Calculus | Differential and Integral Calculus
Calculus was founded by Newton and Leibniz. Calculus is a branch of mathematics that helps us study change. It is used to understand how things change over time or how quantities grow, shrink, or accumulate. There are two main parts of calculus:
- Differential Calculus: It helps us calculate the rate of change of one quantity concerning another. This rate of change is called the derivative.
- Example: Finding how fast a balloon inflates as you pump air into it.
- Calculating the slope of a hill (steepness).
- Integral Calculus: helps us calculate the total accumulation of change. This accumulation is called the integral.
- Example: Calculating the area under a curve (e.g., finding the distance travelled by a car when you know its speed at every moment).
- Determining the total rainfall collected in a reservoir.
Note: The process of finding the value of a derivative is called differentiation, and the process of finding the value of an integral is called integration.
Table of Content
Basic of Calculus
- Functions
- Limits
- Formal Definition of Limits
- One-Sided Limits
- Infinite Limits
- Limits at Infinity
- Techniques for Finding Limits
- Properties of Limits
- Continuity of Functions
- Discontinuity
- Types of Discontinuity
Differential Calculus
- Differentiability
- Derivative
- Rules for Differentiation
- Formulas for Differentiation
- Examples of Derivatives
- Application of Derivatives
- Concavity and Points of Inflection
- Curve Sketching
- Partial Derivatives
- Higher Order Derivatives
- Antiderivatives
- Real-Life Application of Differentiation
Integral Calculus
- Introduction to Integration
- Types of Integrals
- Riemann Sum
- Functions defined by Integrals
- Integration Formulas
- Methods of Integration
- Application of Integration
- Line Integral
- Surface Integral
- Double Integration
- Triple Integral
Differential Eqations
- Introduction to Differential Equations
- Types of Differential Equations
Also Check Calculus Cheat Sheet.
Practice for Calculus
- Limits – Quiz
- Continuity of Functio – Quiz
- Maxima and Minima – Quiz
- Integration – Quiz
- Practice Questions on Calculus
Programs for Calculus
- Calculus with Python
- Program to Differentiate Given Polynomial
- Program to Calculate Double Integration
- Calculus in MATLAB
- Diffrentiation in MATLAB
Calculus – FAQs
What is Calculus in Maths?
Calculus is a branch of mathematics that studies the rate of change. It’s used in mathematical models to find optimal solutions. Calculus is concerned with two basic operations, differentiation and integration.
Define Differential Calculus.
Differential calculus is used to study the problems of calculating the rate at which a function changes in relation to other variables. It is represented in the form of f'(x) = dy/dx
What is Integral Calculus?
The process of calculating the area under a curve or a function is called integral calculus.
Where is calculus used in real life?
Calculus is fundamental to understanding and describing the behavior of physical systems. Engineers use calculus to analyze and design structures, and electrical circuits. Calculus is used to develop financial models and analyze complex financial derivatives.
