01
Secant to tangent: the derivative
Slide a second point in toward the first and watch the secant slope close in on the exact slope, the derivative.
Step 1 · See it
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Step 3 · Quick check
All courses
MTH 263
Calculus I
Presents concepts of limits, derivatives, differentiation of various types of functions and use of differentiation rules, application of differentiation, antiderivatives, integrals, and applications of integration.
How this course is taught: The course textbook, read right here on the page, plus interactive demos.
How to use this page
- Read the section we are covering in the book below, jumping straight to it from the contents.
- Experiment with the matching interactive demo to see the idea move.
- Practice the problems in that section of the book until you can do them on your own.
The book is paced to match class exactly, so the section in class is the section to read and practice here.
Your course textbook
Calculus from Limits to Integration
Written by Dr. Derek Bryant · free and openly licensed
This course uses a textbook I wrote specifically for it. You can read the whole book right here on the page, jump to any section from the contents, or download it to keep. Everything you need for MTH 263 is inside.
On a phone? The buttons above open the book in your device's PDF app, which reads better on a small screen than the in-page reader below.
ILimitsWhere calculus begins
IIDerivativesRates of change
IIIIntegrationAccumulation and area
Read the book
Open to any section
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The book is rendered right here on the page. Use the page arrows, type a page number, or pick any section from the contents. You can also download it or open it in a new tab.
Contents
3 parts · 4 chapters
Official grades, submissions, and course announcements live in Canvas. This site hosts public course materials, explanations, examples, and study resources.
Interactive demos
Explore the ideas, hands on
Calculus is built on a few big pictures: a secant becoming a tangent, rectangles becoming an integral, rates that chain together. Each tool walks through the idea, then hands you the controls. Nothing here is graded, so experiment freely. Not sure how to study this? See Study Strategies. Back to the book
02
A function and its derivative
See how the slope of f at each point becomes the height of f′ below it.
Step 1 · See it
Step 2 · Try it
Step 3 · Quick check
03
Riemann sums to the integral
Fill the area under a curve with rectangles and watch the sum converge to the exact integral as they get thinner.
Step 1 · See it
Step 2 · Try it
Step 3 · Quick check
04
Limits: approaching a point
Creep up on a value from both sides and see why a limit can exist at a hole, but not at a jump or an asymptote.
Step 1 · See it
Step 2 · Try it
Step 3 · Quick check
05
Epsilon and delta
The formal limit, made visual: trap the curve in a target band by choosing a narrow enough strip of x.
Step 1 · See it
Step 2 · Try it
Step 3 · Quick check
06
Optimization: the biggest box
Cut corners from a sheet, fold a box, and find the cut size that maximizes volume, where the derivative is zero.
Step 1 · See it
Step 2 · Try it
Step 3 · Quick check
07
The chain rule: rates multiply
See a composite function as two machines in a row, and why their slopes multiply to give the overall rate.
Step 1 · See it
Step 2 · Try it
Step 3 · Quick check
Turn it in
Your practice report
Every quick check above feeds this report: what you got right on the first try, and what you got right eventually. Download it and upload it to Canvas.
MTH practice report · bryantclass.com