gibson:teaching:spring-2018:math445:lecture:arithmetic
====== Differences ====== This shows you the differences between two versions of the page.
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gibson:teaching:spring-2018:math445:lecture:arithmetic [2018/01/23 13:32] gibson [Math 445 Mathematics and Applications in Matlab] |
gibson:teaching:spring-2018:math445:lecture:arithmetic [2018/01/24 18:05] (current) gibson [basic math functions] |
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| Line 59: | Line 59: | ||
| </code> | </code> | ||
| - | example | + | examples |
| <code> | <code> | ||
| >> 2*5^2-3/4+1 | >> 2*5^2-3/4+1 | ||
| ans | ans | ||
| = 50.25 | = 50.25 | ||
| + | |||
| + | >> (2*5)^2-3/(4+1) | ||
| + | ans = | ||
| + | 99.4000 | ||
| </code> | </code> | ||
| Line 73: | Line 77: | ||
| j imaginary unit for electrical eningeers! | 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) | >> sin(pi) | ||
| ans = | ans = | ||
| 1.2246e-16 % wha...? | 1.2246e-16 % wha...? | ||
| + | </code> | ||
| - | What does this mean? This is shorthand for scientific notation | + | What does this mean? This is scientific notation shorthand: ''1.2246e-16'' means $1.2246 \times 10^{-16}$. So the answer is nearly zero. |
| - | 1.2246e-16 means 1.2246 x 10^(-16) | + | |
| - | Why is sin(pi) not 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 | >> 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==== | ====Variables==== | ||
| + | <code matlab> | ||
| >> x = 4 % assign value of 4 to variable x | >> x = 4 % assign value of 4 to variable x | ||
| x = | x = | ||
| Line 104: | Line 128: | ||
| ans = | ans = | ||
| 12 | 12 | ||
| + | </code> | ||
| ====Evaluating expressions==== | ====Evaluating expressions==== | ||
| + | |||
| + | If you want to evalue the same expression repeatedly with different variables, reset the value of the variables and use the arrow keys to "scroll up" to the expression. Then hit "enter" | ||
| + | |||
| + | <code matlab> | ||
| >> x = 3; | >> x = 3; | ||
| >> y = x^2 - 2*x + 5 | >> y = x^2 - 2*x + 5 | ||
| Line 115: | Line 143: | ||
| y = | y = | ||
| 4 | 4 | ||
| + | </code> | ||
| ==== basic math functions ==== | ==== basic math functions ==== | ||
| - | sin, cos, tan, sec, csc, cot, asin, acos, atan, | + | |
| - | exp, log, log10, abs, sqrt, factorial, mod | + | <code matlab> |
| + | sin, cos, tan, sec, csc, cot, asin, acos, atan % the classic trig funcs, in radians | ||
| + | sind, cosd, tand, secd, cscd, cotd, asind, acosd, atand % the classic trig funcs, in degrees | ||
| + | exp, log, log10, abs, sqrt, factorial, mod % other awesome functions | ||
| + | </code> | ||
| | | ||
| | | ||
gibson/teaching/spring-2018/math445/lecture/arithmetic.1516743170.txt.gz · Last modified: 2018/01/23 13:32 by gibson
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