mathematics

Jacques Charles François Sturm

Jacques Charles François Sturm is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Jacques Charles François Sturm rather than just read about it. In short: Jacques Charles François Sturm (29 September 1803 – 15 December 1855) was a French mathematician, who made a significant addition to equation theory with his work, Sturm's theorem. Early life Sturm was born in Geneva, Switzerland in 1803.

Key takeaways

Jacques Charles François Sturm belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Jacques Charles François Sturm to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Jacques Charles François Sturm from memory before moving on to harder problems.

Reference excerpt

Jacques Charles François Sturm (29 September 1803 – 15 December 1855) was a French mathematician, who made a significant addition to equation theory with his work, Sturm's theorem.

Early life Sturm was born in Geneva, Switzerland in 1803. The family of his father, Jean-Henri Sturm, had emigrated from Strasbourg around 1760—about 50 years before Charles-François's birth. His mother's name was Jeanne-Louise-Henriette Gremay. In 1818, he started to follow the lectures of the academy of Geneva. The death of his father forced Sturm to give lessons to children of the rich in order to support his own family the following year. In 1823, he became tutor to the son of Madame de Staël. At the end of that year, Sturm stayed in Paris for a short time following the family of his student. He resolved, with his school-fellow Jean-Daniel Colladon, to try his fortune in Paris, and obtained employment on the Bulletin universel.

Discovery In 1829, he discovered the theorem that bears his name, and concerns real-root isolation, that is the determination of the number and the localization of the real roots of a polynomial.

Work Sturm benefited from the 1830 revolution, as his Protestant faith ceased to be an obstacle to employment in public high schools. At the end of 1830, he was thus appointed as a professor of Mathématiques Spéciales at the collège Rollin. He was chosen a member of the Académie des Sciences in 1836, filling the seat of André-Marie Ampère. Sturm became répétiteur in 1838, and in 1840 professor in the École Polytechnique. The same year, after the death of Poisson, Sturm was appointed as mechanics professor of the Faculté des sciences de Paris. His works, Cours d'analyse de l'école polytechnique (1857–1863) and Cours de mécanique de l'école polytechnique (1861), were published after his death in Paris, and were regularly republished. He was the co-eponym of the Sturm–Liouville theory with Joseph Liouville. In 1826, with his colleague Jean-Daniel Colladon, Sturm helped make the first experimental determination of the speed of sound in water.

Death and legacy In 1851 his health began to fail. He was able to return to teaching for a while during his long illness, but died in 1855. The asteroid 31043 Sturm is named for him. Sturm's name is one of the 72 names engraved at the Eiffel Tower.

Distinctions Grand prix de Mathématiques (4 December 1834) Member of the academy of Berlin (1835) Member of the academy of Saint-Petersburg (1836) Officier de la Légion d'Honneur (1837) Copley Medal of the Royal Society of London (1840) Member of the Royal Society of London (1840)

Selected writing

Cours de mécanique de l'École polytechnique (in Italian). Vol. 1. Napoli: Gallo. 1871. Cours de mécanique de l'École polytechnique (in Italian). Vol. 2. Napoli: Gallo. 1871. Cours d'analyse de l'Ecole polytechnique. Tome premier (Gauthier-Villars, 1877) Cours d'analyse de l'Ecole polytechnique. Tome second (Gauthier-Villars, 1877) Cours de mécanique de l'Ecole polytechnique (Gauthier-Villars, 1883)

See also Control theory Oscillation theory Spectral theory of ordinary differential equations Submarine signals

References

External links

Gerono, Camille Christophe; Terquem, Olry; Laisant, Charles-Ange; Bricard, Raoul; Boulanger, Auguste (1856), "Notice sur la vie et les travaux de M. Sturm", Nouvelles annales de mathématiques, journal des candidats aux écoles polytechnique et normale, 15: 72 Texts on Wikisource: "Sturm, Jacques Charles François". New International Encyclopedia. 1905. "Sturm, Jacques Charles François". Encyclopædia Britannica (11th ed.). 1911. "Sturm, Jacques-Charles-Francois". Encyclopedia Americana. 1920.

Illustrations

Jacques Charles François Sturm illustration

Worked examples

Example 1 — a first encounter with Jacques Charles François Sturm

Start with the simplest possible case. Write down what Jacques Charles François Sturm claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Jacques Charles François Sturm before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Jacques Charles François Sturm ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Jacques Charles François Sturm

In research: Jacques Charles François Sturm appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Jacques Charles François Sturm in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Jacques Charles François Sturm is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1803 births, 1855 deaths, 19th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jacques Charles François Sturm outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Jacques Charles François Sturm in 20 minutes

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Frequently asked questions

What is Jacques Charles François Sturm in simple terms?

Jacques Charles François Sturm (29 September 1803 – 15 December 1855) was a French mathematician, who made a significant addition to equation theory with his work, Sturm's theorem. Early life Sturm was born in Geneva, Switzerland in 1803.

Why does Jacques Charles François Sturm matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Jacques Charles François Sturm?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Jacques Charles François Sturm.