Calculus

Calculus, developed by Newton and Leibniz, is the branch of mathematics that helps us study how quantities change and how they accumulate. It allows us to understand motion, growth, rates, and areas under curves.

Calculus has two main parts:

1. Differential Calculus – the study of derivatives and rates of change
2. Integral Calculus – the study of accumulation, areas, and total values

Basics of Calculus

This section builds the foundation for calculus by introducing functions, graphs, limits, and continuity.

• Functions and Graph
• Domain and Range
• Types of Functions
• Limits
• Continuity and Discontinuity

Differential Calculus

Differential calculus focuses on the concept of derivatives, which measure how a function changes at any point. This section covers basic rules, formulas, and real-life applications.

• Differentiability
• Derivative
• Rules for Differentiation
• Formulas for Differentiation
• Application of Derivatives
• Concavity and Points of Inflection
• Curve Sketching
• Partial Derivatives
• Higher Order Derivatives
• Real-Life Application of Differentiation

Derivatives of Common Functions

The derivatives of various types of functions are essential concepts in calculus used to analyze rates of change and the behavior of functions.

• Derivatives of Polynomial Functions
• Derivatives of Trigonometric Functions
• Derivatives of Exponential Functions
• Derivatives of Logarithmic Functions
• Derivatives of Inverse Trigonometric Functions
• Derivatives of Inverse Functions
• Derivatives of Composite Functions

Integral Calculus

Integral calculus studies accumulation and the total effect of small changes. It also establishes the relationship between differentiation and integration through the Fundamental Theorem of Calculus.

• Introduction to Integration
• Riemann Sum
• Integration Formulas
• Methods of Integration
• Functions defined by Integrals
• Application of Integration
• Antiderivatives

Types of Integrals

There are different types of integrals used depending on the problem at hand. You will explore each type of integral here:

• Definite Integrals
• Indefinite Integrals
• Improper Integrals

Advance Integrals

• Line Integral
• Surface Integral
• Double Integration
• Triple Integral

Differential Equations

Differential equations describe relationships between functions and their derivatives. They are widely used in physics, engineering, biology, and economics.

• Introduction to Differential Equations
• Order and Degree of Differential Equations
• Solution of Differential Equations

Types of Differential Equations:

Here you will explore the types of differential equations, each with its unique methods of solution.

• Exact Differential Equations
• Separable Differential Equations
• Ordinary Differential Equations
• Partial Differential Equations
• Linear Differential Equations
• Homogeneous Differential Equations
• First Order Differential Equation
• Second Order Differential Equation

Also, check: Calculus Cheat Sheet

Practice for Calculus

This section provides a series of practice quizzes and questions to reinforce your understanding of key calculus concepts. You'll test your knowledge on limits, continuity, maxima and minima, and integration through interactive exercises.

• Limits - Quiz
• Continuity of Function - Quiz
• Maxima and Minima - Quiz
• Integration - Quiz
• Practice Questions on Calculus

Programs for Calculus

This section offers practical programming solutions for implementing calculus operations. You’ll learn how to write efficient code in Python and MATLAB, enhancing your skills in applying mathematical concepts through programming.

• Calculus with Python
• Program to Differentiate Given Polynomial
• Program to Calculate Double Integration
• Calculus in MATLAB
• Differentiation in MATLAB

Limits in Calculus: Definition, Formula, Examples, Limits & Deriatives

Limits in Calculus: Definition, Formula, Examples, Limits & Deriatives

Continuity of Functions: Definition, Types, Condition, Examples

Derivative of a Function - Calculus, Chain Rule and Properties

Rolle's Mean Value Theorem: Statement, Proof, Graph & Examples

Cauchy's Mean Value Theorem: Statement, Proof and Examples

Lagrange's Mean Value Theorem: Statement, Proof, Graph & Examples

Maxima and Minima: Types, Properties, and Real World Applications

Integration by Parts

Definite Integral | Definition, Formula & How to Calculate Definite Integral

Definite Integrals of Piecewise Functions