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gibson:teaching:spring-2018:math445:lecture:arithmetic

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===== Math 445 Mathematics and Applications in Matlab ===== Four goals - learn numerical programming - learn applied mathematics - explore applications - think about science and society - grow in speaking, writing, reading, maturity ====Command line (REPL)==== * Read an expression * Evaluate it * Print the result * Loop back --do it again! example <code matlab> >> 4 + 5 ans = 9 >> </code> ====Arithmetic operators==== + plus - minus * times / divide \ divide ^ power % comment examples <code matlab> >> 4^3 ans = 64 >> 4/3 ans = 1.33333 >> 4\3 ans = 0.75 >> 4+3 % write a comment here, Matlab will ignore it ans = 12 </code> ====Precedence==== <code> ^ first * / \ next + - last </code> examples <code> >> 2*5^2-3/4+1 ans = 50.25 >> (2*5)^2-3/(4+1) ans = 99.4000 </code> ====Special numbers==== pi 3.1415926... inf infinity NaN not a number i imaginary unit j imaginary unit for electrical eningeers! <code matlab> >> 1/0 ans = Inf >> 0/0 ans = NaN >> i^2 ans = -1 >> j^2 ans = -1 >> sin(pi) ans = 1.2246e-16 % wha...? </code> What does this mean? This is scientific notation shorthand: ''1.2246e-16'' means $1.2246 \times 10^{-16}$. So the answer is nearly zero. But why is ''sin(pi)'' not exactly zero? Because computers can store and compute only finite truncations of real numbers. Matlab can't represent $\pi$ exactly, only a truncation of $\pi$ that is accurate to sixteen decimal digits. <code matlab> >> 0.4 - 0.3 - 0.1 ans = 2.7756e-17 % wha...? </code> Here the issue is that computers use binary representations of numbers, not decimal representations. None of the three numbers 0.4, 0.3, and 0.1 can be represented exactly in binary. They're instead represented with binary fractions very nearly equal to 0.4, 0.3, and 0.1. Usually you don't see the difference, but sometimes, like here, you do. ====Variables==== >> x = 4 % assign value of 4 to variable x x = 4 >> y = 3 % assign value of 3 to variable x y = 3 >> x*y % evaluate x times y ans = 12 >> ans % variable ans is value of last expression ans = 12 ====Evaluating expressions==== >> x = 3; >> y = x^2 - 2*x + 5 y = 8 >> x = 1; >> y = x^2 - 2*x + 5 y = 4 ==== basic math functions ==== sin, cos, tan, sec, csc, cot, asin, acos, atan, exp, log, log10, abs, sqrt, factorial, mod ====Workspace commands==== help ; supress format compact format loose format long format short diary on diary off who whos clear x clear all ls or dir pwd cd

gibson/teaching/spring-2018/math445/lecture/arithmetic.1516744018.txt.gz · Last modified: 2018/01/23 13:46 by gibson