Topics
Relations and Functions
Relations and Functions
Algebra
Inverse Trigonometric Functions
Matrices
- Concept of Matrices
- Types of Matrices
- Equality of Matrices
- Operations on Matrices> Addition and Subtraction of Matrices
- Operations on Matrices>Scalar Multiplication
- Operations on Matrices> Matrix Multiplication
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrices
- Invertible Matrices
- Overview of Matrices
Calculus
Determinants
Vectors and Three-dimensional Geometry
Continuity and Differentiability
- Continuous and Discontinuous Functions
- Algebra of Continuous Functions
- Concept of Differentiability
- Derivatives of Composite Functions
- Derivative of Implicit Functions
- Derivative of Inverse Function
- Exponential and Logarithmic Functions
- Logarithmic Differentiation
- Derivatives of Functions in Parametric Forms
- Second Order Derivative
- Overview of Continuity and Differentiability
Linear Programming
Probability
Applications of Derivatives
Integrals
- Introduction of Integrals
- Integration as an Inverse Process of Differentiation
- Properties of Indefinite Integral
- Methods of Integration> Integration by Substitution
- Methods of Integration>Integration Using Trigonometric Identities
- Methods of Integration> Integration Using Partial Fraction
- Methods of Integration> Integration by Parts
- Integrals of Some Particular Functions
- Definite Integrals
- Fundamental Theorem of Integral Calculus
- Evaluation of Definite Integrals by Substitution
- Properties of Definite Integrals
- Overview of Integrals
Sets
Applications of the Integrals
Differential Equations
- Basic Concepts of Differential Equations
- Order and Degree of a Differential Equation
- General and Particular Solutions of a Differential Equation
- Methods of Solving Differential Equations> Variable Separable Differential Equations
- Methods of Solving Differential Equations> Homogeneous Differential Equations
- Methods of Solving Differential Equations>Linear Differential Equations
- Overview of Differential Equations
Vectors
- Basic Concepts of Vector Algebra
- Direction Ratios, Direction Cosine & Direction Angles
- Types of Vectors in Algebra
- Algebra of Vector Addition
- Multiplication in Vector Algebra
- Components of Vector in Algebra
- Vector Joining Two Points in Algebra
- Section Formula in Vector Algebra
- Product of Two Vectors
- Overview of Vectors
Three - Dimensional Geometry
Linear Programming
Probability
Introduction
Integral calculus is a branch of mathematics that develops from two main ideas: finding a function when its derivative is known, and finding the area under a curve.
In simple words, differentiation tells how a quantity is changing, while integration helps recover the original quantity or measure the total accumulation of that quantity. The chapter introduces anti-derivatives, indefinite integrals, definite integrals, and the basic idea that these are connected through the Fundamental Theorem of Calculus.
Definition: Indefinite Integral
The collection of all anti-derivatives of a function is called its indefinite integral.
Here: f(x) = integrand, dx = variable of integration, C = constant of integration.
Definition: Definite Integral
A definite integral is connected with finding the area under a curve over a given interval. The chapter introduction presents area as one of the central motivating ideas behind integral calculus.
Key Points: Introduction of Integrals
- Primitive
Another name for anti-derivative. - Indefinite Integral
The family of all anti-derivatives of a function. - Definite Integral
An integral taken between two fixed limits, commonly used to represent area or total accumulation. - Integral Calculus
The branch of calculus dealing with anti-derivatives, accumulation, and areas under curves.
