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: |