Learn Calculus the Intuitive Way
The purpose of this site is to help you learn calculus in an intuitive way. What does that mean? It means that you get the intuition behind every concept and formula. To learn this way sometimes takes more time, and can sometimes be harder. I believe, though, there are some really attractive advantages to this approach:
- It is more fun to learn this way. Rote memorizing and solving routine problems like a machine takes out the pleasure from learning. Understanding the intuitive idea that inspired Newton to invent the notion of derivative is rewarding at a different level.
- You will remember the material far better.
- You will develop intellectual skils that will serve you for life. Trying to understand the intuitive idea behind a concept or a formula sometimes requires more effort than simply memorizing it, but the effort is intellectual training.
In this site you will find explanations and examples that I consider more intuitive that the standard way of presenting the concepts. Sometimes I give algebraic deductions when they are necessary, but I focus mostly on the intuition, and then on solving standard problems that you find on textbooks and calculus exams.
Whether you are at high-school or college taking a calculus course, preparing for a standarized test, or self-studying calculus just for fun, you can tremendously benefit from this website. You can use it to complement your textbook or course material, or use it as your main learning resource.
Learning calculus takes some time and dedication. I hope, though, that this site helps in making sure that work isn't tedious or boring.
Where to Begin?
This site covers all the topics in a first calculus course, and it is expanding to cover topics beyond that. If you are already taking a course in school, you can immediatelly visit the topics you didn't really understand, or the ones you need a little help with.
There is a lot of material, and you can use the search function that is in the left column to find what you need.
Even if you think you understood a topic well, I recommend you to visit the pages about them. The intuitive approach that I use may help you gain another perspective. Be sure to bookmark this site, or even better, subscribe to my free e-zine to receive weekly study tips and other bonuses.
If you have no clue about where to start, follow the sequece:
- Functions: This topic is not usually covered in a calculus course. Understanding functions and knowing how to deal with them is essential for a real understanding of calculus, though.
- Limits: This is the topic most calculus courses start with. The idea of limits is the basic underlying theme in calculus. Spend some time on these pages if you want to deeply understand this idea.
- Derivatives: The derivative, together with the integral, form the inseparable duo in calculus. The derivative can be seen as a generalized slope, or rate of change. It is essential in all sciences.
- Integrals: The integral generalizes the idea of area. As the derivative, it is essential for all sciences. Immerse yourself in these pages to understand this concept and get some practice solving problems.
In all these pages you will learn about these concepts by first forming an intuition, then solving common problems that apply these concepts.
Who am I?
My name is Pablo Antuna and I'm just a guy passionate about math and teaching. I decided to create this site so I can teach calculus the way I wish I had been taught it, and to share my passion for it. You can learn more about me in the about page.
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- A Complete Guide to the Essential Calculus Problems
- The Calculus Problems Manual contains the essential exercises you need to know how to solve to get an outstanding grade in a calculus course.
- Mathematical Functions: An Easy Introduction
- Mathematical functions are the first things you need to understand to master Calculus. The key is to remember that they define the "connection" between two variables.
- Limits and Continuity: An Intuitive Introduction
- In this page we try to intuitively understand the concepts of limits and continuity. The basic ideas presented here form the foundation of a deep understanding of calculus.
- The Derivative of a Function: Intuition and Examples
- The derivative of a function is a central concept in calculus. Here you will form an intuition of what it is, and learn with examples to solve any derivatives problem.
- Integrals Demystified With Intuition and Examples
- Many people say integrals are the most difficult topic in Calculus. Here we'll demystify them. You'll find the intuition behind the definition and plenty of examples.
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