An inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner.Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book.Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
Details e-book Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts
🗸 Author(s): Tristan Needham
🗸 Title: Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts
🗸 Rating : 4.7 from 5 stars (199 reviews)
🗸 ISBN-10: 0691203709
🗸 ISBN-13: 9780691203706
🗸 Languange: English
🗸 Format ebook: PDF, EPUB, Kindle, Audio, HTML and MOBI
🗸 Supported Devices: Android, iOS, PC and Amazon Kindle
✓ Read as many eBooks you want!
✓ Secure Scanned. No Virus Detected
✓ Thousands of eBooks to choose from - Hottest new releases
✓ Click it and Read it! - no waiting to read eBooks, it's instant!
✓ Keep reading your favorite eBooks over and over!
✓ It works anywhere in the world!
✓ No late fees or fixed contracts - cancel anytime!
Readers' opinions about Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts by Tristan Needham
Lindsea Lawrence
This thought-provoking work of non-fiction explores the mysteries of the human mind, delving into the complexities of consciousness and perception. Drawing on the latest scientific research, the author sheds light on the inner workings of the brain, offering fascinating insights into what makes us who we are. Engaging and accessible, this book is a must-read for anyone interested in the workings of the human mind.
Alaina Rodgers
Discover the untold stories of women who have shaped history with this illuminating collection of biographies. From pioneering scientists to revolutionary activists, each chapter shines a light on the remarkable achievements of women throughout the ages. With its inspiring tales of courage and resilience, this book is a celebration of female empowerment and achievement.
Ronae Berry
This poignant memoir offers a deeply personal account of one woman's journey to overcome adversity and find redemption. From childhood trauma to adult struggles, the author shares her experiences with honesty and vulnerability, offering hope and inspiration to readers facing their own challenges. With its raw emotion and powerful storytelling, this book is a testament to the resilience of the human spirit.
