Elementary Differential Geometry Curves and Surfaces by Martin Raussen
| Geometry | |
| Language | English |
| File Type | |
| 1 | |
| Views | 245 views |
| File Size & Downloads | Size 1.8 MiB Downloads 86 |
Short Desciption:
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Contents
Chapter 1. Plane and Space: Linear Algebra and Geometry 5
1. Vectors and Products 5
2. Description of Lines and Planes 13
3. Orthogonal Projections, Distances and Angles 25
4. Change of Coordinate Systems 36
Chapter 2. Curves in plane and space 47
1. Vector functions in one variable 47
2. Parametrized Curves 50
3. Curvature 62
4. Space Curves: Moving Frames and Torsion 78
5. How to use the geometric laboratory – an example 92
Chapter 3. Regular Surfaces 95
1. Parametrizations of surfaces 95
2. Measurement in curved coordinates: the 1. fundamental form 108
3. Normal sections and normal curvature 118
4. Normal and geodesic curvature; the second fundamental form 124
5. Principal curvatures, Gaussian curvature, and Mean curvature 131
6. Special surfaces 146
7. The geometric labotatory for surfaces 157
Index 159
