Elementary Illustrations of the Differential and Integral Calculus by De Morgan

(6 User reviews)   3857
De Morgan, Augustus, 1806-1871 De Morgan, Augustus, 1806-1871
English
Ever felt like calculus is a secret language only mathematicians understand? De Morgan's 19th-century book tries to crack that code. Forget dry formulas – this is a collection of real-world problems that show how calculus actually works. It's like finding the hidden story behind the math you learned in school. The mystery here isn't in a plot, but in seeing how abstract ideas like rates of change and areas under curves explain everything from falling rocks to planetary motion. If you've ever been curious about the 'why' behind calculus, this historical guide offers a surprisingly clear window into its practical soul.
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It was the year of Our Lord one thousand seven hundred and seventy-five. Spiritual revelations were conceded to England at that favoured period, as at this. Mrs. Southcott had recently attained her five-and-twentieth blessed birthday, of whom a prophetic private in the Life Guards had heralded the sublime appearance by announcing that arrangements were made for the swallowing up of London and Westminster. Even the Cock-lane ghost had been laid only a round dozen of years, after rapping out its messages, as the spirits of this very year last past (supernaturally deficient in originality) rapped out theirs. Mere messages in the earthly order of events had lately come to the English Crown and People, from a congress of British subjects in America: which, strange to relate, have proved more important to the human race than any communications yet received through any of the chickens of the Cock-lane brood. France, less favoured on the whole as to matters spiritual than her sister of the shield and trident, rolled with exceeding smoothness down hill, making paper money and spending it. Under the guidance of her Christian pastors, she entertained herself, besides, with such humane achievements as sentencing a youth to have his hands cut off, his tongue torn out with pincers, and his body burned alive, because he had not kneeled down in the rain to do honour to a dirty procession of monks which passed within his view, at a distance of some fifty or sixty yards. It is likely enough that, rooted in the woods of France and Norway, there were growing trees, when that sufferer was put to death, already marked by the Woodman, Fate, to come down and be sawn into boards, to make a certain movable framework with a sack and a knife in it, terrible in history. It is likely enough that in the rough outhouses of some tillers of the heavy lands adjacent to Paris, there were sheltered from the weather that very day, rude carts, bespattered with rustic mire, snuffed about by pigs, and roosted in by poultry, which the Farmer, Death, had already set apart to be his tumbrils of the Revolution. But that Woodman and that Farmer, though they work unceasingly, work silently, and no one heard them as they went about with muffled tread: the rather, forasmuch as to entertain any suspicion that they were awake, was to be atheistical and traitorous. In England, there was scarcely an amount of order and protection to justify much national boasting. Daring burglaries by armed men, and highway robberies, took place in the capital itself every night; families were publicly cautioned not to go out of town without removing their furniture to upholsterers’ warehouses for security; the highwayman in the dark was a City tradesman in the light, and, being recognised and challenged by his fellow-tradesman whom he stopped in his character of “the Captain,” gallantly shot him through the head and rode away; the mail was waylaid by seven robbers, and the guard shot three dead, and then got shot dead himself by the other four, “in consequence of the failure of his ammunition:” after which the mail was robbed in peace; that magnificent potentate, the Lord Mayor of London, was made to stand and deliver on Turnham Green, by one highwayman, who despoiled the illustrious creature in sight of all his retinue; prisoners in London gaols fought battles with their turnkeys, and the majesty of the law fired blunderbusses in among them, loaded with rounds of shot and ball; thieves snipped off diamond crosses from the necks of noble lords at Court...

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Don't expect a novel with characters and a plot twist. This book is a different kind of story. It's the story of how calculus, often seen as this intimidating beast, is actually a powerful tool for describing our world. De Morgan presents a series of standalone problems and examples. He shows you how to use the basic ideas of calculus to figure out things like the path of a reflected light beam, the volume of a wine cask, or the speed of a moving object at any given moment.

Why You Should Read It

What makes this old book special is its focus on seeing the math. De Morgan isn't just giving you rules to memorize. He's connecting the symbols on the page to physical situations you can picture. Reading it feels like getting a peek into the mind of a great teacher who genuinely wants you to get it. The language is old-fashioned, but the intent is timeless: to make a difficult subject feel accessible and, believe it or not, kind of interesting.

Final Verdict

This isn't for everyone. If you need a modern textbook to pass a class, look elsewhere. But if you're a curious person who already knows a bit of calculus and wants to understand its historical roots and practical heart, this is a fascinating read. It's perfect for the lifelong learner, the history of science fan, or anyone who likes seeing the elegant mechanics behind how things work. Think of it as a museum exhibit for math, where the ideas are the artifacts.



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Jessica Hernandez
1 year ago

To be perfectly clear, the storytelling feels authentic and emotionally grounded. Absolutely essential reading.

Mark Thomas
1 year ago

Perfect.

Jennifer Martin
11 months ago

Great read!

Sarah Jackson
3 weeks ago

I stumbled upon this title and the content flows smoothly from one chapter to the next. Thanks for sharing this review.

Paul Lee
1 year ago

If you enjoy this genre, the depth of research presented here is truly commendable. One of the best books I've read this year.

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