Course11110610064 lectures
Differential Equations for Engineers
Prof. Srinivasa Rao Manam · IIT Madras
About
The course is to introduce the essential differential equations and their solution methods.The course is very much essential to all engineering students for its use in any kind of scientific or engineering work. The course offers them a good exposure of both ordinary and partial differential equations that arise in physical and engineering sciences.
Intended audience: Physical Mechanical Sciences and Engineering
Prerequisites: Basic Calculus
Lectures
Week 1
- Lesson 01 - Introduction to Ordinary Differential Equations (ODE)
- Lesson 02 - Methods for First Order ODE's - Homogeneous Equations
- Lesson 03 - Methods for First order ODE's - Exact Equations
- Lesson 04 - Methods for First Order ODE's - Exact Equations ( Continued )
- Lesson 05 - Methods for First order ODE's - Reducible to Exact Equations
- Lesson 06 - Methods for First order ODE's - Reducible to Exact Equations ( Continued )
Week 2
- Lesson 07 - Non-Exact Equations - Finding Integrating Factors
- Lesson 08 - Linear First Order ODE and Bernoulli's Equation
- Lesson 09 - Introduction to Second order ODE's
- Lesson 10 - Properties of solutions of second order homogeneous ODE's
- Lesson 11 - Abel's formula to find the other solution
- Lesson 12 - Abel's formula - Demonstrstion
Week 3
- Lesson 13 - Second Order ODE's with constant coefficients
- Lesson 14 - Euler - Cauchy equation
- Lesson 15 - Non homogeneous ODEs Variation of Parameters
- Lesson 16 - Method of undetermined coefficients
- Lesson 17 - Demonstration of Method of undetermined coefficients
- Lesson 18 - Power Series and its properties
Week 4
- Lesson 19 - Power Series Solutions to Second Order ODE's
- Lesson 20 - Power Series Solutions ( Continued )
- Lesson 21 - Legendre Differential Equation
- Lesson 22 - Legendre Polynomials
- Lesson 23 - Properties of Legendre Polynomials
Week 5
- Lesson 24 - Power series solutions around a regular singular point
- Lesson 25 - Frobenius method of solutions'
- Lesson 26 - Frobenius method of solutions (continued)
- Lesson 27 - Examples on Frobenius method
- Lesson 28 - Bessel differential equation
Week 6
- Lesson 29 - Frobenius solutions for Bessel Equation
- Lesson 30 - Properties of Bessel functions
- Lesson 31 - Properties of Bessel functions (continued)
- Lesson 32 - Introduction to Sturm-Liouville theory
- Lesson 33 - Sturm-Liouville Problems
Week 7
- Lesson 34 - Regular Sturm-Liouville problem
- Lesson 35 - Periodic and singular Sturm-Liouville Problems
- Lesson 36 - Generalized Fourier series
- Lesson 37 - Examples of Sturm-Liouville systems
- Lesson 38 - Examples of Sturm-Liouville systems (continued)
- Lesson 39 - Examples of regular Sturm-Liouville systems
Week 8
- Lesson 40 - Second order linear PDEs
- Lesson 41 - Classification of second order linear PDEs
- Lesson 42 - Reduction to canonical form for equations with constant coefficients
- Lesson 43 - Reduction to canonical form for equations with variable coefficients
- Lesson 44 - Reduction to Normal form-More examples
Week 9
- Lesson 45 - D'Alembert solution for wave equation
- Lesson 46 - Uniqueness of solutions for wave equation
- Lesson 47 - Vibration of a semi-infinite string
- Lesson 48 - Vibration of a finite string
Week 10
- Lesson 49 - Finite length string vibrations
- Lesson 50 - Finite length string vibrations (continued)
- Lesson 51 - Non-homogeneous wave equation
- Lesson 52 - Vibration of a circular drum
- Lesson 53 - Solutions of heat equation-Properties
Week 11
- Lesson 54 - Temperature in an infinite rod
- Lesson 55 - Temperature in a semi-infinite rod
- Lesson 56 - Non-homogeneous heat equation
- Lesson 57 - Temperature in a finite rod
- Lesson 58 - Temperature in a finite rod with insulated ends
Week 12
- Lesson 59 - Laplace equation over a rectangle
- Lesson 60 - Laplace equation over a rectangle with flux boundary conditions
- Lesson 61 - Laplace equation over circular domains
- Lesson 62 - Laplace equation over circular Sectors
- Lesson 63 - Uniqueness of solutions-Laplace equation
- Lesson 64 - Conclusions
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Madras
- Department
- Mathematics
- Teacher
- Prof. Srinivasa Rao Manam
- Level
- Undergraduate
- Language
- English
- Subjects
- Mathematics
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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