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Advanced Partial Differential Equations with Applications
OCW Master Course Number
18.306
Fall 2009
OCW_LOMv1.0
Author
Rosales, Rodolfo
2021-4-27
OCW_LOMv1.0
isbasedon
URI
http://hdl.handle.net/1721.1/56302
Previous version of the course
OCW Course Topics
Mathematics
Differential Equations
OCW Course Topics
Mathematics
Mathematical Analysis
OCW Course Topics
Mathematics
Applied Mathematics
contents/index.htm.xml
Advanced Partial Differential Equations with Applications
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Advanced Partial Differential Equations with Applications
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Plots of grid scale oscillations
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Plot of grid scale oscillations
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Syllabus
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Readings
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Lecture Notes
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Lecture 17
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Lecture 25
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Lecture 18
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Lecture 19
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Incompressible, inviscid, fluid flow in a narrow cyllindirical pipe with elastic thin walls
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Discrete to Continuum Modeling
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Lecture 07
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Lecture 26
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Lecture 08
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Lecture 15
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Lecture 16
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Stability of Numerical Schemes for PDE's
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Hopf Bifurcations
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Lecture 13
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Lecture 06
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Conservation Laws in Continuum Modeling
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Branch Points and Branch Cuts
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Lecture 12
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Lecture 11
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Simplest Car Following Trac Flow Model
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Lecture 04
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Weakly Nonlinear Things: Oscillators
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Lecture 10
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Lecture 21
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Lecture 20
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Lecture 14
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Lecture 02
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Weakly Nonlinear Expansions for Breathers
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Lecture 05
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Lecture 24
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Lecture 01
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Lecture 03
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Lecture 23
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Assignments
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Problem Set Number 02
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Problem Set Number 05
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Problem set #1
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18.306 Problem List
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Problem Set Number 04
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Policies regarding homeworks and Exams
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Problem Set Number 03
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Exams
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Exam Number 02
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18.306 Problem List
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Exam Number 01
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MATLAB Resources
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Legal Notices
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Privacy Statement
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Trademark Notices
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contents/exams/MIT18_306f09_exam01_StmEx200901.pdf.xml
contents/lecture-notes/MIT18_306f09_lec05.pdf.xml
contents/lecture-notes/MIT18_306f09_lec24.pdf.xml
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contents/lecture-notes/MIT18_306f09_lec06.pdf.xml
contents/assignments/MIT18_306f09_pset02_ProblemSet200902.pdf.xml
contents/lecture-notes/MIT18_306f09_lec26_weaklyNLoscilators.pdf.xml
contents/assignments/MIT18_306f09_pset04_ProblemSet200904.pdf.xml
contents/lecture-notes/MIT18_306f09_lec22_Branch_Points_B_Cuts.pdf.xml
contents/assignments/index.htm.xml
contents/exams/MIT18_306f09_assn02_ProblemList20080319.pdf.xml
contents/lecture-notes/MIT18_306f09_lec18.pdf.xml
contents/lecture-notes/MIT18_306f09_lec12.pdf.xml
contents/lecture-notes/MIT18_306f09_lec28_Breathers.pdf.xml
contents/lecture-notes/MIT18_306f09_lec19.pdf.xml
contents/lecture-notes/MIT18_306f09_lec21.pdf.xml
contents/lecture-notes/MIT18_306f09_lec15.pdf.xml
contents/assignments/MIT18_306f09_pset03_ProblemSet200903.pdf.xml
contents/lecture-notes/MIT18_306f09_lec29_Num_Scheme_Stab.pdf.xml
contents/lecture-notes/MIT18_306f09_lec25.pdf.xml
contents/lecture-notes/MIT18_306f09_lec23.pdf.xml
contents/lecture-notes/MIT18_306f09_lec24_CF_Simple_Model.pdf.xml
contents/assignments/MIT18_306f09_assn02_ProblemList20080319.pdf.xml
contents/assignments/MIT18_306f09_pset01_ProblemSet200901.pdf.xml
contents/syllabus/index.htm.xml
contents/lecture-notes/MIT18_306f09_lec01.pdf.xml
contents/lecture-notes/MIT18_306f09_lec03.pdf.xml
contents/assignments/MIT18_306f09_pset05_ProblemSet200905.pdf.xml
contents/lecture-notes/MIT18_306f09_lec10.pdf.xml
contents/lecture-notes/MIT18_306f09_lec20.pdf.xml
contents/lecture-notes/MIT18_306f09_lec13.pdf.xml
contents/lecture-notes/MIT18_306f09_lec23_Conservation_Laws.pdf.xml
contents/assignments/MIT18_306f09_assn01_PSetPolicies.pdf.xml
contents/lecture-notes/MIT18_306f09_lec07.pdf.xml
contents/lecture-notes/MIT18_306f09_lec11.pdf.xml
contents/exams/index.htm.xml
contents/lecture-notes/MIT18_306f09_lec17.pdf.xml
contents/lecture-notes/MIT18_306f09_lec08.pdf.xml
contents/lecture-notes/MIT18_306f09_lec25_Discrete_to_Contin.pdf.xml
contents/matlab-resources/index.htm.xml
contents/lecture-notes/MIT18_306f09_lec02.pdf.xml
contents/exams/MIT18_306f09_exam02.pdf.xml
contents/18-306f09.jpg.xml
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Plots of grid scale oscillations
Numerical calculations showing grid scale oscillations. (Images by Prof. R. Rosales.)
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2021-4-27
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This site (c) Massachusetts Institute of Technology 2021. Content within individual courses is (c) by the individual authors unless otherwise noted. The Massachusetts Institute of Technology is providing this Work (as defined below) under the terms of this Creative Commons public license ("CCPL" or "license") unless otherwise noted. The Work is protected by copyright and/or other applicable law. Any use of the work other than as authorized under this license is prohibited. By exercising any of the rights to the Work provided here, You (as defined below) accept and agree to be bound by the terms of this license. The Licensor, the Massachusetts Institute of Technology, grants You the rights contained here in consideration of Your acceptance of such terms and conditions.
LOMv1.0
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OCW Master Course Number
18.306 Advanced Partial Differential Equations with Applications Fall 2009
The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.
CIP
270399
Applied Mathematics, Other
partial differential equations (pde)
nonlinear pde. Diffusion
dispersion
Initial and boundary value problems
Characteristics and shocks
Separation of variables
transform methods
Green's functions
Asymptotics
geometrical theory
Dimensional analysis
self-similarity
traveling waves
Singular perturbation and boundary layers
Solitons
Variational methods
Free-boundary problems
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