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Differential Geometry
This outstanding textbook by a distinguished mathematical scholar introduces the differential geometry of curves and surfaces in three-dimensional Euclidean space. The subject is presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the geometric significance and theoretical and practical importance of the different concepts, methods and results involved.
The first chapters of the book focus on the basic concepts and facts of analytic geometry, the theory of space curves, and the foundations of the theory of surfaces, including problems closely related to the first and second fundamental forms. The treatment of the theory of surfaces makes full use of the tensor calculus.
The later chapters address geodesics, mappings of surfaces, special surfaces, and the absolute differential calculus and the displacement of Levi-Cività . Problems at the end of each section (with solutions at the end of the book) will help students meaningfully review the material presented, and familiarize themselves with the manner of reasoning in differential geometry.
The first chapters of the book focus on the basic concepts and facts of analytic geometry, the theory of space curves, and the foundations of the theory of surfaces, including problems closely related to the first and second fundamental forms. The treatment of the theory of surfaces makes full use of the tensor calculus.
The later chapters address geodesics, mappings of surfaces, special surfaces, and the absolute differential calculus and the displacement of Levi-Cività . Problems at the end of each section (with solutions at the end of the book) will help students meaningfully review the material presented, and familiarize themselves with the manner of reasoning in differential geometry.
Reprint of the University of Toronto Press, Toronto, Canada, 1959 edition.
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Description
This outstanding textbook by a distinguished mathematical scholar introduces the differential geometry of curves and surfaces in three-dimensional Euclidean space. The subject is presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the geometric significance and theoretical and practical importance of the different concepts, methods and results involved.
The first chapters of the book focus on the basic concepts and facts of analytic geometry, the theory of space curves, and the foundations of the theory of surfaces, including problems closely related to the first and second fundamental forms. The treatment of the theory of surfaces makes full use of the tensor calculus.
The later chapters address geodesics, mappings of surfaces, special surfaces, and the absolute differential calculus and the displacement of Levi-Cività . Problems at the end of each section (with solutions at the end of the book) will help students meaningfully review the material presented, and familiarize themselves with the manner of reasoning in differential geometry.
The first chapters of the book focus on the basic concepts and facts of analytic geometry, the theory of space curves, and the foundations of the theory of surfaces, including problems closely related to the first and second fundamental forms. The treatment of the theory of surfaces makes full use of the tensor calculus.
The later chapters address geodesics, mappings of surfaces, special surfaces, and the absolute differential calculus and the displacement of Levi-Cività . Problems at the end of each section (with solutions at the end of the book) will help students meaningfully review the material presented, and familiarize themselves with the manner of reasoning in differential geometry.
Reprint of the University of Toronto Press, Toronto, Canada, 1959 edition.
algebraic geometry;applied math;calculus textbook;engineering courses;tensor analysis;develops ideas;mathematics required;chapter 0;covers practically;signal processing;functional analysis;projective geometry;numerical methods;coordinate systems;tensor calculus;matrix algebra;math courses;doctoral level;undergraduate engineering;math topic;self study;partial differential;advanced text;applied mathematics;math text;engineering students;advanced study;pure mathematics;electrical engineering;complex analysis;linear algebra;math major;differential equations;advanced topics;bit terse;strong background;graduate students;quantum mechanics;topics covered;riemannian;differentiable;covariant;mappings;coxeter;tensors;manifolds;laplace;fourier;euclidean;curvature;euclid;topology;wylie;theorems;odes;vector;metric;geometric;notation;maths;proofs;curves;surfaces;relativity;engineers;10th;semester;mathematical;cited;introductory;exercises;books on self studies;books on numerical methods;books on math topics;books on engineering courses;books on signal processings;books on calculus textbooks;books on applied maths;books on tensor analysis;books on engineering students;books on matrix algebras;books on electrical engineerings;books on advanced studies;books on pure mathematics;books on math courses;books on math texts;books on algebraic geometries;books on develops ideas;books on applied mathematics;books on projective geometries;books on functional analysis;books on advanced texts
