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Course Objective
The objective of this course is to familiarize the students with partial differential equation, their application and statistical techniques. It aims to present the students with standard concepts and tools at an intermediate to superior level that will provide them well towards undertaking a variety of problems in the discipline.
The students will learn:
The idea of partial differentiation and types of partial differential equations.
The idea of classification of second partial differential equations, wave, heat equation and transmission lines.
The basic ideas of statistics include measures of central tendency, correlation, regression, and their properties.
The idea s of probability and random variables and various discrete and continuous probability distributions and their properties.
The statistical methods of studying data samples, hypothesis testing and statistical quality control, control charts and their properties.
Unit-I (Partial Differential Equations)
Origin of Partial Differential Equations
[Video] [Lecture Notes] [Assignment] [Solutions]
Lagrange’s Equations
[Video-1] [Video-2] [Lecture Notes-1] [Lecture Notes-2] [Assignment] [Solutions]
Charpit’s method,
[Video] [Lecture Notes] [Assignment] [Solutions]
Cauchy’s method of Characteristics,
[Video] [Lecture Notes] [Assignment] [Solutions]
Solution of Linear Partial Differential Equation of Higher order with constant coefficients,
[Video] [Lecture Notes] [Assignment] [Solutions]
Equations reducible to linear partial differential equations with constant coefficients.
[Video] [Lecture Notes] [Assignment] [Solutions]
Unit-II (Applications of Partial Differential Equations:)
Classification of linear partial differential equation of second order,
[Video] [Lecture Notes] [Assignment] [Solutions]
Method of separation of variables,
[Video] [Lecture Notes] [Assignment] [Solutions]
Solution of wave and heat conduction equation up to two dimension,
[Video] [Lecture Notes] [Assignment] [Solutions]
Laplace equation in two dimensions,
[Video] [Lecture Notes] [Assignment] [Solutions]
Equations of Transmission lines.
[Video] [Lecture Notes] [Assignment] [Solutions]
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