified
7Cauchy-Schwartz inequality for vectors from LVSDownload
Verified
8Applications of the Cauchy-Schwartz inequalityDownload
Verified
9Triangle inequalityDownload
Verified
10Linear dependence and independence of vectorsDownload
Verified
11Row reduction of matricesDownload
Verified
12Rank of a matrixDownload
Verified
13Rank of a matrix: consequencesDownload
Verified
14Determinants and their propertiesDownload
Verified
15The rank of a matrix using determinantsDownload
Verified
16Cramer's ruleDownload
Verified
17Square system of equationsDownload
Verified
18Homogeneous equationsDownload
Verified
19The rank of a matrix and linear dependenceDownload
Verified
20Span, basis, and dimension of a LVSDownload
Verified
21Gram-Schmidt orthogonalizationDownload
Verified
22Vector subspacesDownload
Verified
23Linear operatorsDownload
Verified
24Inverse of an operatorDownload
Verified
25Adjoint of an operatorDownload
Verified
26Projection operatorsDownload
Verified
27Eigenvalues and EigenvectorsDownload
Verified
28Hermitian operatorsDownload
Verified
29Unitary operatorsDownload
Verified
30Normal operatorsDownload
Verified
31Similarity and Unitary transformationsDownload
Verified
32Matrix representationsDownload
Verified
33Eigenvalues and Eigenvectors of matricesDownload
Verified
34Defective matricesDownload
Verified
35Eigenvalues and eigenvectors: useful resultsDownload
Verified
36Transformation of BasisDownload
Verified
37A class of invertible matricesDownload
Verified
38Diagonalization of matricesDownload
Verified
39Diagonalizability of matricesDownload
Verified
40Functions of matricesDownload
Verified
41SHM and wavesDownload
Verified
42Periodic functionsDownload
Verified
43Average value of a functionDownload
Verified
44Piecewise continuous functionsDownload
Verified
45Orthogonal basis: Fourier seriesDownload
Verified
46Fourier coefficientsDownload
Verified
47Dirichlet ConditionsDownload
Verified
48Complex Form of Fourier SeriesDownload
Verified
49Other intervals: arbitrary periodDownload
Verified
50Even and Odd FunctionsDownload
Verified
51Differentiating Fourier seriesDownload
Verified
52Parseval's theoremDownload
Verified
53Fourier series to Fourier transformsDownload
Verified
54Fourier Sine and Cosine transformsDownload
Verified
55Parseval's theorem for Fourier seriesDownload
Verified
56Ordinary Differential equationsDownload
Verified
57First order ODEsDownload
Verified
58Linear first order ODEsDownload
Verified
59Orthogonal TrajectoriesDownload
Verified
60Exact differential equationsDownload
Verified
61Special first order ODEsDownload
Verified
62Solutions of linear first-order ODEsDownload
Verified
63Revisit linear first-order ODEsDownload
Verified
64ODEs in disguiseDownload
Verified
652nd order Homogeneous linear equations with constant coefficientsDownload
Verified
66The use of a known solution to find anotherDownload
Verified
67An alternate approach to auxiliary equationDownload
Verified
68Inhomogeneous second order equationsDownload
Verified
69Methods to find a Particular solutionDownload
Verified
70Successive Integration of two first order equationsDownload
Verified
71Illustrative examples.Download
Verified
72Variation of ParametersDownload
Verified
73Vibrations in mechanical systems.Download
Verified
74Forced Vibrations.Download
Verified
75ResonanceDownload
Verified
76Linear SuperpositionDownload
Verified
77Laplace Transform (LT)Download
Verified
78Basic Properties of Laplace TransformsDownload
Verified
79Step functions, Translations, and Periodic functionsDownload
Verified
80The Inverse Laplace TransformDownload
Verified
81Convolution of functionsDownload
Verified
82Solving ODEs using Laplace transformsDownload
Verified
83The Dirac Delta functionDownload
Verified
84Properties of the Dirac Delta functionDownload
Verified
85Green's function methodDownload
Verified
86Green's function method: Boundary value problemDownload
Verified
87Power series methodDownload
Verified
88Power series solutions about an ordinary pointDownload
Verified
89Initial value problem: power series solutionDownload
Verified
90Frobenius method for regular singular pointsDownload
Verified


Sl.No Language Book link
1EnglishNot Available
2BengaliNot Available
3GujaratiNot Available
4HindiNot Available
5KannadaNot Available
6MalayalamNot Available
7MarathiNot Available
8TamilNot Available
9TeluguNot Available