Name: Mathematics : JM & JA Video Lectures
Brand: eSaral
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Know Your Math Faculty

N.K. Gupta Sir

First See These Videos

How to Make Notes

Strategy to Manage Notebooks

Best Way of Study

Faculties in eSaral

Logarithm

Introduction to Logarithms

Basics of Logarithms

Properties of Logarithm - Part 1

Properties of Logarithm - Part 2

Solving Logarithmic Equations

Graph of Logarithmic Functions

Antilogarithm

Characteristic & Mantissa

Compound Angle (Trigonometric Ratios & Identities)

Introduction to Trigonometry

Trigonometric Ratios

Real Definition of Trigonometric Ratios

Trigonometric Ratios of Allied Angles

Trigonometric Graphs

Trigonometric Ratios of Compound Angles

Transformation Formulae - Sum to Product

Transformation Formulae - Product to Sum

Tangent Formula

Trigonometric Ratios of Multiple & Submultiple Angles

Trigonometric Ratios for some Standard Angles

Trigonometric Ratios of the Sum of More Than Two Angles

Trigonometric Identities in a Triangle (Conditional Identities)

Application of Trigonometry in Maximising & Minimising - Type I

Application of Trigonometry in Maximising & Minimising - Type II, III

Application of Trigonometry in Maximising & Minimising - Type IV, V & VI

Summation of Trigonometric Series

Continued Product of Sine & Cosine Series

Quadratic Equations

Polynomials

Quadratic Equations and Nature of Roots

Formation of Quadratic Equations

Symmetric Function of Roots

Roots Under Special Conditions

Identities

Condition for Common Roots

Introduction to Quadratic Graphs

Inequalities

Maximum and Minimum Values of Quadratic and Rational Functions

Location of Roots

Transformation of Quadratic Equations

Theory of Equations

Quadratic Expressions in Two Variables

Modulus Function

Inequalities Involving Modulus Function

Logarithmic Inequalities

Exponential Inequalities

Sequence and Series

Introduction to Sequence, Series and Progression

Introduction to Arithmetic Progression - General Term

Summation of Arithmetic Progression

Properties of Arithmetic Progression

Arithmetic Mean

General Term of Geometric Progression

Summation of Geometric Progression

Properties of Geometric Progression

Geometric Mean

Introduction to Harmonic Progression - General Term

Harmonic Mean

Relation Between A.M., G.M. & H.M.

Arithmetico - Geometric Progression

Special Sequence - Sigma Notation

Special Sequence - Method of Difference

Special Sequence - Splitting the Terms

Special Sequence - Miscellaneous

Trigonometric Equation

Introduction to Trigonometric Equations

General Solution of Trigonometric Equations - Part 1

General Solution of Trigonometric Equations - Part 2

Strategies for Solving Trigonometric Equations - 1. Factorization 2. Reducing to a Quadratic Eq.

Strategies for Solving Trigonometric Equations - 3. Introducing an Auxiliary Argument

Strategies for Solving Trigonometric Equations - 4. Transforming Sum to Product 5. Product to Sum

Strategies for Solving Trigonometric Equations - 6. By Change of Variable/ Substitution

Strategies for Solving Trigonometric Equations - 7. By Boundness 8. By Squaring 9. System of T.E.s

Trigonometric Inequalities & System of Inequalities

Solution of Triangles

Properties & Solution of Triangle

Sine Rule

Cosine Rule

Projection Formula

Tangent Rule

Half Angle Formulae

m-n Theorem

Circumcircle

Incircle

Excircles

Orthocentre

Lengths of Angle Bisector & Median

Regular polygon

Application of Trigonometry

Height and Distance

Some Applications of Trigonometry - Problem Plus

Point

Mathematical Contribution of a Fly

Coordinate System & Distance Formula

Section Formula

Centers of a Triangle - Centroid, Incentre & Excentre

Centers of a Triangle - Orthocentre & Circumcentre

Area of Triangle

Locus

Straight Line

Introduction to Straight Line

Standard Forms of Equations of Straight Lines - Slope, Intercept Form

Standard Forms of Equations of Straight Lines - One Point, Two Point Form

Standard Forms of Equations of Straight Lines - Normal, Parametric, General Form

Point and Line

Length of the Perpendicular from a Point on a Line

Angle between two Straight Lines

Equation of Lines - Parallel & Perpendicular to a given line

Equation of Straight Lines Equally Inclined to a given line

Family of Straight Lines

Concurrency of Straight Lines

Angle Bisectors

Optics

Transformation of Axes

Pair of Straight Lines

General Equation of Second Degree representing a Pair of Straight Lines

Homogenisation

Circle

Center - Radius Form of a Circle

General Form of a Circle

Intercept Form of a Circle

Diametric Form of a Circle

Parametric Equations of the Circle

Point & Circle

Line & Circle

Tangents from an External Point

Chord of Contact

Pair of Tangents to the Circle

Problems Based on Pair of Tangents to the Circle

Chord with Mid-Point

Director Circle

Chord of a Circle

Normal to the Circle

Radical Axis

Family of Circles

Family of Circles - Special Cases

Coaxial System of Circles

Intersection of Circles

Common Tangents to the Circles

Parabola

Standard Parabola - Part 1

Standard Parabola - Part 2

Shifted parabola - Part 1

Shifted parabola - Part 2

Shifted parabola - Part 3

Point and Parabola

Parametric Coordinates of a Parabola

Chord joining two points of a Parabola - Part 1

Chord joining two points of a Parabola - Part 2

Length of Chord of Parabola

Tangents to Parabola - Slope Form

Tangents to Parabola - Cartesian, Parametric Form

Pair of Tangents to Parabola

Normals to Parabola - Cartesian, Parametric Form

Normals to Parabola - Slope Form

Common Tangent

Subtangent & Subnormal

Chord with given Mid-Point

Diameter of Parabola

Highlights about Parabola

Ellipse

Standard Ellipse

Ellipse at a Glance

Problems on Standard Ellipse

Other Forms of Ellipse

Auxilliary Circle and Eccentricity of Ellipse

Point and Ellipse

Tangent to Ellipse - Slope Form

Tangent to Ellipse - Cartesian Form

Tangent to Ellipse - Parametric Form

Normals to Ellipse

Pair of Tangents to Ellipse

Chord with a given Mid-Point

Hyperbola

Standard Hyperbola

Hyperbola at a Glance

Other Forms of Hyperbola

Auxilliary Circle and Eccentricity of Hyperbola

Point and Hyperbola

Tangents to Hyperbola - Slope Form

Tangents to Hyperbola - Parametric Form

Tangents to Hyperbola - Cartesian Form and Chords

Normals to Hyperbola

Pair of Tangents & Chord with given Mid-Point

Asymptotes

Rectangular Hyperbola

Permutation & Combination

Factorial

Formation of Numbers

Permutation and Combination

Selection of 'r' things out of 'n' different things

Permutation of Things which are all Different

Formation of Groups and their Distribution

Combination of Things which are not all Different

Number of Divisors and their Sum

Permutation of Alike Objects Taken All or Some at a Time

Rank of the Word

Circular Permutation: When Objects are Different or Alike

Geometric Problems

Principle of Inclusion and Exclusion

Summation of Numbers

Distribution of Alike Objects

Derangement

Miscellaneous Problems of P&C

Binomial Theorem

Introduction to Binomial Theorem

Expansion of Binomial Theorem

mth-term from the End

Coefficient of x to the power m in the Expansion

Middle Term in the Expansion

Number of Terms in the Expansion

Numerically Greatest Term

Properties of Binomial Cofficient - Type 1

Properties of Binomial Cofficient - Type 2

Properties of Binomial Cofficient - Type 3

Properties of Binomial Cofficient - Type 4

Sum of Coefficients in an Expansion

Applications of Binomial Theorem

Multinomial Theorem

Binomial Theorem for Negative & Fractional Index

Approximation

Complex Number

Algebra of Complex Number

Conjugate of Complex Number

Modulus of Complex Number

Argument of Complex Number

Polar Form

Cartesian & Vector Form

De-Moivre's Theorem

Cube Roots of Unity

nth Roots of Unity

Geometry

Rotation

Equation of Straight Line

Geometry Conic Section

Locus

Triangular Inequality

Statistics

Measure of Central Tendency - Arithemetic Mean

Properties of Arithemetic Mean

Measure of Central Tendency - Weighted Mean & Combined Mean

Harmonic Mean and Geometric Mean

Measure of Central Tendency - Median

Measure of Central Tendency - Mode

Measures of Dispersion - Range and Mean Deviation

Measures of Dispersion - Variance and Standard Deviation

Properties of Variance

Principle of Mathematical Induction

Subjective Approach to Induction

Objective Approach to Induction

Mathematical Reasoning

Logical Operator : AND and OR

Logical Operator : Conditional and Bi-conditional

Algebra of Statements

Sets

Introduction to Sets

Types of Sets

Operations on Sets

Important Results on Sets

Relations

Introduction to Relations

Types of Relations

Classification of Relations

Function

Value of the Function

Domain, Co-domain & Range of the Function

Constant & Identity Functions

Signum Function

Exponential & Logarithmic Functions

Absolute Value Function

Greatest Integer Function

Fractional Part Function

Polynomial Function

Algebraic & Rational Functions

Algebraic Operations on Function

Range of a Function

Applications of Functional Rule

Equal or Identical Functions

Homogeneous Function

Bounded, Implicit & Explicit Functions

Classification of Functions

Composite Functions

Inverse of a Function

Odd & Even Functions

Periodic Functions

Transformation of the Graphs

Inverse Trigonometric Function (ITF)

Domain, Range & Graphs of arc sinx

Domain, Range & Graphs of arc cosx

Domain, Range & Graphs of arc tanx

Domain, Range & Graphs of arc cotx

Domain, Range & Graphs of arc secx & arc cosecx

Properties of Inverse Trigonometric Functions : 1

Properties of Inverse Trigonometric Functions : 2 & 3

Properties of Inverse Trigonometric Functions : 4

Properties of Inverse Trigonometric Functions : 5

Properties of Inverse Trigonometric Functions : 6 & 7

Properties of Inverse Trigonometric Functions : 8

Simplification & Transformation of Inverse Functions by Elementary Substitution & their Graphs

Equations Involving Inverse Trigonometric Functions

Simultaneous In-equations Involving ITF

Summation of Series using ITF

Limit

Concept of Limit

Existence of Limit

0/0 Form - Factorisation

0/0 Form - Rationalization

0/0 Form - Standardization

Infinity by Infinity Form

(Zero into Infinity) and (Infinity into Infinity) Form

Limit of Trigonometric Functions - Part 1

Limit of Trigonometric Functions - Part 2

Limit Using Series Expansion

Limit of Exponential Functions

Limit of Logarithmic Functions

One to the power Infinity Form

Built in Limit

Application of Limit in Geometry

Limit of Composite Functions

L'Hospital Rule

(Zero to the power Zero) & (Infinity to the power Infinity) Form

Sandwich Theorem

Continuity

Concept of Continuity

Formulative Definition

Reasons & Types of Discontinuities

Continuity in an Interval

Continuity of Functions defined by Functional Rule

Continuity of Composite Functions

Intermediate Value Theorem (IMVT)

Important Points about Continuity

Continuity over Countable Set

Differentiability

Concept of Derivative

Existence of Derivative

Derivability & Continuity

Algebra of Differentiability

Important Concepts

Determination of Function satisfying the Functional Rule

Method of Differentiation

Derivative by First Principle

Derivative of Standard Functions

Theorems of Differentiation

Chain Rule

Logarithmic Differentiation

Parametric Differentiation

Derivative of One Function w.r.t. Another Function

Derivative of Implicit Function

Derivative of Infinite Series

Derivative of Homogeneous Equation

Derivative of Inverse Functions

Derivatives of Inverse Trigonometric Functions

Successive Differentiation

L'Hospital Rule

Derivative of Functions Expressed in the Determinant Form

Deduction of New Identities by Differentiating a Given Identity

Application of Derivative

Nature of Function at a Point

Increasing and Decreasing Nature of a Function over an Interval

Problems based on Monotonicity of Function

Greatest and Least Value of a Function

Establishing Inequalities

Rolle's Theorem

Lagrange's Mean Value Theorem

Introduction to Maxima & Minima

Derivative Test For Ascertaining Maxima /Minima

Special Points on a Given Curve

Optimization Problems

Maximum & Minimum Distance of a Fixed Point From a Given Curve

Roots of a Cubic Equation

Rate Measure

Approximation

Tangent and Normal at a Point

Tangent and Normal in Parameric Form

Equation of Tangent and Normal in Some Special Cases

Angle Between Two Curves

Length of Tangent, Normal, Subtangent and Subnormal

Indefinite Integration

Elementary Integrals

Integration by Substitution - Part 1

Integration by Substitution - Part 2

Integration by Substitution - Part 3

Integration by Parts - General

Integration by Parts - Some Special Formulae

Integration by Parts - Classic Integrands

Integration of Trigonometric Functions - Part 1

Integration of Trigonometric Functions - Part 2

Integration by Partial Fraction

Integration of Algebraic Expressions

Integrand Involving Even Powers of x

Integration of Irrational Algebraic Expressions

Reduction Formula

Miscellaneous Integrals

Definite Integration

Geometrical Interpretation of Definite Integration

Evaluating Definite Integrals by Finding Antiderivatives

Invalid Substitution

Properties of Definite Integration-Property 1, 2 & 3

Walli's Theorem

Properties of Definite Integration-Property 4

Properties of Definite Integration-Property 5

Properties of Definite Integration-Property 6

Properties of Definite Integration-Property 7

Properties of Definite Integration-Property 8

Derivative of Antiderivatives (Newton – Leibnitz Formula)

Summation of Series using Definite Integration

Reduction Formula

Applications of Integrals (Area Under The Curve)

Introduction to Area Under Curve

Area Between Two Curves

Some Standard Areas

Area Where the curve sketching is significant

Areas Dealing with Inequalities

Area by Shifting of Origin

Area for Curves Represented Parametrically

Area Enclosed by Inverse Function

Determination of Unknown Parameters

Concept of Variable Area

Differential Equation

Order & Degree of Differential Equation

Formation of Differential Equation

Solution of Differential Equation

Variable Seperable Form Differential Equation

Equations Reducible to Variable Seperable Form

Homogeneous Form Differential Equations

Equations Reducible to Homogeneous Form

Linear Differential Equation

Differential Equations Reducible to linear Form

Exact Differential Equation

Miscellaneous Problems of Differential Equations

Higher Order & Higher Degree Differential Equations

Use of Polar Coordinates to Solve Differential Equations

Matrices

Introduction to Matrices

Types of Matrices

Algebra of Matrices

Multiplication of Matrices - Part-01

Multiplication of Matrices - Part-02

Matrix Polynomial

Transpose of a Matrix

Symmetric & Skew Symmetric Matrix

Adjoint of a Matrix

Inverse of a Matrix

Elementary Operations (Transformation) of a Matrix

Special Matrix

Application of Matrices and Determinants

Determinant

Introduction to Determinants

Minors and Cofactors

Properties of Determinants - Part 1

Properties of Determinants - Part 2

Special Determinants

Problems on Properties

Factor Theorem

Multiplication of Determinants

Cramer's Rule : System of Linear Equations

Differentiation of Determinants

Vector

General Definitions

Vector Addition

Geometry of Vectors

Linear Combination of Vectors

Test of Collinearity

Scalar Product (Dot Product)

Vector Product (Cross Product)

Vector Equation of a Line

Vector Equation of the Angle Bisectors

Fundamental Theorem in Plane

Shortest Distance between Two Skew Lines

Product of Three or More Vectors

Vector Triple Product

Scalar Product of Four Vectors

Coplanarity of Four Points

Reciprocal System of Vectors

Solving Vector Equations

3D Coordinate Geometry

Distance Formula

Section Formula

Direction Cosines of a Vector/Line

General Equation of a Plane

Equation of a Plane Passing Through Three Given Points

Intercept Form of a Plane

Perpendicular Distance of a Point from a Plane

Angle Between Two Planes

Equation of the Bisector Planes

Family of Planes

Two Sides of a Plane

Straight Lines

Problems Based on Straight lines

Angle Between a Line and a Plane

General Equation of the Plane Containing a Line or Lines

Shortest Distance Between Two Lines

Unsymmetrical Form of Straight Line

Line of Greatest Slope in a Plane

Probability

Basic Definitions Related to Probability

Classical Definition of Probability

Odds in Favour and Odds in Against

Algebra of Probability

Addition Theorem of Probability

Conditional Probability

Multiplication Theorem of Probability

Dependent and Independent Events

Probability Associated with Three Events

Total Probability Theorem

Bayes' Theorem

Probabilities Through Stochastic Tree Diagram

Mathematical Expectation

Geometrical Probability

Probability Distribution

Binomial Probability Distribution

Linear Programming Problems

Introduction to Linear Programming Problems (LPP)

Basic Problems on LPP

Types of LPP

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Mathematics : JM & JA Video Lectures