{"product_id":"catastrophe-theory-and-its-applications-revised","title":"Catastrophe Theory and Its Applications (Revised)","description":"\n\u003ctable align=\"center\" border=\"0\" cellpadding=\"2\" cellspacing=\"0\" width=\"100%\"\u003e\n\u003ctr\u003e\n\u003ctd class=\"productDetailSmallElements\"\u003e\n\u003cp\u003e\n\u003cstrong\u003eMarc Notes\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tOriginally published: London;San Francisco: Pitman, 1978. (Surveys and reference works in mathematics;2).\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eTable of Contents\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tPreface \n\u003cbr\u003e1 Smooth and sudden changes \n\u003cbr\u003e 1. Catastrophes \n\u003cbr\u003e 2. The Zeeman catastrophe machine \n\u003cbr\u003e 3. Gravitational catastrophe machines \n\u003cbr\u003e 4. Catastrophe theory \n\u003cbr\u003e2 Multidimensional geometry \n\u003cbr\u003e 1. Set-theoretic notation \n\u003cbr\u003e 2. Euclidean space \n\u003cbr\u003e 3. Linear transformations \n\u003cbr\u003e 4. Matrices \n\u003cbr\u003e 5. Quadratic forms \n\u003cbr\u003e 6. Two-variable cubic forms \n\u003cbr\u003e 7. Polynomial geometry \n\u003cbr\u003e3 Multidimensional calculus \n\u003cbr\u003e 1. Distance in Euclidean space \n\u003cbr\u003e 2. The derivative as tangent \n\u003cbr\u003e 3. Contours \n\u003cbr\u003e 4. Partial derivatives \n\u003cbr\u003e 5. Higher derivatives \n\u003cbr\u003e 6. Taylor series \n\u003cbr\u003e 7. Truncated algebra \n\u003cbr\u003e 8. The Inverse Function Theorem \n\u003cbr\u003e 9. The Implicit Function Theorem \n\u003cbr\u003e4 Critical points and transversality \n\u003cbr\u003e 1. Critical points \n\u003cbr\u003e 2. The Morse Lemma \n\u003cbr\u003e 3. Functions of a single variable \n\u003cbr\u003e 4. Functions of several variables \n\u003cbr\u003e 5. The Splitting Lemma \n\u003cbr\u003e 6. Structural stability \n\u003cbr\u003e 7. Manifolds \n\u003cbr\u003e 8. Transversality \n\u003cbr\u003e 9. Transversality and stability \n\u003cbr\u003e 10. Transversality for mappings \n\u003cbr\u003e 11. Codimension \n\u003cbr\u003e5 Machines revisited \n\u003cbr\u003e 1. The Zeeman machine \n\u003cbr\u003e 2. The canonical cusp catastrophe \n\u003cbr\u003e 3. Dynamics of the Zeeman machine \n\u003cbr\u003e 4. The gravitational machines \n\u003cbr\u003e 5. Formulation of a general problem \n\u003cbr\u003e6 Structural stability \n\u003cbr\u003e 1. Equivalence of families \n\u003cbr\u003e 2. Structural stabillty of families \n\u003cbr\u003e 3. Physical interpretations of structural stability \n\u003cbr\u003e 4. The Morse and Splitting Lemmas for families \n\u003cbr\u003e 5. Catastrophe geometry \n\u003cbr\u003e7 Thom's classification theorem \n\u003cbr\u003e 1. Functions and families of functions \n\u003cbr\u003e 2. One-parameter families \n\u003cbr\u003e 3. Non-transversaliity and symmetry \n\u003cbr\u003e 4. Two-parameter families \n\u003cbr\u003e 5. \"Three-, four- and five-parameter families\" \n\u003cbr\u003e 6. Higher catastrophes \n\u003cbr\u003e 7. Thom's theorem \n\u003cbr\u003e8 Determinacy and unfoldings \n\u003cbr\u003e 1. Determine and strong determinacy \n\u003cbr\u003e 2. One-variable jet spaces \n\u003cbr\u003e 3. Infinitesimal changes of variable \n\u003cbr\u003e 4. Weaker determinacy conditions \n\u003cbr\u003e 5. Transformations that move the origin \n\u003cbr\u003e 6. Tangency and transversality \n\u003cbr\u003e 7. Codimension and unfoldings \n\u003cbr\u003e 8. Transversality and universality \n\u003cbr\u003e 9. Strong equivalence of unfoldings \n\u003cbr\u003e 10. Numbers associated with singularities \n\u003cbr\u003e 11. Inequalities \n\u003cbr\u003e 12. Summary of results and calculation methods \n\u003cbr\u003e 13. Examples and calculations \n\u003cbr\u003e 14. Compulsory remarks on terminology \n\u003cbr\u003e9 The first seven catastrophe geometries \n\u003cbr\u003e 1. The objects of study \n\u003cbr\u003e 2. The fold catastrophe \n\u003cbr\u003e 3. The cusp catastrophe \n\u003cbr\u003e 4. The swallowtail catastrophe \n\u003cbr\u003e 5. The butterfly catastrophe \n\u003cbr\u003e 6. The elliptic umbilic \n\u003cbr\u003e 7. The hyperbolic umbilic \n\u003cbr\u003e 8. The parabolic umbilic \n\u003cbr\u003e 9. Ruled surfaces \n\u003cbr\u003e10 Stability of ships \n\u003cbr\u003e Static equilibrium \n\u003cbr\u003e 1. Buoyancy \n\u003cbr\u003e 2. Equilibrium \n\u003cbr\u003e 3. Stability \n\u003cbr\u003e 4. The vertical-sided ship \n\u003cbr\u003e 5. Geometry of the buoyancy locus \n\u003cbr\u003e 6. Metacentres \n\u003cbr\u003e Ship shapes \n\u003cbr\u003e 7. The elliptical ship \n\u003cbr\u003e 8. The rectangular ship \n\u003cbr\u003e 9. Three dimensions \n\u003cbr\u003e 10. Oil-rigs \n\u003cbr\u003e 11. Comparison with current methods \n\u003cbr\u003e11. The geometry of fluids \n\u003cbr\u003e Background on fluid mechanics \n\u003cbr\u003e 1. What we are describing \n\u003cbr\u003e 2. Stream functions \n\u003cbr\u003e 3. Examples of flows \n\u003cbr\u003e 4. Rotation \n\u003cbr\u003e 5. Complex variable methods \n\u003cbr\u003e Stability and experiment \n\u003cbr\u003e 6. Changes of variable \n\u003cbr\u003e 7. Heuristic programme \n\u003cbr\u003e 8. Experimental realization \n\u003cbr\u003e Combining polymer molecules \n\u003cbr\u003e 9. Non-Newtonian behaviour \n\u003cbr\u003e 10. Extensional flows \n\u003cbr\u003e Degenerate flows \n\u003cbr\u003e 11. The six-roll mill \n\u003cbr\u003e 12. The non-local bifurcation set of the elliptic umbilic \n\u003cbr\u003e 13. The six-roll mill with polymer solution \n\u003cbr\u003e 14. The 2n-roll mill \n\u003cbr\u003e12 Optics and scattering theory \n\u003cbr\u003e Ray optics \n\u003cbr\u003e 1. Caustics \n\u003cbr\u003e 2. The rainbow \n\u003cbr\u003e 3. Variational principles \n\u003cbr\u003e 4. Scattering \n\u003cbr\u003e Wave optics \n\u003cbr\u003e 5. Asymptotic solutions of wave equations \n\u003cbr\u003e 6. Oscillatory integrals \n\u003cbr\u003e 7. Universal unfoldings \n\u003cbr\u003e 8. Orders of caustics \n\u003cbr\u003e Applications \n\u003cbr\u003e 9. Scattering from a crystal lattice \n\u003cbr\u003e 10. Other caustics \n\u003cbr\u003e 11. Mirages \n\u003cbr\u003e 12. Sonic booms \n\u003cbr\u003e 13. Giant ocean waves \n\u003cbr\u003e13 Elastic structures \n\u003cbr\u003e General theory \n\u003cbr\u003e 1. Objects under stress \n\u003cbr\u003e 2. Elastic equilibria \n\u003cbr\u003e 3. Infinite-dimensional peculiarities \n\u003cbr\u003e Euler struts \n\u003cbr\u003e 4. Finite element vision \n\u003cbr\u003e 5. Classical (1744) variational version \n\u003cbr\u003e 6. Perturbation analysis \n\u003cbr\u003e 7. Modern functional analysis \n\u003cbr\u003e 8. The buckling of a spring \n\u003cbr\u003e 9. The pinned strut \n\u003cbr\u003e The geometry of collapse \n\u003cbr\u003e 10. Imperfection sensitivity \n\u003cbr\u003e 11. \"(r, s)-Stability\" \n\u003cbr\u003e 12. Optimization \n\u003cbr\u003e 13. Symmetry: rods and shells \n\u003cbr\u003e Buckling plates \n\u003cbr\u003e 14. The von Kármán equations \n\u003cbr\u003e 15. Unfolding a double eigenvalue \n\u003cbr\u003e Dynamics \n\u003cbr\u003e 16. Soft modes \n\u003cbr\u003e 17. Stiffness \n\u003cbr\u003e14 Thermodynamics and phase transitions \n\u003cbr\u003e Equations of state \n\u003cbr\u003e 1. van der Waals' equation \n\u003cbr\u003e 2. Ferromagnetism \n\u003cbr\u003e Thermodynamic potentials \n\u003cbr\u003e 3. Entropy \n\u003cbr\u003e 4. Transforming the maximum entropy principle \n\u003cbr\u003e 5. Legendre transformations \n\u003cbr\u003e 6. Explicit potentials \n\u003cbr\u003e 7. The Landau theory \n\u003cbr\u003e Fluctuations and critical exponents \n\u003cbr\u003e 8. Classical exponents \n\u003cbr\u003e 9. Topological tinkering \n\u003cbr\u003e 10. The rôle of fluctuations \n\u003cbr\u003e 11. Spatial variation \n\u003cbr\u003e 12. Partition functions \n\u003cbr\u003e 13. Renormalization group \n\u003cbr\u003e 14. Structural stability of renormalization \n\u003cbr\u003e The rôle of symmetry \n\u003cbr\u003e 15. Even functions \n\u003cbr\u003e 16. The shapes of rotating stars \n\u003cbr\u003e 17. Symmetry breaking \n\u003cbr\u003e 18. Tricritical points \n\u003cbr\u003e 19. Crystal symmetries \n\u003cbr\u003e 20. Spectrum singularities \n\u003cbr\u003e15 Laser physics \n\u003cbr\u003e Preliminaries \n\u003cbr\u003e 1. Atoms \n\u003cbr\u003e 2. Field \n\u003cbr\u003e 3. Interaction \n\u003cbr\u003e 4. Measurement \n\u003cbr\u003e The laser catastrophe \n\u003cbr\u003e 5. Unfolded Hamiltonian \n\u003cbr\u003e 6. Equations of motion \n\u003cbr\u003e 7. Mean field approximation \n\u003cbr\u003e 8. Boundary conditions \n\u003cbr\u003e 9. Non-equilibrium stationary manifold \n\u003cbr\u003e Experiments \n\u003cbr\u003e 10. Laser transition \n\u003cbr\u003e 11. Optical bistability \n\u003cbr\u003e 12. Photocount distributions \n\u003cbr\u003e Analytic correspondence \n\u003cbr\u003e 13. Equilibrium boundary conditions \n\u003cbr\u003e 14. Equilibrium manifold \n\u003cbr\u003e 15. Thermodynamic phase transition \n\u003cbr\u003e 16. Critical behaviour \n\u003cbr\u003e 17. Analytic correspondence of experiments \n\u003cbr\u003e \u0026amp;\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003ePublisher Marketing\u003c\/strong\u003e:\u003cbr\u003e\n\u003c\/p\u003e\n\u003cp\u003eThis first integrated treatment of the main ideas behind René Thom's theory of catastrophes aims to make them accessible to scientists wishing to apply the theory in their own fields of research. The mathematical basis of the theory is therefore explained with a minimum of technicalities, although some knowledge of the calculus of variables is assumed.\u003cbr\u003eThom's now-famous list of seven elementary catastrophes, broadly classifying various types of discontinuous change, is elucidated, as are the reasons for its appearance. Nearly half the book concentrates on detailed applications of the theory, emphasizing its uses in the physical sciences where applications can be made quantitative and can be experimentally verified. The more controversial and speculative applications to areas in the social sciences are also mentioned, but not discussed in detail.\u003cbr\u003eOver 200 illustrations help clarify the ideas and applications in this volume, which will be of interest to researchers and postgraduate students in such diverse disciplines as engineering, mathematics, physics, and biology. 1978 edition. Bibliography.\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\n\n\u003cbr\u003e\n\u003cbr\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n","brand":"Dover Publications","offers":[{"title":"Default Title","offer_id":46431145328771,"sku":"SPTM-9780486692715","price":29.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0564\/6830\/8099\/files\/9780486692715_spiral.png?v=1769660214","url":"https:\/\/sebink.com\/products\/catastrophe-theory-and-its-applications-revised","provider":"Sebink","version":"1.0","type":"link"}