Single-Variable Calculus

Maclaurin polynomials of sin x

Each polynomial follows the sine over a wider interval before it leaves.

About the book

A course in the calculus of one real variable, written for a reader who has met algebra and trigonometry in school and is ready to see why the methods of calculus work. Every result is proved in the text or in an appendix. The book is organised around the differential operator: dx is the differential of the coordinate function, and integrals integrate 1-forms. From the third chapter, the book states limits, continuity, the derivative and convergence in normed spaces. The sup norm on a space of functions stands beside the absolute value on the line. Every section ends with problems graded by difficulty, each with a hint, an answer and a full solution, and every answer is checked by computer algebra.