Introduction to Inverse Trigonometric Functions

Basic Concepts

Inverse of Sine Function and its Graph

Inverse of Cosine Function and its Graph

Inverse of Tangent Function and its Graph

Inverse of Cotangent Function and its Graph

Inverse of Cosecant Function and its Graph

Inverse of Secant Function and its Graph

Properties of Inverse Trigonometric Functions-I

Properties of Inverse Trigonometric Functions-II

Properties of Inverse Trigonometric Functions-III

Properties of Inverse Trigonometric Functions-IV

Properties of Inverse Trigonometric Functions-V

Examples-I

Examples-II

Examples-III

Examples-IV

Examples-V

Introduction to Matrices

Representation of Vertices of Geometrical Figures

Types of Matrices

Equality of Matrices

Addition of Matrices

Multiplication of a Matrix by a Scalar

Difference of Matrices

Properties of Matrix Addition

Properties of Scalar Multiplication of a Matrix

Multiplication of Matrices

More about Multiplication of Matrices

Properties of Multiplication of Matrices-I

The Properties of Multiplication of Matrices-II

Transpose of a Matrix

Symmetric and Skew Symmetric Matrices

Theorems Relating Symmetric and Skew Symmetric Matrices

Elementary Operation (Transformation) of a Matrix

Invertible Matrices

Inverse of a Matrix by Elementary Operations

Introduction to Determinants

Determinants of Matrices of Orders 1 and 2

Determinant of a Matrix of order 3

Expansion along the First Row

Expansion along Second Row

Expansion along First Column

Some Rules Related to the Determinants

Properties of Determinants-I

Properties of Determinants-II

Properties of Determinants-III

Properties of Determinants-IV

Area of a Triangle

Properties of Determinants-V

Properties of Determinants-VI

Minors of Elements of Determinants

Cofactors of Elements of Determinants

Adjoint of a Matrix

Theorem Related to the Adjoint of a Matrix

More Theorems

Theorem on Invertible Matrices

Introduction To Continuity

Problems Based on Continuous Functions

Introduction To Differentiability

Basics Of Chain Rule

Problems Based On Chain Rule

Derivative of Implicit Functions

Derivative of Inverse Trigonometric Function

Problem Based on Derivative of Inverse Trigonometric Function

Exponential Functions

Features of Exponential Functions

Properties of Exponential Functions

Introduction to Logarithmic Function

Plot of Logarithmic Function

Properties of Logarithmic Function

Derivatives of Exponential and Logarithmic Functions

Logarithmic Differentiation

Derivatives of Functions in Parametric Forms

Introduction to Second Order Derivatives

Problems Based on Second Order Derivative

Rolle’s Theorem

Rate of Change of Quantities

Introduction To Increasing and Decreasing Functions

Derivative test for Increasing and Decreasing Functions

Finding intervals in which a given Polynomial Function is Increasing or Decreasing

Tangents

Equation of the Tangent

Normal

Equation of the Normal

Introduction to Approximations

Finding Approximate Value of Polynomials

Word Problem Involving Approximations

Introduction to Maxima and Minima

First Derivative Test

Second Derivative Test

Second Derivative Test: Example I

Second Derivative Test: Example II

Maximum and Minimum Values of a Function in a Closed Interval

Introduction to Integrals

Integrals of Important Functions-I

Integrals of Important Functions-II

Properties of Indefinite Integrals

Calculating Integrals

Integration by Substitution

Integrals of Trigonometric Functions

Example Based on Integration using Substitution

Integration Using Trigonometric Identities

Integration of Some Particular Functions-I

Integration of Some Particular Functions-II

Integrals of Some Particular Functions- III

Integration by Partial Functions-I

Integration by Partial Functions-II

Integration by Partial Functions-III

Integration by Parts

Integral of the Type

Integrals of Some More Types

Definite Integral as the Limit of a Sum

Fundamental Theorem of Calculus

Finding area Under a Simple Curve

Problem Based on Finding the Area Under a Simple Curve

Area of the Region Bounded by a Curve and a Line

Area Between Two Curves

Basic Concepts of Differential Equation

General and Particular Solutions of a Differential Equation

Formation of a Differential Equation

Equations in Variable Separable Form

Problem Based on Variable Separable Form

Introduction to Homogenous Functions

Solving Homogeneous Differential Equations

Linear Differential Equations

Solving Linear Differential Equations

Introduction to Vectors

Position Vector, Direction Cosines and Direction Ratios

Adding and Subtracting Vectors

Properties of Vector Addition

Components of a Vector

Scalar (or dot) Product of Two Vectors

Unit Vector in the Direction of a Given Vector

Section Formula-II

Scalar (or dot) Product of Two Vectors

Projection of a Vector on a Line and Another Vector

Vector Product of Two Vectors-I

Vector Product of Two Vectors-II

Vector Product of Two Vectors-III

Direction Cosines and Direction Ratios of a Line

Introduction to Three Dimensional Geometry

Direction Cosines and Direction Ratios of a Line

Equation of a Line in Space

Angle Between Two Lines

Shortest Distance Between Two Lines

Plane

Coplanarity of Two Lines

Angle Between Two Planes

Distance of a Point from a Plane

Angle Between a Line and a Plane

Introduction to Linear Programming

Formulating Linear Programming Problems Mathematically

Rules of Solving the Linear Programming Problems Graphically

Solving LPP Graphically

Introduction to Linear Programming

Linear Programming Problem

Mathematical Formulation of the Linear Programming Problem

Graphical Method of Solving Linear Programming Problems

Different Types of Linear Programming Problems

Diet Problem Types of Linear Programming

Manufacturing Problems Types of Linear Programming

Allocation Problems Types of Linear Programming

Transportation Problems Types of Linear Programming

Corner Point Method of Solving linear Programming Problem

Introduction to Probability

Conditional Probability

Properties of Conditional Probability

Multiplication Theorem on Probability

Multiplication Theorem on Probability

Baye’s Theorem

Probability Distribution of a Random variable

Random Variables and its Probability Distributions

Mean of a Random Variable

Variance of a Random Variable