10 34 Numerical Methods Applied to Chemical Engineering Prof William Green Lecture 1 Using MatLab to Evaluate and Plot Expressions In this course you will learn various numerical methods to solve equations you may encounter here at the Institute Before you make a computation know the answer ahead of time This way you will be prepared for a surprise should there be one The homework will be difficult As far as textbooks go Beers text is comprehensive and dense I advise you to read Numerical Recipes first then Beers text and then follow the references in either book for additional information First we will solve systems of equations F x 0 A special case is when F is linear in x a non iterative exact solution is possible The equation to solve is M x b 0 When we encounter nonlinear systems we will attempt to linearize them Then we will examine eigenvalues and eigenvector bases We will apply the eigenvector bases to differential equations Other topics include singular value decomposition ordinary differential equations differential algebraic equations optimization boundary value problems involving partial differential equations We will study models and data including Bayesian analysis The remainder of the course we will study some special topics which include stochastic differential equations turbulence fourier transforms and calculus of variations MatLab Introduction Please read the first 37 pages of the MatLab tutorial available on line The pages below refer to the MatLab tutorial I illustrated how to Make a matrix pp 10 12 Make a vector Transpose a vector Hermitian Multiply a matrix and vector I warn you that often times errors occur with matrices and vectors that have incorrect dimensions Create a function with one output and several inputs Note every function must contain your name date and what it does pp 42 49 Add comments into your function Specify scalar multiplication and exponentiation with and With many chemical engineering calculations you will want to use scalar computations as oppose to matrix computations Create an x y plot pp 23 27 Distinguish between global variable and local variables to a function Create a function with several outputs and several inputs Save a function file as its function name m Invoke help Cite as William Green Jr course materials for 10 34 Numerical Methods Applied to Chemical Engineering Fall 2006 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Some of the commands used include M 1 2 5 3 4 V 300 400 500 750 V function whos log10 plot help linspace 300 1000 Example of Matlab program Save as rate m Function k rate T A n Ea returns the rate constant corresponding to input temperature by Bill Green 9 6 06 input T in Kelvin output k in 1 second R 8 314 Ea 1000 Ea k A T n exp Ea R T Note Use period before etc to do scalar math Note Use semi colon at end of each line to prevent program from printing all values Plot X Y creates graph of line X vs Y Plot X Y o creates graph of points X vs Y linspace creates vector of increment space N vector linspace X Y N 10 34 Numerical Methods Applied to Chemical Engineering Prof William Green Lecture 1 Page 2 of 2 Cite as William Green Jr course materials for 10 34 Numerical Methods Applied to Chemical Engineering Fall 2006 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY
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