Modules / Lectures

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Sl.No Chapter Name English
1Lecture 01 - Introduction to Ordinary Differential Equations (ODE)PDF unavailable
2Lecture 02 - Methods for First Order ODE's - Homogeneous EquationsPDF unavailable
3Lecture 03 - Methods for First order ODE's - Exact EquationsPDF unavailable
4Lecture 04 - Methods for First Order ODE's - Exact Equations ( Continued )PDF unavailable
5Lecture 05 - Methods for First order ODE's - Reducible to Exact EquationsPDF unavailable
6Lecture 06 - Methods for First order ODE's - Reducible to Exact Equations ( Continued )PDF unavailable
7Lecture 07 - Non-Exact Equations - Finding Integrating FactorsPDF unavailable
8Lecture 08 - Linear First Order ODE and Bernoulli's EquationPDF unavailable
9Lecture 09 - Introduction to Second order ODE'sPDF unavailable
10Lecture 10 - Properties of solutions of second order homogeneous ODE's PDF unavailable
11Lecture 11 - Abel's formula to find the other solutionPDF unavailable
12Lecture 12 - Abel's formula - DemonstrstionPDF unavailable
13Lecture 13 - Second Order ODE's with constant coefficientsPDF unavailable
14Lecture 14 - Euler - Cauchy equationPDF unavailable
15Lecture 15 - Non homogeneous ODEs Variation of ParametersPDF unavailable
16Lecture 16 - Method of undetermined coefficientsPDF unavailable
17Lecture 17 - Demonstration of Method of undetermined coefficientsPDF unavailable
18Lecture 18 - Power Series and its propertiesPDF unavailable
19Lecture 19 - Power Series Solutions to Second Order ODE'sPDF unavailable
20Lecture 20 - Power Series Solutions ( Continued )PDF unavailable
21Lecture 21 - Legendre Differential EquationPDF unavailable
22Legendre PolynomialsPDF unavailable
23Properties of Legendre PolynomialsPDF unavailable
24Power series solutions around a regular singular pointPDF unavailable
25Frobenius method of solutionsPDF unavailable
26Frobenius method of solutions (continued)PDF unavailable
27Examples on Frobenius methodPDF unavailable
28Bessel differential equationPDF unavailable
29Frobenius solutions for Bessel EquationPDF unavailable
30Properties of Bessel functionsPDF unavailable
31Properties of Bessel functions (continued)PDF unavailable
32Introduction to Sturm-Liouville theoryPDF unavailable
33Sturm-Liouville ProblemsPDF unavailable
34Regular Sturm-Liouville problemPDF unavailable
35Periodic and singular Sturm-Liouville ProblemsPDF unavailable
36Generalized Fourier seriesPDF unavailable
37Examples of Sturm-Liouville systemsPDF unavailable
38Examples of Sturm-Liouville systems (continued)PDF unavailable
39Examples of regular Sturm-Liouville systemsPDF unavailable
40Second order linear PDEsPDF unavailable
41Classification of second order linear PDEsPDF unavailable
42Reduction to canonical form for equations with constant coefficientsPDF unavailable
43Reduction to canonical form for equations with variable coefficientsPDF unavailable
44Reduction to Normal form-More examplesPDF unavailable
45D'Alembert solution for wave equationPDF unavailable
46Uniqueness of solutions for wave equationPDF unavailable
47Vibration of a semi-infinite stringPDF unavailable
48Vibration of a finite stringPDF unavailable
49Finite length string vibrationsPDF unavailable
50Finite length string vibrations (continued)PDF unavailable
51Non-homogeneous wave equationPDF unavailable
52Vibration of a circular drumPDF unavailable
53Solutions of heat equation-PropertiesPDF unavailable
54Temperature in an infinite rodPDF unavailable
55Temperature in a semi-infinite rodPDF unavailable
56Non-homogeneous heat equationPDF unavailable
57Temperature in a finite rodPDF unavailable
58Temperature in a finite rod with insulated endsPDF unavailable
59Laplace equation over a rectanglePDF unavailable
60Laplace equation over a rectangle with flux boundary conditionsPDF unavailable
61Laplace equation over circular domainsPDF unavailable
62Laplace equation over circular SectorsPDF unavailable
63Uniqueness of the boundary value problems for Laplace equationPDF unavailable
64ConclusionsPDF unavailable

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