You learned the rules but never the point
You could differentiate but not say what it meant.
Courses
Start with three things you can do today
Calculus explained with simple examples
Understand derivatives and integrals as ideas before you learn the rules.
Start with speed and distance, the everyday version of calculus, then see how a derivative measures a rate of change and an integral adds up small pieces. Each idea is worked through with numbers you can check, so the notation arrives after the meaning.
Type this when Cadence asks what you want to learn
I want to understand what calculus is actually about. I have heard it is the maths of change, and I would like to understand derivatives and integrals in plain terms before I worry about all the rules.
Change any word so it fits your situation. The course is built from what you type and a few setup questions.
Start today
Three things you can do before the course exists.
Useful on their own. The course is for when you want the whole skill, not just the first move.
-
Estimate a slope at a point
For y = x squared, find the slope between x = 3 and x = 3.1: (9.61 minus 9) divided by 0.1 is 6.1. Between x = 3 and x = 3.01 it is 6.01. The slopes approach 6, which is the derivative at x = 3. That shrinking gap is what a limit means.
-
Read an integral as distance
Drive at a steady 60 kilometres an hour for 2 hours and the area under the flat speed graph is 60 times 2, which is 120 kilometres travelled. When speed changes, an integral adds up many thin strips of that area in the same way.
-
See the two ideas undo each other
Speed is the rate of change of distance; distance is the accumulated total of speed. Write the same pair for another quantity, for example the flow rate from a tap and the litres in a bucket, before you meet the formal theorem.
Sources: OpenStax: Calculus Volume 1, a free open textbook on limits, derivatives and integrals. Practical examples are starting points, not promised results.
- Best for
- Math & numbers
- Prerequisites
- None. Bring the situation you have.
- Course length
- 7 to 30 lessons, sized to your goal
- Lesson pace
- About 10 minutes a day
- Format
- Read it, or play the audio
- Access
- Available on the App Store, with early features and Android testing access
Before the course is built
Setup asks about your situation first.
Lesson 1 opens on the moment you describe, and the examples use your role. For this request, expect questions like these.
- Why calculus: a course, an exam, your work, or curiosity?
- How comfortable are you with algebra and graphs right now?
- Have you studied calculus before, and how did it go?
Right for now
If any of this sounds familiar, start here.
You are starting a course that uses it
Economics, physics, engineering or a return to study.
You are curious about the idea
People call it one of the great inventions and you want to see why.
Course arc
Where the course goes, in order.
Cadence writes the lessons for you, so the exact path follows your answers. This is the ground a course built from this sentence covers.
01 / 06Change and rates
Average speed, slopes of lines and why curves are harder.
Limits
Getting closer and closer, the idea that makes calculus work.
The derivative
Slope at a point, and what it tells you about a changing quantity.
Using derivatives
Finding where something is largest, smallest or changing fastest.
The integral
Area under a curve as an accumulated total.
The fundamental theorem
Why rates and totals undo each other.
What changes
What you will be able to do, and what you will stop believing.
You will be able to
Explain a derivative
Describe it as a rate of change and as the slope of a curve at a point.
Explain an integral
Describe it as adding up many small pieces to get a total.
Connect the two
Explain why finding rates and finding totals are reverse processes.
Ideas this course corrects
Calculus is mainly about memorising rules
The rules are shortcuts for two ideas, rates of change and accumulated totals, which you can understand with arithmetic and a graph.
Derivatives only matter in physics
Any quantity that changes with something else has a rate of change, including costs, populations and temperatures.
Course questions
What to know before you start.
Calculus explained with simple examples: what can I do today?
Estimate a slope at a point. For y = x squared, find the slope between x = 3 and x = 3.1: (9.61 minus 9) divided by 0.1 is 6.1. Between x = 3 and x = 3.01 it is 6.01. The slopes approach 6, which is the derivative at x = 3. That shrinking gap is what a limit means. Read an integral as distance. Drive at a steady 60 kilometres an hour for 2 hours and the area under the flat speed graph is 60 times 2, which is 120 kilometres travelled. When speed changes, an integral adds up many thin strips of that area in the same way. See the two ideas undo each other. Speed is the rate of change of distance; distance is the accumulated total of speed. Write the same pair for another quantity, for example the flow rate from a tap and the litres in a bucket, before you meet the formal theorem.
Is this a fixed course?
No. Cadence builds the course when you type the sentence and answer a few setup questions, so the lessons follow your situation. This page describes what a course built from this request covers. You see the whole path before Lesson 1.
Who is this course for?
Start with speed and distance, the everyday version of calculus, then see how a derivative measures a rate of change and an integral adds up small pieces. Each idea is worked through with numbers you can check, so the notation arrives after the meaning. It sits under Math & numbers in the Ideas & discovery part of the library.
Do I need any prior experience?
No. Setup asks what you already know and where you want to use it, and the course starts from there. Bring a real situation if you have one; the examples are built around it.
How long does it take?
Courses run 7 to 30 lessons of about 10 minutes, sized to what you asked for. One lesson a day is the intended pace, and you can go faster. Lessons can be read or played as audio.
Does this course award a certificate or degree?
No. Cadence is for practical self-learning and does not award accredited degrees or professional certification.
Start today
Type it, answer a few questions, open Lesson 1.
The sentence to type
I want to understand what calculus is actually about. I have heard it is the maths of change, and I would like to understand derivatives and integrals in plain terms before I worry about all the rules.