Limits and Introduction to Calculus

What the resources cover

The unit starts with limits and moves through differentiation into integration. The mind map C2: Limits & Continuity sets out the limit at a finite point, with intuitive and formal definitions, basic examples, uniqueness and one-sided limits, then moves on to infinite limits. There are also several resources simply called Limits, in mind map, flashcard and note form, plus notes on Continuity and on indeterminate forms and L’Hôpital’s Rule.

Differentiation is the largest theme. The Differentiation mind map lays out the chain rule, product rule and quotient rule. Integration appears in many mind maps on strategy, plus the notes What is Integration?, which covers the Fundamental Theorem of Calculus and the power rule.

Where to start

1. Open the Calculus mind map for an overview of the derivative as an instantaneous rate of change and the main rules.
2. Read the limits mind maps and notes before moving to derivatives.
3. Work through the Differentiation Flash Cards, which ask how to apply each step of the chain rule, product rule and quotient rule.
4. Move on to integration notes and the integration strategy maps.

Using quizzes and maps together

Read a map first, then test yourself. The Differentiation and Integration Quiz begins with finding a gradient from first principles, so it checks whether you can follow the working, not just recall a rule. The Differentiation quiz uses fill-in-the-blank answers, which suit quick checks. When an answer is wrong, go back to the matching map branch and read it again.

Exam-style practice

If you are preparing for AP Calculus, the flashcard decks on the 2003 AB multiple-choice questions without a calculator, and the BC and AB exam decks, give timed-style practice. A-level students can look at the A2 Maths Formulas deck and the A-Level Maths core notes.

Where it fits

This unit sits in the Calculus strand of Mathematics. Choose one resource today, and add your own notes or cards as you go.