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# Matlab and Matrices

 The Computing Engine Matlab is a calculator on Steroids Has hundreds of built-in mathematical functions that are built upon efficient algorithms Some simple examples: Numerically computes most calculus concepts such as derivatives and integrals Matrix operations such as numerically solving complex systems of equations Quick Intro to Variables Variables Like on your TI-83, you can assign variables to remember answers, objects, and user input. Example in Matlab: x = 3; Note: the semicolon suppresses the output on the command line, try x = 3 without it and you will see! Now you can use this variable x later in different mathematical operations (if used in the command line window, it is a global variable meaning it can be used anywhere in Matlab) Keep track of your variable names!!!!! Let’s add some numbers… 2 + 2 on the command line See the answer that comes out (hopefully 4) The ans variable Stands for “answer” Default variable for all common unassigned operations done in command line window See how it appears in the variable workspace window? Order of Operations PEMDAS “Please Excuse My Dear Aunt Sally” Parentheses, Exponent, Multiplication Division, Addition, Subtraction Try it out: 2 + 2 / 4 = 2.5 (2 + 2) / 4 = 1 Matlab and Matrices The name Matlab “Matrix Laboratory” Originally an open application that came out of the Argonne government research institution (free!) Initially designed for doing complex algorithms involving matrices in linear algebra and engineering applications Matrices in Matlab A foundational programming type  Representing it in Matlab: A = [1 2 3; 2 0 2; 3 1 9] Semi-colons mean new lines, spaces between numbers represent row placement (you can also use commas) More Matrices Keep in mind that a matrix can be a single row! Some call this a vector. A 3 element row-vector ( a 1x3 matrix) is easy to type out, but what if you need a 100 element row-vector? Try the syntax: t = 1:100 or t = 1: 1: 100 What if you did “t = 1 : 0.01 : 100” ? Matrix Operations Multiply a 3 x 3 Matrix with another:  A x B Built-in Matlab Functions Determinant of our Matrix A det(A) Inverse of our Matrix B inv(B) Built-in Matlab Functions Some more basic operations: sqrt(4) – takes a square root of a number mod(4,3) – modulus (we will use this later) reciprocal(5) – gives the reciprocal of a number cos(t) – gives the cosine of variable t Note: if t is a row-vector, Matlab is adept enough to recognize that it should take the cosine of each element in t, and returns a row vector that is same length of t exp(4) – represents e4 log(4) – represents the natural log of 4 ( ln(4) ) Exercise! Assign variables x, y, a, b for different values of a sine function Put these variables into a row-vector A Plot A over a domain of 4 values Get a good representative plot of a sine function Improve the “resolution” by specifying more values for the independent variable