mathematics

Germund Dahlquist

Germund Dahlquist 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 Germund Dahlquist rather than just read about it. In short: Germund Dahlquist (16 January 1925 – 8 February 2005) was a Swedish mathematician known primarily for his early contributions to the theory of numerical analysis as applied to differential equations. Dahlquist began to study mathematics at Stockholm University in 1942 at the age of 17, where he cites the Danish mathematician Harald Bohr (who was living in exile after the occupation of Denmark during World War II) as…

Key takeaways

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

Reference excerpt

Germund Dahlquist (16 January 1925 – 8 February 2005) was a Swedish mathematician known primarily for his early contributions to the theory of numerical analysis as applied to differential equations. Dahlquist began to study mathematics at Stockholm University in 1942 at the age of 17, where he cites the Danish mathematician Harald Bohr (who was living in exile after the occupation of Denmark during World War II) as a profound influence. He received the degree of licentiat from Stockholm University in 1949, before taking a break from his studies to work at the Swedish Board of Computer Machinery (Matematikmaskinnämnden), working on (among other things) the early computer BESK, Sweden's first. During this time, he also worked with Carl-Gustaf Rossby on early numerical weather forecasts. Dahlquist returned to Stockholm University to complete his Ph.D., Stability and Error Bounds in the Numerical Solution of Ordinary Differential Equations, which he defended in 1958, with Fritz Carlson and Lars Hörmander as his advisors. As part of this work he introduced the logarithmic norm (also introduced by Russian mathematician Sergei Lozinskii the same year). In 1959 he moved to the Royal Institute of Technology (KTH), where he would later establish what became the Department of Numerical Analysis and Computer Science (NADA) in 1962 (now part of the School of Computer Science and Communication), and become Sweden's first Professor of Numerical Analysis in 1963. He helped establish the Nordic journal of numerical analysis, BIT, in 1961. In 1965 he was elected into the Royal Swedish Academy of Engineering Sciences (IVA). The software package COMSOL Multiphysics, for finite element analysis of partial differential equations, was started by a couple of Dahlquist's graduate students based upon codes developed for a graduate course at KTH.

See also First and second Dahlquist barriers

Honors and awards SIAM 1988 John von Neumann lecturer. SIAM 1991 Peter Henrici Prize. SIAM Germund Dahlquist Prize, established 1995, "Awarded to a young scientist (normally under 45) for original contributions to fields associated with Germund Dahlquist, especially the numerical solution of differential equations and numerical methods for scientific computing". Three honorary doctorates, from Hamburg (1981), Helsinki (1994), and Linköping (1996).

Notes

Illustrations

Worked examples

Example 1 — a first encounter with Germund Dahlquist

Start with the simplest possible case. Write down what Germund Dahlquist 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 Germund Dahlquist 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 Germund Dahlquist 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 Germund Dahlquist

In research: Germund Dahlquist 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 Germund Dahlquist 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: Germund Dahlquist is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1925 births, 2005 deaths, 20th-century Swedish mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Germund Dahlquist 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 Germund Dahlquist in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Germund Dahlquist means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Germund Dahlquist out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Germund Dahlquist in simple terms?

Why does Germund Dahlquist 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 Germund Dahlquist?

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 Germund Dahlquist.