Compact Textbooks in Mathematics

Differential Geometry

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Reihe: Compact Textbooks in Mathematics

Die Reihenfolge beginnt mit dem Buch "Differential Geometry". Wer alle Bücher der Reihe nach lesen möchte, sollte mit diesem Band von Ulrich Pinkall beginnen. Der zweite Teil der Reihe "Elementary Numerical Mathematics for Programmers and Engineers" ist am 15.09.2024 erschienen. Die Reihe umfasst derzeit 2 Bände. Der neueste Band trägt den Titel "Elementary Numerical Mathematics for Programmers and Engineers".

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Diese Reihenfolge enthält 2 unterschiedliche Autoren.

Cover: Differential Geometry
  • Autor: Pinkall, Ulrich
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  • Medium: Buch
  • Veröffentlicht: 14.02.2024
  • Genre: Sonstiges

Differential Geometry

This open access book covers the main topics for a course on the differential geometry of curves and surfaces. Unlike the common approach in existing textbooks, there is a strong focus on variational problems, ranging from elastic curves to surfaces that minimize area, or the Willmore functional. Moreover, emphasis is given on topics that are useful for applications in science and computer graphics. Most often these applications are concerned with finding the shape of a curve or a surface that minimizes physically meaningful energy. Manifolds are not introduced as such, but the presented approach provides preparation and motivation for a follow-up course on manifolds, and topics like the Gauss-Bonnet theorem for compact surfaces are covered.
Cover: Elementary Numerical Mathematics for Programmers and Engineers
  • Autor: Stoyan, Gisbert
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  • Medium: Buch
  • Veröffentlicht: 15.09.2024
  • Genre: Sonstiges

Elementary Numerical Mathematics for Programmers and Engineers

This book covers the basics of numerical methods. Avoiding the definition-theorem-proof style, it instead focuses on numerical examples and simple pseudo-codes.

The text begins with a chapter on floating point arithmetic before moving on to discuss norms, conditions numbers, solutions of systems of equations, the least squares problem, eigenvalue problems, interpolation, numerical integration, ordinary differential equations, optimization (including a detailed case study), and practical error estimations. Exercises (partly in MATLAB) are provided at the end of each chapter. Suitable for readers with minimal mathematical knowledge, the book not only offers an elementary introduction to numerical mathematics for programmers and engineers but also provides supporting material for students and teachers of mathematics.

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