In mathematics, global analysis, also called analysis on manifolds, is the study of the global and topological properties of differential equations on manifolds and vector bundles.[1][2] Global analysis uses techniques in infinite-dimensional manifold theory and topological spaces of mappings to classify behaviors of differential equations, particularly nonlinear differential equations.[3] These spaces can include singularities and hence catastrophe theory is a part of global analysis. Optimization problems, such as finding geodesics on Riemannian manifolds, can be solved using differential equations, so that the calculus of variations overlaps with global analysis. Global analysis finds application in physics in the study of dynamical systems[4] and topological quantum field theory.
^Smale, S. (January 1969). "What is Global Analysis". American Mathematical Monthly. 76 (1): 4–9. doi:10.2307/2316777.
^Richard S. Palais (1968). Foundations of Global Non-Linear Analysis(PDF). W.A. Benjamin, Inc.
^Andreas Kriegl and Peter W. Michor (1991). The Convenient Setting of Global Analysis(PDF). American Mathematical Society. pp. 1–7. ISBN 0-8218-0780-3.
^Marsden, Jerrold E. (1974). Applications of global analysis in mathematical physics. Berkeley, CA.: Publish or Perish, Inc. p. Chapter 2. ISBN 0-914098-11-X.
In mathematics, globalanalysis, also called analysis on manifolds, is the study of the global and topological properties of differential equations on...
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The error analysis for the Global Positioning System is important for understanding how GPS works, and for knowing what magnitude of error should be expected...
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analysis, because differential equations arising from variational principles have a strong geometric content. Geometric analysis also includes global...
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harmonic analysis and on related questions in geometric measure theory and partial differential equations." 2002 – Bôcher Memorial Prize for: Global regularity...
instance, the analysis does not include the impact on business, the cost of fear from terrorism or the cost of counterterrorism. The global economic impact...
Leamer: I have proposed a form of organized sensitivity analysis that I call 'global sensitivity analysis' in which a neighborhood of alternative assumptions...
State of the Climate GlobalAnalysis, April 2010". Archived from the original on 16 June 2010. Retrieved 15 June 2010. "Global Surface Temperature Anomalies"...