Guillaume de l’Hôpital

Guillaume de l’Hôpital (1661–1704) was a French mathematician whose 1696 textbook, Analyse des infiniment petits, was the first published textbook on differential calculus. It presented the rule later named after him.

Johann Bernoulli: A Swiss mathematician who helped establish calculus and taught Guillaume de l’Hôpital. Bernoulli supplied much of the mathematical instruction and material behind l’Hôpital’s textbook.
Differential calculus: The branch of calculus that studies rates of change and quantities that vary continuously. L’Hôpital’s 1696 book introduced this subject systematically to its readers.
L’Hôpital’s rule: A theorem that evaluates certain limits of quotients by taking the limit of the quotient of their derivatives. This is the rule presented in l’Hôpital’s textbook and later named for him.
Analyse des infiniment petits: A 1696 French textbook by Guillaume de l’Hôpital that systematically presented differential calculus. This book made l’Hôpital’s name inseparable from early calculus instruction.
Jacob Bernoulli: A Swiss mathematician whose work helped develop calculus, probability, and the study of infinite series. His brother Johann was l’Hôpital’s calculus teacher and collaborator.
Differential notation: A notation for infinitesimal changes, commonly written with symbols such as dx and dy. The textbook used Leibnizian differentials to express derivatives and rules of calculation.
Indeterminate form: A limit form, such as 0/0 or ∞/∞, whose appearance alone does not determine the limit. L’Hôpital’s rule applies to particular indeterminate quotient forms.
Bernoulli–l’Hôpital correspondence: A surviving body of correspondence documenting the mathematical exchange between Johann Bernoulli and Guillaume de l’Hôpital. The letters illuminate how Bernoulli’s teaching and results informed the textbook.
Gottfried Wilhelm Leibniz: A German polymath who independently developed calculus and introduced much of its standard notation. Leibniz’s differential calculus is the subject of l’Hôpital’s textbook.
Derivative: A measure of how a function changes as its input changes, defined through a limiting rate. Derivatives are the central objects developed in l’Hôpital’s calculus text.

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