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Last updated: Apr 29, 2022

Engineering Mathematics

This blog series is about the basic mathematics that is a fundamental and essential component in all streams of undergraduate studies in sciences and engineering. The blog series consists of topics in set theory, functions, logic & propositional, relations, boolean algebra, binary trees, graph theory, probability theory, linear algebra, calculus, probability and distributions, numerical methods & statistics, and differential equations with applications to various engineering problems.

Set Theory

Set Theory starts very simply; it examines whether an object belongs, or does not belong, to a set of objects which has been described in some non-ambiguous way. From this simple beginning, an increasingly complex series of ideas can be developed, which leads to notations and techniques with many varied applications. A set can be defined as an unordered collection of entities that are related because they obey a certain rule.
Set Theory EASY
In this blog, we will discuss sets and set theory. We will also discuss set representation, set types, and the Venn diagram, then various set operations such as union, intersection, complement, difference, and cartesian product. Finally, we will discuss the inclusion-exclusion principle and derangement.
Set Operations EASY
This article will cover the operations performed on the sets along with examples.
Multisets
In this blog, we will learn what multisets are, associated terminologies, and operations on multisets.
Algebra of Sets EASY
This article will cover the topic of Algebra of Sets.
Inclusion-Exclusion Principle
In this blog, we will learn what the Inclusion-Exclusion principle is all about, and also its applications.
Mathematical Induction
In this blog, we will learn about mathematical Induction and will verify the statement problems using Mathematical Induction Theorem.

Relations

Relation between two sets is a collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x,y) is in the relation. Let's explore this blog series to learn more about relations.
Binary Relations
We will see what a Binary relation is and its properties and Examples.
Representation of Relations EASY
This article deals with the different representations of relations in detail.
Composition of Relations EASY
In mathematics, the composition of relations is an operation that combines two or more relations to create a new relation. The composition of relations is known as relative multiplication in the calculus of relations
Types of relation
This article deeply discussed Types of Relations and examples that will help you gain a better understanding.
Properties of Relation
This article explains the properties of relation and examples to help you understand better.
Equivalence of Relations
This blog mainly covers different aspects of equivalent relations, like what is an equivalence relation? What are the different properties of an equivalence relation? How to identify whether a relation is equivalent or not etc.
Partial Order Relations EASY
In this article, we will discuss partial order relations, POSETS, total order relations, and equivalent class.

Graph Theory

Graphs are discrete mathematical structures that have many applications in a diversity of fields including chemistry, network analysis, algorithms, and social sciences. Graph Theory is the study of the graph. A graph is determined as a mathematical structure that represents a particular function by connecting a set of points. It is used to create a pairwise relationship between objects.
Graph Types and Applications EASY
This blog will discuss types of Graphs and applications of Graphs.
Graph Representations EASY
This article will briefly describe how the graph is represented.
Euler and Hamilton paths
In this article, We will discuss Euler's Path, Euler Circuits, Euler circuit's theorem, Hamilton's Path with some examples.
Isomorphic and homeomorphic graphs
This blog will discuss Isomorphic graphs and homeomorphic graphs, examples, and detailed explanations.
What is Undirected Graph? MEDIUM
In this blog, we will learn about What is Undirected Graph. We will understand its core concepts, its applications, and much more for better understanding.
Planar and Non-Planar Graphs
In this blog, we will learn about two main types of graphs, i.e., planar and non-planar graphs with examples and properties, and we will also learn about graph coloring with examples.
Matching in Graph Theory
In this article, we will learn about matching in Graph theory.
Strongly Connected Components EASY
In this blog, we will learn about Strongly Connected Components. We will understand its core concepts, its usage, and much more for better understanding.
Regular and Bipartite graphs
In this blog, we will learn about different types of graphs, including a complete chart, regular graph, bipartite graph, and complete bipartite graph, and we will also learn about the Euler path.
Dijkstra’s Algorithm
In this article, we will discuss the introduction of Dijkstra's Algorithm and a detailed example to understand it properly
Centrality Measure in Graph Theory
In this post, we will learn different centrality measures used in Graph theory.
Graph Measurements
In this article, we will learn different Graph measurement methods.

Calculus

Calculus is one of the most important branches of mathematics that deals with continuous change. The two major concepts that calculus is based on are derivatives and integrals. The derivative of a function is the measure of the rate of change of a function, while the integral is the measure of the area under the curve of the function. Let’s together explore more about Limits, Continuity, and Differentiability, Cauchy’s Mean Value Theorem, Lagrange’s Mean Value Theorem, and Rolle’s Mean Value Theorem.
Limits, Continuity and Differentiability
In this article, we are going to discuss the concepts of limits, continuity and differentiability in detail.
Cauchy's Mean Value Theorem EASY
This article discusses Cauchy's Mean Value Theorem.
Lagrange’s Mean Value Theorem
This article discusses Lagrange's Mean Value Theorem the conditions required for it to hold along its applications.
Rolle's mean value theorem
In this article, we will discuss Rolle's mean value theorem
Inverse functions EASY
This article discusses the theory of inverse functions and how to find them.
Indefinite Integrals
This blog mainly focuses on Indefinite Integrals. You will learn every concept regarding the indefinite integrals starting from scratch. This blog covers definitions, different properties, fundamental formulas and some important examples.

Linear Algebra

Linear Algebra is one of the important branches of Mathematics. Linear algebra is basically the study of linear functions. It is a key concept for almost all areas of mathematics. The most important topics covered in linear algebra include Determinants, Matrix, Linear Transformations, EigenValue and Eigenvectors, System of Linear Equations, Doolittle Algorithm, Cayley-Hamilton Theorem, and Reduction to diagonal form.
Determinants
In this blog, we will learn about determinants, how to calculate determinants and their different properties.
Matrix
In this blog, we will discuss matrix, properties, transpose of a matrix, adjoint, application, operations can perform on matrix, and much more with a full explanation.
Types of Matrix
 In this blog, we will learn types of matrices with a proper explanation and their examples.
Operations On Matrices EASY
In this blog, we will be discussing various operations that can be performed on matrices and their associated properties.
Rank of Matrix
Meta Description: In this blog, we are going to learn about the concept of matrices. We will discuss the rank of a matrix in detail.
Transpose of a Matrix
This article will cover the Transpose of a matrix, its properties, and its Examples.
Adjoint and Inverse of a Matrix
This blog will discuss the Adjoint and Inverse of a matrix with a full explanation.
Linear Transformations EASY
In this article, we will discuss the linear transformation of matrices
System of Linear Equations
In this blog, we will learn about the system of linear equations.
Gaussian Elimination to Solve Linear Equations MEDIUM
Gaussian elimination is like a step-by-step trick to solve a bunch of math problems where you have a bunch of equations. Let's explore how the gaussian elimination method helps us find the solutions to the linear equations
Reduction of Matrix to Diagonal Form EASY
This article will show the Reduction of the Matrix to Diagonal Form will all the steps.

Differential Equations

Differential Equations are very common in science and engineering, as well as in many other fields of quantitative study because what can be directly observed and measured for systems undergoing changes are their rates of change. The solution of a differential equation is, in general, an equation expressing the functional dependence of one variable upon one or more others; it ordinarily contains constant terms that are not present in the original differential equation. Let’s get started with differential equations.
Partial Differential Equations
In this blog, we will learn about partial differential equations, how to represent them, their classification, and types with the help of examples.
Linear Differential Equations
In this blog, we will learn about Linear differential equations and how to solve linear differential equations.
Difference Between Linear And Non-Linear Differential Equations EASY
In this blog, we will learn about linear and nonlinear differential equations and their difference.
Homogeneous Differential Equations EASY
Differential equations are essential in the mathematical modeling of physical systems. In this article, we will learn to solve the Homogeneous Differential equation.
Nonhomogeneous Differential Equations
In this blog, we will learn about nonhomogeneous linear equations and how to solve nonhomogeneous linear equations.

Numerical Methods & Statistics

Statistics is more about how we handle various data using different techniques. It helps to represent complicated data in a very easy and understandable way. Statistics has a huge application nowadays in data science professions. In upcoming blogs, we’re going to learn about Mean, Variance, Standard Deviation, Exponential Distribution, Covariance and Correlation, Homogeneous Poisson Process, and Non-Homogeneous Poisson Process.
Mean, variance, standard deviation
In this article, we will discuss mean, variance, and standard deviation.
Exponential Distribution
In this article, we will discuss the exponential distribution topic.
Covariance and Correlation EASY
Covariance and Correlation are two opposite terms used in statistics and regression analysis. In this article, we will learn about Covariance and Correlation.
Confidence Intervals in Inferential Statistics MEDIUM
This article will discuss the confidence intervals in inference statistics, why they are essential, how to calculate them, and the proper interpretation of the confidence intervals examples.
Homogeneous Poisson Process
In this blog, we will learn about the Homogeneous Poisson Process and its uses in real life.
Nonhomogeneous Poisson Process EASY
Nonhomogeneous Poisson process model represents the number of failures experienced up to time t. In this article, we will learn about the Nonhomogeneous Poisson process.
Scales of Measurements
In this blog, we will learn about the scales of measurement and different types of scales.
Top 75 Statistics Interview Questions & Answers 2023 MEDIUM
In this article, we will discuss about various statistics interview questions and answers.
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Transforms

Laplace Transform is a powerful tool to solve differential equations. It transforms an Initial Value Problem in Ordinary Differential Equations into algebraic equations. Laplace Transform is an integral transform named after its inventor Pierre Simon Laplace. Let's together learn more about Laplace's transformation to have a better understanding.
Laplace Transform
This article will discuss the topic Laplace Transform, its properties, applications, and solved examples.
Laplace Transform Properties EASY
This article will cover the Laplace Transform Properties in detail.
Laplace transform of a unit step function EASY
The Laplace transform is used for solving linear differential equations that use integral transforms. In this article, we will find the Laplace transform of a unit step function.
Laplace Transform of Periodic Function EASY
In this blog, we will be studying the application of Laplace Transform in engineering mathematics.
Initial Value Theorem of Laplace Transform EASY
Laplace transform is very useful in the various fields of science and technology as Laplace transform replaces operations of calculus by operation of algebra.
Convolution Theorem For Laplace Transform EASY
In this blog, we will be studying the Convolution theorem for the Laplace transform in detail.
Linearity Property of Laplace Transform
This blog covers the linearity property of Laplace transform and some numerical examples.