0 A Treatise on the Differential Geometry of Curves and Surfaces

Title	:	A Treatise on the Differential Geometry of Curves and Surfaces
Authors	:	Luther Pfahler Eisenhart
	:	1910

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0 Elementary Differential Geometry: Curves and Surfaces; Edition 2008

Title	:	Elementary Differential Geometry: Curves and Surfaces; Edition 2008
Authors	:	Martin Raussen
	:	DEPARTMENT OF MATHEMATICAL SCIENCES, AALBORG UNIVERSITY

Plane and Space: Linear Algebra and Geometry
1. Vectors and Products
2. Description of Lines and Planes
3. Orthogonal Projections, Distances and Angles
4. Change of Coordinate Systems

Curves in plane and space
1. Vector functions in one variable
2. Parametrized Curves
3. Curvature
4. Space Curves: Moving Frames and Torsion
5. How to use the geometric laboratory - an example

Chapter 3. Regular Surfaces
1. Parametrizations of surfaces
2. Measurement in curved coordinates: the 1. fundamental form
3. Normal sections and normal curvature
4. Normal and geodesic curvature; the second fundamental form
5. Principal curvatures, Gaussian curvature, and Mean curvature
6. Special surfaces
7. The geometric labotatory for surfaces

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0 Differential Geometry: A First Course in Curves and Surfaces

Title	:	Differential Geometry: A First Course in Curves and Surfaces
Authors	:	Theodore Shifrin
	:	Preliminary Version; Fall, 2015

CURVES

1. Examples, Arclength Parametrization
2. Local Theory: Frenet Frame
3. Some Global Results

SURFACES: LOCAL THEORY

1. Parametrized Surfaces and the First Fundamental Form
2. The Gauss Map and the Second Fundamental Form
3. The Codazzi and Gauss Equations and the Fundamental Theorem of Surface Theory
4. Covariant Differentiation, Parallel Translation, and Geodesics

SURFACES: FURTHER TOPICS

1. Holonomy and the Gauss-Bonnet Theorem
2. An Introduction to Hyperbolic Geometry
3. Surface Theory with Differential Forms
4. Calculus of Variations and Surfaces of Constant Mean Curvature

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0 Differential Geometry of Curves and Surfaces: A Concise Guide

Title	:	Differential Geometry of Curves and Surfaces: A Concise Guide
Authors	:	Victor Andreevich Toponogov
	:	2006 Birkhauser Boston

The study of curves and surfaces forms an important part of classical differential geometry. Differential Geometry of Curves and Surfaces: A Concise Guide presents traditional material in this field along with important ideas of Riemannian geometry. The reader is introduced to curves, then to surfaces, and finally to more complex topics. Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels.

Key topics and features:

• Covers central concepts including curves, surfaces, geodesics, and intrinsic geometry
• Substantive material on the Aleksandrov global angle comparison theorem, which the author generalized for Riemannian manifolds (a result now known as the celebrated Toponogov Comparison Theorem, one of the cornerstones of modern Riemannian geometry)
• Contains many nontrivial and original problems, some with hints and solutions
  Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels

This rigorous exposition, with well-motivated topics, is ideal for advanced undergraduate, first-year graduate students seeking to enter the fascinating world of geometry, and students specializing in geometry. The material is given in two parallel streams.

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0 Transformasi Data Skala Ordinal ke Interval dengan Menggunakan Makro Minitab

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0 Soal Latihan dan Pembahasan: Matriks

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