MIT 18 306 - Advanced Partial Differential Equations with Applications (73 pages)

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Advanced Partial Differential Equations with Applications



Previewing pages 1, 2, 3, 4, 5, 34, 35, 36, 37, 38, 69, 70, 71, 72, 73 of actual document.

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Advanced Partial Differential Equations with Applications

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Pages:
73
School:
Massachusetts Institute of Technology
Course:
18 306 - Advanced Partial Differential Equations with Applications

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MIT OpenCourseWare http ocw mit edu 18 306 Advanced Partial Differential Equations with Applications Fall 2009 For information about citing these materials or our Terms of Use visit http ocw mit edu terms 18 306 Problem List Rodolfo R Rosales Department of Mathematics Massachusetts Inst of Technology Cambridge Massachusetts MA 02139 March 19 2008 Abstract Problem list for 18 306 These problems may be assigned in problem sets and or exams Contents 1 Linear First Order PDE 4 1 1 Statement Linear 1st order PDE problem 01 4 1 2 Statement Linear 1st order PDE problem 02 4 1 3 Statement Linear 1st order PDE problem 03 4 1 4 Statement Linear 1st order PDE problem 04 5 1 5 Statement Linear 1st order PDE problem 05 5 1 6 Statement Linear 1st order PDE problem 06 5 1 7 Statement Linear 1st order PDE problem 07 5 1 8 Statement Discontinuous Coe cients in Linear 1st order pde 01 6 1 9 Statement Discontinuous Coe cients in Linear 1st order pde 02 7 1 10 Statement Discontinuous Coe cients in Linear 1st order pde 03 8 1 11 Statement Discontinuous Coe cients in Linear 1st order pde 04 9 1 12 Statement Discontinuous Coe cients in Linear 1st order pde 05 10 2 Semi Linear First Order PDE 12 2 1 Statement Semi Linear 1st order PDE problem 01 12 2 2 Statement Semi Linear 1st order PDE problem 02 12 1 Rosales 18 306 Problem List 2 3 Kinematic Waves 12 3 1 Statement Conservation Equation in Chromatography 12 3 2 Statement Dispersive Waves and Modulations 13 3 3 Statement Channel Flow Rate Function 15 3 4 Statement Road capacity 16 3 5 Statement Initial Values for a Kinematic Wave problem 01 16 3 6 Statement Initial Values for a Kinematic Wave problem 02 17 3 7 Statement In nite conservation laws for kinematic waves 20 3 8 Statement Tra c Flow problem 01 20 3 9 Statement Tra c Flow problem 02 21 3 10 Statement Envelopes and cusps 25 4 Hamilton Jacobi and Eikonal Problems 25 4 1 Statement Eikonal equation problem 01 25 4 2 Statement Eikonal equation problem 02 27 5 HyperbolicEquations 5 1



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