Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics)

Book Details

• Publisher: Springer

• Author: Tapp, Kristopher

• Language: English

• Edition: Softcover reprint of the original 1st ed. 2016

• ISBN: 9783319819693

• Pages: 366

• Cover: Paperback

• Dimensions: 9.4 x 6.3 x 1.1 inches

About The Book

Differential Geometry: A Visual Introduction for Beginners by Kristopher Tapp, published by Springer, offers a refreshingly intuitive and visually rich approach to one of mathematics' most abstract subjects. Ideal for a wide range of learners—from undergraduates with minimal prerequisites to advanced students preparing for graduate study in mathematics or physics—this 366-page textbook balances accessibility with mathematical rigor.

What sets this book apart is its innovative use of over 300 color illustrations, which illuminate complex geometric concepts with clarity that grayscale text cannot match. Key definitions and theorems are color-coded for visual structure, enhancing readability and comprehension. The author provides a clear and concise development of differential geometry, beginning with the fundamentals and gradually introducing deeper global theorems, ensuring that readers of all backgrounds can engage with the material.

Rich in real-world applications, the book connects theory to practice with captivating examples. From conformal mapping in cartography to the historical development of cycloids by Christiaan Huygens, from Green’s Theorem and planimeters to Foucault’s Pendulum and the concept of parallel vector fields, the applications are not only illustrative but deeply motivating. These thoughtful connections demonstrate how differential geometry underpins technologies like GPS and shapes the foundations of modern physics.

With its engaging visuals, thorough explanations, and strong pedagogical design, this book is perfect for classroom use or independent study. It offers a powerful gateway to understanding one of the most elegant areas of mathematics.