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Wikipedia says the following about Maria Gaetana Agnesi:
She is credited with writing the first book discussing both differential and integral calculus and was a member of the faculty at the University of Bologna, although she never served.
What was the title of this first book book containing both differential and integral calculus?
The book is a work in two volumes: Maria Gaetana Agnesi, "Instituzioni Analitiche ad uso della gioventù italiana", Milan 1748. The title roughly translates to "Foundations of Analysis for use by Italian youth". As the title suggests, this is a textbook, and it was written in the vernacular rather than in Latin.
Google's scan of the first volume (tomo I) is here, a scan of the second volume (tomo II) is here. An English translation by the Rev. John Colson was published in London by Taylor and Wilks in 1801. A scan of it can be found at Google. According to the editor's note at the front of the book, Colson was Lucasian Professor of Mathematics at the University of Cambridge. It further notes:
That learned and ingenious man, who had obliged his Country with an English Translation of Sir ISAAC NEWTON's Fluxions [...] found, after all, the Analytical Institutions of Agnesi to be so excellent, that he was at pains of learning the Italian Language, at an advanced age, for the sole purpose of translating that work into English; that the British Youth might have the benefit of it as well as the Youth of Italy.
