13 best differential geometry
Differential geometry is a branch of mathematics that combines elements of both geometry and calculus. It focuses on the study of curves, surfaces, and manifolds, using techniques from calculus and linear algebra. This field has applications in various areas of science, including physics, computer science, and engineering.
Key concepts in differential geometry include:
Curves and Surfaces:
- Curves: In differential geometry, a curve is often described using parametric equations that relate the coordinates of points on the curve to a parameter. The curvature and torsion of a curve are important measures.
- Surfaces: Surfaces are two-dimensional objects embedded in three-dimensional space. They can be described using parametric equations or implicit equations.
Manifolds:
- A manifold is a topological space that locally resembles Euclidean space near each point.Manifolds can be one-dimensional (curves), two-dimensional (surfaces), or higher-dimensional.
Tangent Spaces and Vectors:
- The tangent space at a point on a manifold is the space of all possible tangent vectors at that point. Tangent vectors represent the direction and rate of change of a curve or surface at a given point.
Metrics and Connections:
- Metrics define notions of distance and angles on manifolds. Riemannian geometry, a subfield of differential geometry, studies manifolds equipped with a metric.
- Connections describe how tangent spaces vary smoothly from point to point on a manifold.
Curvature:
- Curvature measures how a curve or surface deviates from being a straight line or a flat plane. Gaussian curvature and mean curvature are important measures for surfaces.
Geodesics:
- Geodesics are curves that locally minimize distance. They play a crucial role in understanding the geometry of curved spaces.
Applications:
- Differential geometry finds applications in various fields, including physics (general relativity, classical mechanics), computer graphics, and computer-aided design (CAD).
Books on Differential Geometry:
- "Elementary Differential Geometry" by Andrew Pressley
- "Differential Geometry of Curves and Surfaces" by Manfredo P. do Carmo
- "Introduction to Smooth Manifolds" by John M. Lee
- "Riemannian Geometry" by Peter Petersen
- "A Comprehensive Introduction to Differential Geometry" by Michael Spivak
These books provide different levels of depth and coverage, catering to both beginners and those seeking a more advanced understanding of the subject.
Below you can find our editor's choice of the best differential geometry on the market
Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts
Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)
Product features
A Five Star Favorite From Keith in Folsom, CA!
"Differential Geometry by Do Carmo is a classic. It is great to see Dover update and publish it."
About The Text
The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems. The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry.
Differential Geometry: Connections, Curvature, and Characteristic Classes (Graduate Texts in Mathematics, 275)
Differential Geometry (Dover Books on Mathematics)
Dover Publications
Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics)
Elementary Differential Geometry, Revised 2nd Edition
Elementary Differential Geometry (Springer Undergraduate Mathematics Series)
Introduction to Differential Geometry of Space Curves and Surfaces: Differential Geometry of Curves and Surfaces
A Visual Introduction to Differential Forms and Calculus on Manifolds
Neurofeedback 101: Rewiring the Brain for ADHD, Anxiety, Depression and Beyond (without medication)
Center for Brain Training
A First Course in Differential Geometry: Surfaces in Euclidean Space
A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics (IOP Concise Physics)
Mathematics for the Nonmathematician
Product features
Mathematics for the Nonmathemetician
Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Contains exercises and problems. (0486248232)
Short-Cut Math
Clear, concise compendium of about 150 time-saving math short-cuts features faster, easier ways to add, subtract, multiply, and divide. Each problem includes an explanation of the method, a step-by-step solution, the short-cut solution, and proof, as well as an explanation of why it works. No special math ability needed. (0486246116)
Mathematics, Magic and Mystery
Why do card tricks work? How can magicians do astonishing feats of mathematics mentally? Why do stage "mind-reading" tricks work? As a rule, we simply accept these tricks and "magic" without recognizing that they are really demonstrations of strict laws based on probability, sets, number theory, topology, and other branches of mathematics. Nontechnical, detailed, and clear, this volume contains 115 sections discussing tricks with cards, dice, coins, etc.; topological tricks with handkerchiefs, cards, etc.; geometrical vanishing effects; demonstrations with pure numbers; and dozens of other topics. (0486203352)
How To Calculate Quickly
Double or triple the speed with which you calculate using this tried and true method for helping you in the mathematics of daily life — addition, subtraction, multiplication, division, and fractions. (048620295X)
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