L9 - OPTI 280: Computer Programming Workshop Robin Palit...

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OPTI 280 Spring 2010, Lecture 9 R.Palit, 1 OPTI 280: Computer Programming Workshop Robin Palit College of Optical Sciences University of Arizona [email protected]
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OPTI 280 Spring 2010, Lecture 9 R.Palit, 2 Lesson Plan Symbolic Toolbox Install MatLab 2009b (or higher) w/ toolboxes. MuPAD notebooks Systems of Linear Equations Matrix Inverse Gaussian Elimination Finding the roots of a polynomial Quiz 4
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OPTI 280 Spring 2010, Lecture 9 R.Palit, 3 Symbolic Algebra Symbolic algebra in computers began in the early 1970s as a result of research in artificial intelligence. The first popular systems were Reduce, Derive and Macsyma. Current market leaders are Maple and Mathematica. For a good review of existing programs, see http://www.mathcom.com/corpdir/ techinfo.mdir/q520.html#q520.1
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OPTI 280 Spring 2010, Lecture 9 R.Palit, 4 MATLAB Symbolic Math Toolbox Powered by the MuPAD symbolic engine. The symbolic math toolbox consists of a set of functions that allow the user to execute symbolic computations. Computation is requested by MATLAB, assessed by MuPAD, and the result is returned to MATLAB. MuPAD MATLAB
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OPTI 280 Spring 2010, Lecture 9 R.Palit, 5 Types of Symbolic Computations Simplification, Factoring, Expanding Solving Equations Differentiation Integration dy dx x 2 + xy + y 2 x 3 y 3 + x 2 y 2 4 + xy 3 3 ( x 3 + 5 x 2 + 8 x 4) ( x 1)( x 2) 2 y = mx + b x = y b m x x 2 + y 2 ( ) 2 x Linear Algebra Transforms Etc.
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OPTI 280 Spring 2010, Lecture 9 R.Palit, 6 Defining Symbolic Objects A single symbolic object can be defined using the sym() command. Symbolic objects can be variables or numbers. Multiple symbolic objects can be simultaneously be defined using the syms() command. Each object is stored into a symbolic object that has the same name as the symbolic variable. Symbolic Objects Symbolic Variable
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OPTI 280 Spring 2010, Lecture 9 R.Palit, 7 Defining Symbolic Objects By default symbolic objects are defined to be complex. The syms() command can be used to impose assumptions (real, positive) on symbolic objects. These assumptions are passed into the MuPAD engine for use during computations. Assumptions can also be cleared using the syms() command.
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R.Palit, 8 Symbolic Expressions Mathematical expressions written in terms of symbolic variables are called symbolic expressions. findsym() can be used to determine the symbolic objects within an expression. Can include numerical variables that have been
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This note was uploaded on 05/23/2010 for the course OPTI 280 taught by Professor Pau during the Spring '10 term at Arizona.

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L9 - OPTI 280: Computer Programming Workshop Robin Palit...

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