Differential geometry has a long, wonderful history it has found relevance in areas ranging from machinery design of the classification of. For undergraduate courses in Differential Geometry. Designed not just for the math major but for all students of science, this text provides an introduction to the . Differential geometry has a wide range of applications, going far beyond strictly John Oprea’s second edition of Differential Geometry and Its.
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Account Options Sign in. This book studies the differential geometry of surfaces with the goal My library Help Advanced Book Search. Differential Geometry and Its Applications. MAASep 6, – Mathematics – pages. Differential geometry has a long, wonderful history it has found relevance in areas ranging from machinery design of the classification of four-manifolds to the creation of theories of nature’s fundamental forces to the study of DNA.
This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole, it mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences.
Differential geometry is not just diffferential mathematics majors, it is also for students in engineering and the sciences. Into the mix of these ideas comes the opportunity to visualize concepts through the use of computer algebra systems such as Maple.
“Differential Geometry and its Applications” by John F. Oprea
The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics.
Students will also see how particles move under constraints. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.
Selected pages Title Page. Constant Mean Curvature Surfaces.
Mathematical Association of America Textbooks: Differential Geometry and its Applications
Geodesies Metrics and Isometries. Holonomy and the GaussBonnet Theorem.
The Calculus of Variations and Geometry. A Glimpse at Higher Dimensions.
A List of Examples. Examples in Chapter 3. Examples in Chapter 7.
B Hints and Solutions to Selected Problems. Suggested Projects for Differential Geometry. References to this book Riemannian Geometry: