NOC:Differential Equations for Engineers (USB)

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111106100



Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. Srinivasa Manam

NPTEL Co-ordinating Institute : IIT Madras

NPTEL Lecture Count : 64

NPTEL Course Size : 24 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)


Lecture Titles:

Lecture 1 - Introduction to Ordinary Differential Equations (ODE)
Lecture 2 - Methods for First Order ODE's - Homogeneous Equations
Lecture 3 - Methods for First order ODE's - Exact Equations
Lecture 4 - Methods for First Order ODE's - Exact Equations (Continued...)
Lecture 5 - Methods for First order ODE's - Reducible to Exact Equations
Lecture 6 - Methods for First order ODE's - Reducible to Exact Equations (Continued...)
Lecture 7 - Non-Exact Equations - Finding Integrating Factors
Lecture 8 - Linear First Order ODE and Bernoulli's Equation
Lecture 9 - Introduction to Second order ODE's
Lecture 10 - Properties of solutions of second order homogeneous ODE's
Lecture 11 - Abel's formula to find the other solution
Lecture 12 - Abel's formula - Demonstration
Lecture 13 - Second Order ODE's with constant coefficients
Lecture 14 - Euler - Cauchy equation
Lecture 15 - Non homogeneous ODEs Variation of Parameters
Lecture 16 - Method of undetermined coefficients
Lecture 17 - Demonstration of Method of undetermined coefficients
Lecture 18 - Power Series and its properties
Lecture 19 - Power Series Solutions to Second Order ODE's
Lecture 20 - Power Series Solutions (Continued...)
Lecture 21 - Legendre Differential Equation
Lecture 22 - Legendre Polynomials
Lecture 23 - Properties of Legendre Polynomials
Lecture 24 - Power series solutions around a regular singular point
Lecture 25 - Frobenius method of solutions
Lecture 26 - Frobenius method of solutions (Continued...)
Lecture 27 - Examples on Frobenius method
Lecture 28 - Bessel differential equation
Lecture 29 - Frobenius solutions for Bessel Equation
Lecture 30 - Properties of Bessel functions
Lecture 31 - Properties of Bessel functions (Continued...)
Lecture 32 - Introduction to Sturm-Liouville theory
Lecture 33 - Sturm-Liouville Problems
Lecture 34 - Regular Sturm-Liouville problem
Lecture 35 - Periodic and singular Sturm-Liouville Problems
Lecture 36 - Generalized Fourier series
Lecture 37 - Examples of Sturm-Liouville systems
Lecture 38 - Examples of Sturm-Liouville systems (Continued...)
Lecture 39 - Examples of regular Sturm-Liouville systems
Lecture 40 - Second order linear PDEs
Lecture 41 - Classification of second order linear PDEs
Lecture 42 - Reduction to canonical form for equations with constant coefficients
Lecture 43 - Reduction to canonical form for equations with variable coefficients
Lecture 44 - Reduction to Normal form-More examples
Lecture 45 - D'Alembert solution for wave equation
Lecture 46 - Uniqueness of solutions for wave equation
Lecture 47 - Vibration of a semi-infinite string
Lecture 48 - Vibration of a finite string
Lecture 49 - Finite length string vibrations
Lecture 50 - Finite length string vibrations (Continued...)
Lecture 51 - Non-homogeneous wave equation
Lecture 52 - Vibration of a circular drum
Lecture 53 - Solutions of heat equation-Properties
Lecture 54 - Temperature in an infinite rod
Lecture 55 - Temperature in a semi-infinite rod
Lecture 56 - Non-homogeneous heat equation
Lecture 57 - Temperature in a finite rod
Lecture 58 - Temperature in a finite rod with insulated ends
Lecture 59 - Laplace equation over a rectangle
Lecture 60 - Laplace equation over a rectangle with flux boundary conditions
Lecture 61 - Laplace equation over circular domains
Lecture 62 - Laplace equation over circular Sectors
Lecture 63 - Uniqueness of the boundary value problems for Laplace equation
Lecture 64 - Conclusions

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