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Preface Chapter 1.Ordinary difierential equations 1.1.General theory 1.2.Gronwall's inequality 1.3.Bootstrap and continuity arguments 1.4.Noether's theorem 1.5.Monotonicity formulae 1.6.Linear and semilinear equations 1.7.Completely integrable systems Chapter 2.Constant coefficient linear dispersive equations 2.1.The Fourier transform 2.2.Fundamental solution 2.3.Dispersion and Strichartz estimates 2.4.Conservation laws for the SchrSdinger equation 2.5.The wave equation stress¡ªenergy tensor 2.6.Xs£¬b spaces Chapter 3.Semilinear dispersive equations 3.1.On scaling and other symmetries 3.2.What is a solution? 3.3.Local existence theory 3.4.Conservation laWS and global existence 3.5.Decay estimates 3.6.Scattering theory 3.7.Stability theory 3.8.Illposedness results 3.9.Almost conservation laws Chapter 4.The Korteweg de Vries equation 4.1.Existence theory 4.2.Correction terms 4.3.Symplectic non-squeezing 4.4.The Benjamin-Ono equation and gauge transformations Chapter 5.Energy-critical semilinear dispersive equations 5.1.The energy-critical NLW 5.2.Bubbles of energy concentration 5.3.Local Morawetz and non.concentration of mass 5.4.Minimal-energy blowup solutions 5.5.Global Morawetz and non¡ªconcentration of mass Chapter 6.Wave maps 6.1.Local theory 6.2.Orthonormal frames and gauge transformations 6.3.Wave map decay estimates 6.4.Heat flow Chapter A.Appendix£ºtools from harmonic analysis Chapter B.Appendix£ºconstruction of ground states Bibliography