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Visual Differential Geometry and Forms

A Mathematical Drama in Five Acts

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The book presents a unique approach to differential geometry, emphasizing geometric intuition through 235 hand-drawn diagrams. It revisits classical results using Newton's methods and offers distinct geometrical proofs of significant theorems, including the Global Gauss-Bonnet theorem and Gauss's Theorema Egregium. The final act introduces differential forms, covering advanced topics like Maxwell's equations, de Rham cohomology, and Einstein's field equations, making complex concepts accessible to undergraduates. The chapters can be read independently, enhancing flexibility for learners.

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Visual Differential Geometry and Forms, Tristan Needham

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Released
2021
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Subtitle
A Mathematical Drama in Five Acts
Language
English
Released
2021
Format
Hardcover
Pages
536
ISBN13
9780691203690
Series
Rating
4.75 out of 5
Description
The book presents a unique approach to differential geometry, emphasizing geometric intuition through 235 hand-drawn diagrams. It revisits classical results using Newton's methods and offers distinct geometrical proofs of significant theorems, including the Global Gauss-Bonnet theorem and Gauss's Theorema Egregium. The final act introduces differential forms, covering advanced topics like Maxwell's equations, de Rham cohomology, and Einstein's field equations, making complex concepts accessible to undergraduates. The chapters can be read independently, enhancing flexibility for learners.