4301Intro20080903

4301Intro20080903 - Lecture #1 (Part A) 3 September 2008...

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Applied Mathematics 4301: Numerical Methods for PDEs Course Introduction Wed aft. 4:10-6:40 S. W. Mudd Bldg. 1024 Prof. David Keyes, instructor S. W. Mudd Bldg. 215 apma4301@gmail.com Yan Yan, teaching assistant S. W. Mudd Bldg. 292 yy2250.columbia.edu Lecture #1 (Part A) 3 September 2008
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Course description • Introduction to the concepts and selected algorithms and applications for numerical methods for PDEs • More precisely: “algorithms for approximating the solutions of PDEs computationally” – emphasis on practical aspects: • construction of methods • characteristics of methods (esp., complexity, accuracy, robustness) • appropriate use (advantages/disadvantages, efficiency) – not on theoretical aspects • proofs of convergence (we do some, but see instead APMA 6302) – not on highest-end use • parallel implementation (we do some, see instead APMA/AMCS 4302) • Students run demonstration codes provided and do a modest amount of their own programming – using PETSc, the “Portable, Extensible Toolkit for Scientific computing" (freely available from Argonne National Laboratory) – or MATLAB (from MathWorks, licensed for academic use at CU)
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Course purpose and flavor • Goal: “numerical literacy” – develop intelligent critics and consumers, primarily among applications scientists and engineers (not developers per se ) – acquaint student researchers with standard scientific software tools (PETSc, MATLAB, etc.) – prepare students for follow-on specialized courses – relate numerical PDEs to other courses in mathematics, computer science, and applications • Limited primarily to lectures and readings (for compatibility with the philosophy of our CVN companions) – optional laboratory sessions – optional office hours – not as “hands on” as would be ideal – see me out of class for additional work, spring 2009 project possibilities, etc.
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Curricular dependencies • Official prerequisites – Linear algebra, APMA 3101 – Partial differential equations, APMA 3102/APMA 4200 – Numerical analysis, APMA 4300 – Programming ability in C/C++ or F77/F90 • In-class “running start” and pointers to review materials should help those who feel rusty or underprepared, but 4301 cannot become a substitute for these classes, or we don’t push ahead far enough beyond their aggregate in a semester • This class can be a partial synthesis of the above topics • Survey (to be returned today) should help me to decide where to spend limited time in review
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Examples of what you should know • Linear algebra (e.g., Strang) – Conditions for unique solvability of a linear system, Gaussian elimination via factorization – Eigensystem analysis
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This note was uploaded on 08/30/2011 for the course APMA 4301 taught by Professor Keyes during the Fall '08 term at Columbia.

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4301Intro20080903 - Lecture #1 (Part A) 3 September 2008...

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