DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES 3ED (HB 2023) Hardcover

Building on the strengths of its earlier editions, the third edition of this popular and accessible textbook continues to blend analytical/theoretical concepts with visual and intuitive insights into the local and global behavior of curves and surfaces. Requiring only knowledge of multivariable calculus and linear algebra, the book fosters geometric understanding through interactive graphics applets available in Maple workbook format, compatible with the free Maple Player. These tools allow students to manipulate parametric curves and surfaces, explore examples in depth, and better grasp complex theorems through dynamic visualizations rather than static illustrations. The inclusion of investigative project suggestions also promotes independent exploration and research. Responding to user feedback, this edition features a broader range of exercises, including more introductory-level problems, while positioning more challenging questions later in the sets for a smoother learning progression. Hints are provided to assist with tackling tougher exercises. With a student-friendly layout and clear explanations, this edition adds more strategically placed examples to improve comprehension. The section on the Gauss-Bonnet Theorem has been revised to include more intuitive steps and clearer intermediate reasoning. Furthermore, recognizing that the concept of homeomorphism may be unfamiliar to many students, the authors have added additional examples to help clarify and demonstrate how to prove that a function is a homeomorphism.