EGR 102Lecture 33MATLABMATLAB is both a software tool and a MATLAB is both a software tool and a computer language. A variety of numerical functions, symbolic computations, and visualization tools have been added to the matrix manipulations.Other languages & libraries include:FORTRAN (IMSL), C++,FORTRAN (IMSL), C++,…EGR 102Lecture 34Numerical Methods …•Solving a system of algebraic equations / inverting matrices•Finding roots of equations•Solving matrices (linear algebra)•Regression / Curve-fitting•Numerical Integration•Solving ODE’s (Ordinary Differential Equations)•More advanced topics ( e.g., solving PDEs) …
EGR 102Lecture 35Finite Element AnalysisMillions of simultaneous equationsEGR 102Lecture 36Matrix Math ReviewMatrices used to:Describe linear equationsTrack coefficients of linear transformationsRecord data that depend on multiple parameters Matrices can be added, multiplied, and decomposed in various ways
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EGR 102Lecture 37Matrix Math ReviewThe horizontal lines in a matrix are called rowsThe vertical lines are called columns. A matrix with mrows & ncolumns is called an m-by-nmatrix mand nare called its dimensions. The dimensions of a matrix are always given with the number of rows first, then the number of columns. It is commonly said that an m-by-nmatrix has an order(size) of m×n. ⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧=121110987654321AEGR 102Lecture 38Matrix Math ReviewAlmost always capital letters denote matrices with the corresponding lower-case letters with two indices representing the entries. For example, the entry of a matrix Athat lies in the i-th row and the j-thcolumn is written as ai,jand called the i,jentry or (i,j)-th entry of A. Alternative notations for that entry are A[i,j] or Ai,j. The row is always noted first, then the column. ⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧=121110987654321Aa2,3= ?