Free Online Calculus Courses

19 Calculus Courses

Calculus

Khan Academy

Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the...

Calculus / First Semester - Limits, Continuity, Derivatives

PatrickJMT

This play list should be pretty much in order with the way many people will see material in the class. Of course, not all classes are the same, so some of my videos may be out...

Calculus Revisited: Single Variable Calculus

Massachusetts Institute of Technology

Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released...

Convex Optimization I

Stanford University

Concentrates on recognizing and solving convex optimization problems that arise in engineering. Topics include: Convex sets, functions, and optimization problems. Basics of convex...

Convex Optimization II

Stanford University

Continuation of Convex Optimization I. Topics include: Subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating...

Differential & Integral Calculus, Math 31A

University of California, Los Angeles

Math 31A is a course that provides insight into differential calculus and applications as well as an introduction to integration.

Differential Equations

Khan Academy

Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus before starting here.

Differential Equations

Massachusetts Institute of Technology

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary...

Discrete Stochastic Processes

Massachusetts Institute of Technology

Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course aims to...

Engineering Mathematics

University of New South Wales

Playlist of solved problems and examples from engineering mathematics, presented by Dr Chris Tisdell, UNSW, Sydney. Topics covered will include important aspects of applied mathematics...

Highlights of Calculus

Massachusetts Institute of Technology

Highlights of Calculus is a series of short videos that introduces the basic ideas of calculus — how it works and why it is important. The intended audience is high school students,...

Calculus is a branch of mathematics that focuses on the study of change and motion. It provides the tools for understanding and modeling dynamic systems, making it an invaluable subject for students in various fields, including engineering, physics, economics, and more.

This subject is divided into two main branches: differential calculus and integral calculus. Differential calculus deals with the concept of the derivative, which represents the rate of change of a function. Integral calculus, on the other hand, focuses on the accumulation of quantities and the area under curves. Together, these two branches form the foundation of calculus.

Key Concepts in Calculus

  • Limits: The fundamental concept that underlies all of calculus, limits describe the behavior of functions as they approach certain points.
  • Derivatives: Used to determine the slope of a function at a given point, derivatives have applications in various fields, such as physics to describe velocity and acceleration.
  • Integrals: They allow for the calculation of areas under curves and the accumulation of quantities, essential in statistics and probability.
  • The Fundamental Theorem of Calculus: This crucial theorem links differentiation and integration, showing that they are inverse processes.

Studying calculus not only enhances problem-solving skills but also fosters logical reasoning and critical thinking. As students delve into calculus, they will encounter diverse applications, such as:

  1. Analyzing the motion of objects in physics.
  2. Determining profit maximization in economics.
  3. Modeling population growth in biology.
  4. Designing curves and shapes in engineering.

With its extensive applications and fundamental importance, calculus is a stepping stone for advanced studies in mathematics and science. Our comprehensive online courses in calculus are tailored to guide learners through these challenging concepts, ensuring a thorough understanding and application in real-world scenarios.