Curves and Singularities: A Geometrical Introduction to Singularity TheoryCambridge University Press, 1992/11/26 - 321 ページ The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors take a novel approach by casting the theory into a new light, that of singularity theory. The second edition of this successful textbook has been thoroughly revised throughout and includes a multitude of new exercises and examples. A new final chapter has been added that covers recently developed techniques in the classification of functions of several variables, a subject central to many applications of singularity theory. Also in this second edition are new sections on the Morse lemma and the classification of plane curve singularities. The only prerequisites for students to follow this textbook are a familiarity with linear algebra and advanced calculus. Thus it will be invaluable for anyone who would like an introduction to the modern theories of catastrophes and singularities. |
目次
III | 1 |
IV | 10 |
V | 13 |
VI | 15 |
VII | 18 |
VIII | 23 |
IX | 28 |
X | 32 |
XXXVI | 200 |
XXXVII | 206 |
XXXVIII | 207 |
XXXIX | 211 |
XL | 216 |
XLI | 220 |
XLII | 222 |
XLIII | 226 |
XI | 41 |
XII | 48 |
XIII | 54 |
XIV | 55 |
XV | 59 |
XVI | 60 |
XVII | 65 |
XVIII | 74 |
XIX | 85 |
XX | 95 |
XXI | 99 |
XXII | 107 |
XXIII | 110 |
XXIV | 118 |
XXV | 131 |
XXVI | 133 |
XXVII | 134 |
XXVIII | 148 |
XXIX | 153 |
XXX | 160 |
XXXII | 168 |
XXXIII | 178 |
XXXIV | 182 |
XXXV | 192 |
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多く使われている語句
a₁ a₂ apparent contour arclength bifurcation set caustic centre of curvature change of coordinates chapter circle condition consider corresponding deduce defined definition diffeomorphism differential distance-squared functions ellipse envelope equation evolute example Exercises f₁ function f geometrical germ given height functions Hence inflexions Jacobian matrix k-jet k-point contact Let f Let y(t linear local diffeomorphism Monge-Taylor Morse lemma n-manifold neighbourhood never zero nonzero normal null set ordinary cusp orthotomic osculating p)versal parabola parallel parametrized 1-manifold plane curve points of regression polynomial projection proof prove R-equivalent regular curve regular value resp result Sard's theorem Show singularities smooth function smooth manifold smooth map space curve Suppose surface symmetry set t₁ tangent line tangent space tangent vector Thom's transverse U₁ unit speed variables versal unfolding vertex vertices write x-axis x₁ y(to