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1.

図書

図書
J.W. Bruce and P.J. Giblin
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984  xii, 222 p. ; 24 cm
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目次情報: 続きを見る
Preface to the second edition
Preface to the first edition
Introductory example: a gravitational catastrophe machine / 1:
Curves, and functions on them / 2:
Parametrized curves
Tangent vectors
Contact
Reparametrization
Curvature
Functions on plane curves
Space curves
More about functions / 3:
Right equivalence
Flat functions
Jets
Regular values and smooth manifolds / 4:
Smooth maps and parametrized manifolds
Regular values
Tangent spaces
The Morse lemma
Morse lemma with parameters
Envelopes / 5:
Families and envelopes
Other definitions of envelope
Local structure of envelopes
Examples of envelopes
Envelopes and differential equations
Unfoldings / 6:
Unfoldings and (p)versal unfoldings
Versal unfoldings
Cusps
Unfoldings: applications / 7:
Distance-squared and height functions
Developable surfaces and the tangent developable of a space curve
Some different local pictures
Symmetry sets
Caustics by reflexion
Duals and differential equations
Transversality / 8:
Smooth manifolds
Thom's transversality lemma
Algebraic surfaces and more on apparent contours
Open and dense properties
Generic properties of curves / 9:
The Monge-Taylor map
A transversality theorem for space curves
More on unfoldings / 10:
Determining the power series
Proof of convergence
Singular points, several variables, generic surfaces / 11:
The geometry of surfaces in Euclidean 3-space
Functions of one variable (again)
Families of differential equations
Differential equations
Functions of several variables
R-trivial families
A little algebra
The determinacy theorem
Classification of functions
Surfaces in Euclidean 3-space again
Moduli and simple singularities
Simple singularities
Null sets and Sard's theorem / Appendix:
Historical note
Further reading
References
Index of notation
Index
Preface to the second edition
Preface to the first edition
Introductory example: a gravitational catastrophe machine / 1:
2.

図書

図書
Roberto Cipolla, Peter Giblin
出版情報: Cambridge ; New York : Cambridge University Press, 2000  viii, 184 p. ; 26 cm
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3.

図書

図書
J.W. Bruce, P.J. Giblin
出版情報: New York : Cambridge University Press, 1992  xviii, 321 p. ; 23 cm
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目次情報: 続きを見る
Preface to the second edition
Preface to the first edition
Introductory example: a gravitational catastrophe machine / 1:
Curves, and functions on them / 2:
Parametrized curves
Tangent vectors
Contact
Reparametrization
Curvature
Functions on plane curves
Space curves
More about functions / 3:
Right equivalence
Flat functions
Jets
Regular values and smooth manifolds / 4:
Smooth maps and parametrized manifolds
Regular values
Tangent spaces
The Morse lemma
Morse lemma with parameters
Envelopes / 5:
Families and envelopes
Other definitions of envelope
Local structure of envelopes
Examples of envelopes
Envelopes and differential equations
Unfoldings / 6:
Unfoldings and (p)versal unfoldings
Versal unfoldings
Cusps
Unfoldings: applications / 7:
Distance-squared and height functions
Developable surfaces and the tangent developable of a space curve
Some different local pictures
Symmetry sets
Caustics by reflexion
Duals and differential equations
Transversality / 8:
Smooth manifolds
Thom's transversality lemma
Algebraic surfaces and more on apparent contours
Open and dense properties
Generic properties of curves / 9:
The Monge-Taylor map
A transversality theorem for space curves
More on unfoldings / 10:
Determining the power series
Proof of convergence
Singular points, several variables, generic surfaces / 11:
The geometry of surfaces in Euclidean 3-space
Functions of one variable (again)
Families of differential equations
Differential equations
Functions of several variables
R-trivial families
A little algebra
The determinacy theorem
Classification of functions
Surfaces in Euclidean 3-space again
Moduli and simple singularities
Simple singularities
Null sets and Sard's theorem / Appendix:
Historical note
Further reading
References
Index of notation
Index
Preface to the second edition
Preface to the first edition
Introductory example: a gravitational catastrophe machine / 1:
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