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Faculty of GATE. Top Educator - GATE (Engineering Mathematics). 

Sanjay Yadav

This course is designed as a complete course on Engineering Mathematics for the GATE examination. It covers all the small topics which are mentioned in the syllabus and also described each and every short tricks to solve the problem in less time. The topics are going to be discussed during this courses are : 
1. Linear Algebra
2. Calculus
3. Vector Analysis 
4. Differential Equations
5. Complex Analysis 
6. Probability and Statistics
7. Numerical Methods.

GATE (Graduate Aptitude Test in Engineering) 2020 & 2021 complete preparation with best educators. Know about the detailed syllabus, best books, exam pattern and dates, previous year question papers a

GATE & ESE

English

Complete Course on Engineering Mathematics : GATE

Crash Course

Engineering Mathematics

GA, GS and Mathematics

GATE & ESE - ME & CH

GATE, ESE and IIT-JAM

Ace the toughest competitive and government exams in India 

Test Preparation

Important Conceptual Questions on Linear Algebra.

Daily Quiz on Engineering Mathematics

Most Expected Question from Linear Algebra for GATE 2019

Most Expected Question from Limit for GATE 2019

In this lesson we will discuss about the course structure, syllabus of Engineering Mathematics, about the the outcome of this course, importance of Engineering Mathematics for the GATE examination. We will also understand about our strategy to learn the engineering mathematics for the GATE.

Course Overview

This is the first lesson of the course Engineering Mathematics, where we will discuss about the standard properties of a determinant, and some tips and techniques to tackle the problem of matrix in the GATE examination.

MATRIX : Properties of Determinant

In this lesson we will understand about the concept of Upper Triangular Matrix, Lower Triangular Matrix, Scalar Matrix, Diagonal Matrix, Identity Matrix,  We will also learn the trick to find the determinant of above said matrix. At the end of the lesson we will solve the problem based on the discussed concept.

MATRIX : Upper and Lower Triangular Matrix

In this lesson we will learn about how to find the determinant of a matrix which is order of 3 rows and 3 columns. We will understand how to apply the trick and method to simplify the problem. At then end of the lesson we will also solve problems based on this concept.

MATRIX : Finding Determinant of a 3X3 Matrix

In this lesson we will learn about how to find the determinant of a matrix which is order of 4 rows and 4 columns. We will understand how to apply the trick and method to simplify the problem. At then end of the lesson we will also solve problems based on this concept.

MATRIX : Finding Determinant for 4x4 Matrix

In this lesson we will understand the concept of Transpose of a matrix, properties of a Transpose. We will also understand about the symmetric matrix and condition to satisfy the symmetric matrix. We will also cover the topic skew symmetric matrix and understand it's properties as well.

MATRIX : Symmetric and Skew Symmetric Matrix

In this lesson we will understand the concept of Invertible matrix. We will also understand the concept of Singular and non singular matrix as well. At the end of the lesson we will solve the problem based on the concept we learnt in the lesson.

MATRIX : Invertible, Singular and Non Singular Matrix

In this lesson we will learn the concept how to find the inverse of matrix which is order 2 x 2. We will also learn the trick to remember to find the adjoint of matrix. We will  also solve many GATE oriented problems and also discuss about the problem which appeared in the GATE examination.

MATRIX : Inverse of 2X2 Matrix

In this lesson we will learn the concept how to find the inverse of matrix which is order 3 x 3. We will learn the concept of minor and cofactor in a matrix and  also learn how to find them with an example. We will also solve our homework problem which was discussed in our last lesson.

MATRIX : Inverse of 3x3 Matrix

In this lesson we will complete our topic inverse of a matrix for a 3 x 3 matrix. We will understand the trick how to find adjoint of a matrix. We will also solve the problem appeared in GATE to find the inverse of a matrix.

MATRIX : Inverse of a 3 x 3 Matrix Cont.

In this lesson we will understand our approach to solve some standard problems on Matrix algebra. We will learn the concept how to solve the determinant of matrix by using row and column operation and we will also understand how to determine the determinant for a matrix of an order 4.

MATRIX : GATE Problem Series - SET 1

MATRIX : GATE Problem Series - SET 2

In this lesson we will discuss about the properties of adjoint matrix. We have also validated those properties as well in step by step so we could remember it. This lesson also help us to understand how to establish the formula between inverse of matrix and adjoint of matrix

MATRIX : Properties of Adjoint Matrix - Part 1

In this lesson we will discuss about the properties of adjoint matrix. We have also validated those properties as well in step by step so we could remember it. This lesson also help us to understand how to establish the formula between matrix and adjoint of matrix. At the end of the lesson we have also solved the problem based on the concept we understood.

MATRIX : Properties of Adjoint Matrix Part 2

In this lesson we will solve problems on the Matrix algebra utilising our concept that we learnt so far. We will also understand how to utilise the concept of Invertible matrix to identify the inverse of a matrix.

MATRIX : GATE Problem Series - SET 3

In this lesson we will solve problems on the Matrix algebra utilising our concept that we learnt so far. We will also solve the problem which appeared in the GATE examination from linear algebra.

MATRIX : GATE Problem Series - SET 4

In this lesson we will solve problems on the Matrix algebra utilising our concept that we learnt so far. We will also solve the problem which appeared in the GATE examination from the topic linear algebra.

MATRIX : GATE Problem Series SET 5

MATRIX : GATE Problem Series SET 6

MATRIX : GATE Problem Series SET 7

MATRIX : GATE Problem Series SET 8

In this lesson we will understand the concept of sub matrix and minor.  We will also understand how to find the rank of matrix. Properties of Rank of Matrix is also explained in detailed way with an example.

Rank of MATRIX: Part 1

In this lesson we will understand the concept of row echelon form and column echelon form and their properties.  We will also understand the important information regarding rank of matrix.  At the end of the lesson we will solve the problem on Rank of Matrix.

Rank of MATRIX: Part 2

In this lesson we have solved the previous year GATE Problem and also GATE oriented problems on the topic Rank of Matrix.  We have understood the approach how to identify the rank of matrix while solving the problem.

MATRIX : GATE Problem Series SET 9

In this lesson we will understand the concept of system of linear equations.  We will understand about consistent and inconsistent system. We will also understand about the concept of unique and infinite solution,  concept of Homogenous system of linear equation is also covered in this lesson.

System of Linear Equation

In this lesson we will solve the numerical on the concept that we have learnt from the system of linear equation.  We will understand the concept how the system is determined as consistent and inconsistent.  We will also uderstand the concept of rank of augemented matrix and rank of coefficient matrix.

MATRIX : GATE Problem Series SET 10

MATRIX: GATE Problem Series SET 11

MATRIX : GATE Problem Series SET 12

In this lesson we will solve the problem based on the concept of system of linear equation. We will also understand the summary of system of linear equation based on one chart. We will also discuss the summary of the topics that we have discussed so far in this course.

MATRIX : GATE Problem series SET 13

In this lesson we will understand the concept of Eigen value and Eigen vector.  We will also solve the numerical utilising the concept of Eigen value and Eigen vector.

Eigen Value and Eigen Vector

In this lesson we will understand the properties of Eigen value and based on these properties we will also solve the problems.  We will understand the concept of sum of the Eigen value is equals to the sum of principle diagonal elements,  and product of the Eigen values is equals to its determinant.

Properties of Eigen Value

In this lesson we will understand the properties of Eigen value and based on these properties we will also solve the problems.  We will understand the concept of sum of the Eigen value is equals to the sum of principle diagonal elements,  and product of the Eigen values equals to its determinant.

MATRIX : GATE Problem Series SET 14

MATRIX : GATE Problem Series SET 15

In this lesson we will understand the concept of Cayley Hamilton Theorem,  and utilize this concept in order to find the higher and negative powers of the given matrix.

Cayley Hamilton Theorem

This is the final lesson for the topic linear algebra,  which is under the course engineering mathematics.  We will solve the PYQs appeared from the topic Cayley Hamilton Theorem under linear algebra.

MATRIX : GATE Problem Series SET 16

In this lesson we have covered the introduction to limit and when does the limit exist for a given function.  We have also understood about the left handed limit and right handed limit.  The concept of existence of limit is also covered in this lesson with a numerical example.

Calculus : Introduction to Limit

In this lesson we will understand about the concept of Existence of limit for Greatest Integer Function and Fractional Part Function. We will analyze why limit does not exist for Greatest Integer Function at all integer.

Existence of Limit : Greatest Integer Function

In this lesson we will understand about the concept of Fractional Part Function. We will analyze why limit does not exist for Fractional Part Function at all integer. At the end of the lesson we will solve some numerical based on the concept of existence of limit.

Existence of Limit : Fractional Part Function

In this lesson we will understand about basic properties of limit and also understand factoring method,  conjugate method, and substitution method to solve the problems on limit.

Properties of Limit

In this lesson we will understand the concept of limit Inderminate form and also understand the concept of L' Hospitals Rule. We will solve various examples of Limit inderminate form utilizing L' Hospitals Rule.

Limit Indeterminate Form

In this lesson we will understand the concept how to address the problem when the limit appraches to infinity.  We will discuss all the possible cases and solve the numerical as well.  At the end of the lesson we will revise all the important results in limit which is important to solve the numerical.

Limit Approaches to Infinity

In this lesson we will solve the PYQs which appeared in GATE examination from the concept of Limit.  We will also revise all the concept that we learnt from the previous lesson.

Limit : GATE Problem Series Set 1

Limit : GATE Problem Series Set 2

Limit : GATE Problem Series Set 3

In this lesson we will understand about the concept of one sided limit and test the behaviour of the important function.  We will also understand  concept of continuity and how to test continuity at a given point.

Introduction to Continuity

In this lesson we will understand the different type of discontinuity and analyze with respect to graph.  At the end of the lesson we will also understand about some important continuous function.

Type of Discontinuity

In this lesson we will understand about the continuity at an open and closed interval respectively. We will also test  the existence of limit and continuity for  Piecewise linear function.

Continuity: Piecewise Linear Function

In this lesson we will discuss the numericals based on the conept of continuity.  We will also test the three fold conditions while checking the continuity behaviour for that function at that point.

Continuity:GATE Problem Series SET 4

Continuity: GATE Problem Series SET 5

In this lesson we will solve the home work problem and then understand the concept of differentiability. We will also learn if a function is differentiable at a given point,  then it should be continuous at that point.

Concept of Differentiability: Part 1

In this lesson we will understand following concept:  

1. When a function is not continuous at a given point,  then it is always not differentiable at that point. 
 
2. When a function is diffrentiable at the given point,  then it is always continuous at that point. 

3. When a function is continuous at a given point,  then it is not gurantee that it will be differentiable at that point.

Concept of Differentiability: Part 2

In this lesson we will solve the numerical based on the concept of differentiability which is very important for the GATE examination.

Differentiability : GATE Problem Series SET 6

Differentiability : GATE Problem Series SET 7

Differentiability : GATE Problem Series SET 8

In this lesson we will understand the basic introduction about the maxima and minima,  concept of stationary point and turning point.  We will also understand about the local maxima and local minima

Introduction to Maxima and Minima

In this lesson we will understand how to identify the local maxima and local minima for the given function using first derivative test. We will also understand about the concept of point of inflection.

Maxima and Minima: 1st Derivative Test

In this lesson we will understand gow to identify the local maxima and local minima for the given function using second derivative test. We will also solve the numerical based on the concept that we learnt.

Maxima and Minima: 2nd Derivative Test

In this lesson we will solve numerical based on concept of Maxima and Minima using second derivative test.  We will also understand the concept of inflection in 2nd derivative test.

Maxima and Minima : Point of Inflection

In this lesson we will understand the concept of point of inflection using the concavity test.

Maxima and Minima: Concavity Test

In this lesson we will solve the numerical based on the concept of concavity test and find the inflection point.

Concavity Test : GATE Problem Series SET 9

In this lesson we will solve the numerical on topic Maxima and Minima and utilize the concept that we have learnt so far while solving the problem.

Maxima and Minima : GATE Problem Series SET 10

Maxima and Minima : GATE Problem Series SET 11

Maxima and Minima: GATE PYQs

In this lesson we will understand the concept of Maxima and Minima for a two variable function. We will also solve numerical based on this concept.

Maxima and Minima : Two Variables Function

In this lesson we will understand how to solve the Maxima and minima problem for a two variables function.

Maxima and Minima : GATE Problen Series SET 12

In this lesson we will understand how to find the Maxima and Minima for a application based question.

Maxima and Minima: GATE Problem Series SET 13 (in Hindi)

In this lesson we will understand about the concept of Rolle's theorem and how to solve numerical on Rolle's theorem.

Mean Value Theorem : Rolle's Theorem

In this lesson we will solve the numerical based on the concept of Rolle's theorem and as well as, we will also understand the concept of Lagrange's mean value theorem.

Lagrange's Mean Value Theorem

In this lesson we will solve the numerical based on the concept of Lagrange's mean value theorem.

Mean Value Theorem: GATE Problem Series SET 14

In this lesson we will understand the concept of Cauchy's mean value theorem.  We will also try to visualize the concept with the help of Graph.

Cauchy's Mean Value Theorem

In this lesson we will solve the numerical based on the concept of Cauchy's Mean Value Theorem.

Cauchy's Mean Value Theorem :GATE Problem Series SET 15

In this lesson we will understand the basic concept about the Taylor Series.

Concept of Taylor Series: Part 1

In this lesson we will understand about the concept of Taylor series and solve the numerical as well.

Concept of Taylor Series: Part 2 (in Hindi)

Taylor Series: GATE Problem Series SET 16

In this lesson we will solve the numericals on Taylor series and understand the concept of Taylor series in more detail.

Taylor Series: GATE Problem Series SET 17

Taylor Series: GATE Problem Series SET 18

Taylor Series : GATE Problem Series SET 19

In this lesson we will solve the numerical based on the topic of Mean Value Theorem.

Mean Value Theorem : GATE Problem Series SET 20

In this lesson we will understand about the basic concept of partial derivatives  and how it is different from the normal differentiation.  We will also understand the concept of first and second order partial derivatives.

Concept of Partial Derivatives: Part 1

In this lesson we will understand about the basic concept of partial derivatives and how to find the higher order partial derivatives

Concept of Partial Derivatives: Part 2

In this lesson we will understand about the concept of Homogenous function and also understand how to find the degree for the homogenous function.

Homogenous Function

In this lesson we will understand about the concept of Explicit and Implicit function.  We will also understand how to find the first and  second order derivative for the implicit function using partial derivatives.

Explicit and Implicit Function

In this lesson we will solve the numericals on the partial derivatives and understand the concept in more detail.

Partial Derivatives: GATE Problem Series SET 21

Partial Derivatives: GATE Problem Series SET 22

In this lesson we will understand the method to write the chain rule equation for any multi variable function.

Multivariable Chain Rule: Part 1

In this lesson we will understand how to write the chain rule equations for the multivariable function and we will also solve the numerical to clear the concept in more detail.

Multivariable Chain Rule: Part 2

In this lesson we will understand how to solve the numerical on partial derivatives for the multivariable function using the chain rule equation.

Partial Derivatives: GATE Problem Series SET 23

In this lesson we will understand about the basic of Euler's Theorem.  We will understand how to write the first order partial derivatives equations for both algebraic and non algebraic function.

Euler's Theorem

In this lesson we will understand about the concept of Applications of Euler's Theorem.  We will derive the formula for the second order partial derivatives for both Algebraic and non Algebraic function.  At the end of the lesson we have splved numerical as well based on this concept.

Application of Euler's Theorem

In this lesson we will solve the numerical based on the concept of Partial Derivatives.  We will also solve the GATE PYQs on this topic.

Partial Derivatives: GATE Problem Series SET 24

In this lesson we will understand the basics of Definite Integral and also understand its definition

Definite Integral: Introduction

In this lesson we will understand the properties of Definite Integral and also revise the formula.

Properties of Definite Integral

In this lesson we will understand about the basic concepts of Integration by parts and I LATE rule.  We will also understand few short tricks that we can apply directly on the numericals.

Definite Integral: GATE Problem Series SET 25

In this lesson  we will understand how to solve the numerical on definite integral utilizing the property that we have learnt in the previous lessons.

Definite Integral: GATE Problem Series SET 26

In this lesson we will understand how to solve the numerical on definite integral utilizing the property that we have learnt in the previous lessons.

Definite Integral : GATE Problem Series SET 27

Definite Integral : GATE Problem Series SET 28

Mentored 81,000+ Students | My Multiple Students secured AIR Below 100 in GATE | Joined top IISc, IITs & NITs | Joined PSUs | 5+ Years Exp.

Sweta Kumari

This course will cover complete concept of Graphs in Discrete Mathematics.

(Hindi) Graphs in Discrete Mathematics + PYQs - GATE (CS/IT)

As I am here as a DMS educator , I would say , I have won maths olympiad state level once at 12th standard, I have interned with HP.

Chinmaya Sahoo

Discrete Mathematics is one of the most important part for any gate aspirants. It covers as much as 14-15 % of the total syllabus. It is very easy to understand the concepts and learn discrete mathematics.

Discrete Mathematics

I am an E&Tc Engineer, technical freelancer, I like to teach, write, explore new places. 

Vinod Singh Jadon

The course of Engineering Mathematics focuses on GATE and other competitive exams for all Engineers. All the key concepts of Engineering Mathematics has been covered along with examples. This course aims a quick and effective
revision of the subject.

Lessons

126 lessons • 24h 7m