Preface
Introduction
Chapter 1: Calculus on Euclidean Space:
Euclidean Spa ce. Tangent Vectors. Directional Derivatives. Curves in R3. 1-forms. Dif ferential Forms. Mappings.
Chapter 2: Frame Fields:
Dot Product. Curves. The Frenet Formulas. Arbitrar ySpeed Curves. Covariant Derivatives. Frame Fields. Connection Forms. Th e Structural Equations.
Chapter 3: Euclidean Geometry:
Isometries of R3. The Tangent Map of an Isometr y. Orientation. Euclidean Geometry. Congruence of Curves.
Chapter 4: Calculus on a Surface:
Surfaces i n R3. Patch Computations. Differentiable Functions and Tangent Vectors. Differential Forms on a Surface. Mappings of Surfaces. Integration of Fo rms. Topological Properties. Manifolds.
Chap ter 5: Shape Operators:
The Shape Operator of M R3. Normal Curvature. Gaussian Curvature. Computational Techniques. The Implicit C ase. Special Curves in a Surface. Surfaces of Revolution.
Introduction
Chapter 1: Calculus on Euclidean Space:
Euclidean Spa ce. Tangent Vectors. Directional Derivatives. Curves in R3. 1-forms. Dif ferential Forms. Mappings.
Chapter 2: Frame Fields:
Dot Product. Curves. The Frenet Formulas. Arbitrar ySpeed Curves. Covariant Derivatives. Frame Fields. Connection Forms. Th e Structural Equations.
Chapter 3: Euclidean Geometry:
Isometries of R3. The Tangent Map of an Isometr y. Orientation. Euclidean Geometry. Congruence of Curves.
Chapter 4: Calculus on a Surface:
Surfaces i n R3. Patch Computations. Differentiable Functions and Tangent Vectors. Differential Forms on a Surface. Mappings of Surfaces. Integration of Fo rms. Topological Properties. Manifolds.
Chap ter 5: Shape Operators:
The Shape Operator of M R3. Normal Curvature. Gaussian Curvature. Computational Techniques. The Implicit C ase. Special Curves in a Surface. Surfaces of Revolution.
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