Little by Little

What this book is about

Calculus is usually taught as a set of rules to memorise before anyone explains what the rules are *for*. This book does it the other way round. It starts with two very ordinary questions — how fast is this changing right now, and how much has piled up so far — and then builds every idea needed to answer them, one small step at a time. That is where the title comes from.

Nothing is assumed beyond school algebra. Limits are not dropped on the reader as a definition; they arrive because you genuinely need them and nothing else will do. The derivative shows up as a slope you can see. The integral shows up as an area you can count in squares before you ever get a formula for it. And the fundamental theorem — the moment the two halves turn out to be the same thing viewed from opposite ends — is treated as the surprise it actually is, not as a line in a syllabus.

There are more than sixty figures, because most people who "cannot do calculus" simply were never shown the picture.

What is inside

• Rates of change, from average speed to instantaneous speed
• Limits, introduced only when they become unavoidable
• Derivatives: slope, rules, and what they mean physically
• Integrals as accumulation, built from counting squares upward
• The fundamental theorem, and why it is startling
• Worked problems, activities, a bilingual glossary and a quiz

The English edition, Little by Little, was made for a class-11 English-medium reader and his classmates. Every technical term keeps its Bangla twin in the glossary, so a student can move between the two editions without getting lost.