Differential Equation, Complex Variable and Harmonic Analysis

Topics

Part-A

Ordinary Differential Equation
PartialDifferential Equation
Laplace Transform
Complex Variable

Part-B

Fourier Series
Fourier Transform
Boundary Value Problem
Bessel’s Equation
Legendry’s Polynomial

Books

“Thermal Engineering by R.S. Khurmi & J.K. Gupta” is used as textbook and “Thermal Engineering by Mahesh M. Rathore” & “Thermodynamics An Engineering Approach by Yunus A. Çengel & Michael A. Boles” are used as reference book.

Chapter Wise Books

Lectures

Previous Lectures

Dalim Sir's Lecture

Nuruzzaman Sir's Lecture

Assignments

⚠ The solutions are to help your thinking so that you can understand whether your thinking is correct or not. Don’t just copy and paste them. First do it yourself and then see the solution.

Notes

Updates

Semester Question Pattern

Section-A

ODE 1st Order – 1 set Qsn
ODE Higher Order – 1 set Qsn
Laplace Transform – 1 set Qsn
Complex Variables – 1 set Qsn

Section-B

Fourier Series – 1 set Qsn
Fourier Transform – 1 set Qsn
PDE + Boundary Value Problem – 1 set Qsn
Bessel’s Equation + Legendry’s Polynomial – 1 set Qsn

Question patterns may vary depending on the situation.

YouTube Lessons

ODE

Playlist Videos

Differential Equation | Order And Degree With Concept & Example By GP Sir

Differential Equation | Formation Of Differential Equation - Concept & Example By GP Sir

Differential Equation | Variable Separable Method - Concept & Example By GP Sir

Differential Equation | Reducible Into Separation Of Variable - Concept & Example By GP Sir

Differential Equation | HOMOGENEOUS Differential Equation - Concept & Example By GP Sir

Differential Equation | REDUCIBLE HOMOGENEOUS Differential Equation - Concept & Example By GP Sir

Differential Equation | Linear Differential Equation - Concept & Example By GP Sir

Differential Equation | Reducible Linear Differential Equation - Concept & Example By GP Sir

Differential Equation | Exact Differential Equation - Concept & Example By GP Sir

Differential Equation | Reducible Exact Differential Equation PART 1 - Concept & Example By GP Sir

Differential Equation | Reducible Exact Differential Equation PART 2 - Concept & Example By GP Sir

Differential Equation | Reducible Exact Differential Equation PART 3 - Concept & Example By GP Sir

Differential Equation | First Order And Higher Degree (Solvable For P) | By GP Sir

Differential Equation | First Order And Higher Degree (Solvable For X) | By GP Sir

Differential Equation | First Order And Higher Degree (Solvable For Y) | By GP Sir

Differential Equation | Clairaut's Equation | First Order & Higher Degree | By GP Sir

Differential Equation | Higher Order Differential Equations - Complementary Function | By GP Sir

Differential Equation | Higher Order Differential Equations - Particular Integral | By GP Sir

Differential Equation | Higher Order Differential Equations - Particular Integral Part 2 | By GP Sir

Differential Equation | Higher Order Differential Equations - Particular Integral Part 3 | By GP Sir

Differential Equation | Higher Order Differential Equations - Particular Integral Part 4 | By GP Sir

Differential Equation | Higher Order Differential Equations - Particular Integral Part 5 | By GP Sir

Differential Equation | Higher Order Differential Equations - Particular Integral Part 6 | By GP Sir

Differential Equation | Reducible Into Differential Equation With Constant Coefficient | By GP Sir

Differential Equation | Reducible Into Differential Equation With Constant Coefficient Part 2 GP Sir

Linear Higher Order Differential Equation | CF & PI |Lecture-I

Linear Higher Order Differential Equations, Rules of CF & PI By GP Sir

Successive Differentiation | Differential Calculus | Concepts & Examples

Successive Differentiation | nth Derivative | Differential Calculus

PDE

Playlist Videos

First Order Partial Differential Equation -Solution of Lagrange Form

Non Linear Partial Differential Equations Standard Form-I By GP Sir

Non Linear Partial Differential Equations-Standard Form-II By GP Sir

Non Linear Partial Differential Equations-Standard Form-III By GP Sir

Non Linear Partial Differential Equation Standard form-IV | Clairaut's Form

Charpit's Method For Non Linear Partial Differential Equation By GP

Partial Differential Equation | Homogeneous PDE | CF & PI | Part -I

Partial Differential Equation | Homogeneous PDE | CF & PI | Part-II

Partial Differential Equation | Homogeneous PDE | CF & PI | Part-III

Partial Differential Equation | Homogeneous PDE | CF & PI | Part-IV

Partial Differential Equation | General Method To Find PI | Part-V

Partial Differential Equation | Non Homogeneous PDE | Rules of CF & PI

Partial Differential Equation | Non Homogeneous PDE | Rules of PI

Partial Derivative | Function Of Two Variable | Examples By Limit Definition

Classification of Second-Order PDE | Partial Differential Equation Example & Concepts by GP Sir

Separation of Variables Method | Partial Differential Equation | Example & Concepts by GP Sir

Heat Equation | Separation of Variables Method in PDE | Example & Concepts by GP Sir

Wave Equation | Separation of Variables Method in PDE | Example & Concepts by GP Sir

Laplace Equation | Separation of Variables Method in PDE | Example & Concepts by GP Sir

Laplace Transform

Playlist Videos

Laplace Transform | Overview & Laplace Transform of Elementary Function by GP Sir

Laplace Transform | First Shifting Theorem | Concept & Example by GP Sir

Laplace Transform | Second Shifting Theorem | Concept & Example by GP Sir

Laplace Transform | Multiplication Property | Concept & Example by GP Sir

Laplace Transform | Division Property | Concept & Example by GP Sir

Laplace Transform | Convolution Theorem | Concept & Example by GP Sir

Laplace Transform | Periodic Function | Concept & Example by GP Sir

Laplace Transform | Change of Scale Property | Concept & Example by GP Sir

Laplace Transform | Solution of Ordinary Differential Equation | Concept & Example by GP Sir

Laplace Transform | Partial Differential Equation | Concept & Example by GP Sir

Laplace Transform 2.O | Heat Equation | Concept & Example by GP Sir

Laplace Transform 2.O | Wave Equation | Concept & Example by GP Sir

Laplace Transform 2.O | Integral Equation | Concept & Example by GP Sir

Integral Equation | Overview & Basic Terminology | Concept & Example by GP Sir

Integral Equation | Solution of Linear Integral Equation | Concept & Example by GP Sir

Integral Equation | Conversion Initial Value Problem into Integral Equation by GP Sir

Integral Equation | Conversion of Volterra Integral Equation into Initial Value Problem by GP Sir

Integral Equation | Conversion of Boundary Value Problem into Integral Equation by GP Sir

Integral Equation | Conversion of Fredholm Integral Equation into Boundary Value Problem by GP Sir

Formula of Laplace Transform and Inverse Laplace Transform | By Gp Sir

Laplace Transform - First Shifting Theorem with Example | By GP Sir

Laplace & Inverse Laplace Transform - Second Shifting Theorem | GP Sir

Laplace & Inverse Laplace Transform - Multiplication Property | Gp Sir

Laplace & Inverse Laplace Transform - Division Property | By Gp Sir

Inverse Laplace Transform -Convolution Theorem Examples | By GP Sir

Complex Variable

Playlist Videos

Complex Analysis | Analytic Function | Cauchy Riemann Equation BY GP sir

Complex Analysis - Short Trick To Find Harmonic Conjugate By GP Sir

Complex Analysis - Analytic Function | Milne Thomson Method | Example & Solutions

Complex Analysis - Bilinear transformation | Conformal Mappings By GP

Complex Analysis - Complex Integration Line Integral Example & Solution

Cauchy's Integral Formula For Analytic Function | Example & Solution

Complex Analysis - Cauchy's Residue Theorem & Its Application by GP

Complex Analysis- Contour Integration | Application of Residue Theorem

Complex Analysis - Contour integration | Evaluation of Improper Integrals

Complex Analysis - Taylor Series For Complex Variable | Problems By GP

Complex Analysis -Laurent Series For Complex Number | Problems By GP

Singularity - Types of Singularity | Isolated & Non-Isolated Singularity | Complex Analysis

Singularity | Removable Singularity - Concepts with Examples | Complex Analysis

Singularity | Isolated Singularity - Pole and Order Of Pole | Complex Analysis

Singularity | Isolated Singularity - Isolated Essential Singularity | Complex Analysis

Singularity | Non-Isolated Singularity - Non-Isolated Essential Singularity | Complex Analysis

Residue - Complex Analysis | Residue at Infinity | Short Trick With Examples

Residue - Complex Analysis | Residue at Essential Singularity | Short Trick With Examples

Singularity | Isolated Singularity at Infinity | Complex Analysis

Radius of Convergence - Power Series | Complex Analysis

Fourier Series

Playlist Videos

Fourier Series examples and solutions for Even and Odd Function

Half Range Fourier Sine and Cosine Series Example | Lecture II by GP Sir

Harmonic Analysis 2018 in Fourier Series | Lecture III By GP Sir

Fourier Series 2.0 | Overview, Concept and Example by GP Sir

Fourier Series 2.0 | Fourier Series for Interval (-L,L) & (0,2L) by GP Sir

Fourier Series 2.0 | Fourier Series for Even Function by GP Sir

Fourier Series 2.0 | Fourier Series for Odd Function by GP Sir

Fourier Series 2.0 | Fourier Series for Half Range Cosine Series by GP Sir

Fourier Series 2.0 | Fourier Series for Half Range Sine Series by GP Sir

Fourier Series 2.0 | Parseval's Identity for Fourier Series | Proof & Example by GP Sir

Fourier Series 2.0 | Harmonic Analysis for Fourier Series by GP Sir

Fourier Transform

Playlist Videos

Fourier Transform Examples and Solutions | Inverse Fourier Transform

Fourier Sine and Cosine Transform Examples and Solutions By GP Sir

Application of Fourier Transforms to Boundary Value (PDE) Problems

Fourier Transform 2.0 | Example & Solutions in Fourier Transform by GP Sir

Fourier Transform 2.0 | Solution of Boundary Value Problem (PDE) by Fourier Cosine Transform

Fourier Transform 2.0 | Fourier Cosine Transform Example & Solutions by GP Sir

Fourier Transform 2.0 | Fourier Sine Transform Example & Solutions by GP Sir

Fourier Transform 2.0 | Solution of Boundary Value Problem (PDE) by Fourier Sine Transform

Fourier Transform 2.0 | Solution of Boundary Value Problem (PDE) by Fourier Transform

Fourier Transform | Discrete & Inverse Discrete Fourier Transform by GP Sir

Bessel's Equation & Legendry's Polynomial

Playlist Videos

Bessel's Function | Recurrence Relation of Bessel's Function | Proofs

Bessel's Function | Recurrence Relation of Bessel's Function | Part-II

Bessel's Function | Important Example Problem of Bessel's Function

Bessel's Function | Orthogonal Property of Bessel Function | Proof

Legendre Polynomial | Rodrigues Formula | Proof of Rodrigues Formula

Legendre Polynomials | Generating Function of Legendre Polynomial

Legendre Polynomials | Recurrence Relation Of Legendre Polynomials

Legendre Polynomial | Orthogonal Properties of Legendre Polynomial

Fourier Transform

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