GET130 Intro to Engineering Technology Fall 2013 J. Sumey

Transcription

1 GET130 Intro to Engineering Technology Fall 2013 J. Sumey

2 All fields of engineering rely heavily on math By extension, engineering technology areas also use math mid level in B.S. programs lower level in A.S. programs i.e. what are the math requirements in your program? statistics calculus trigonometry geometry algebra Thus, it is an important skill to understand and apply math in ET programs 2

3 We have already seen a glimpse of how a spreadsheet program (i.e. Excel) can be used as a math-solving tool solution of a complete problem all unknown variables instantly data visualization to aid in human understanding with large and/or complex data sets As always, the calculator continues to also be an important tool for ET 3

4 HP and TI are considered pioneers of calculator development Technological improvements have also affected our calculators built-in Operating Systems provide many powerful functions LCDs and power-savvy microprocessors provide long battery life graphing feature provides visualization programmability provides expansion of usefulness 4

5 plus owner s manual! 5

6 One of most well-developed & widely-accepted calculators in many engineering fields Impressive feature set (link) Required in GET130 & CET/EET programs Highly useful in all MAT and future MTR courses Tip: obtain electronic PDF version of the Guidebook see 6

7 Number line / signed numbers ++, --, +-, -+ Algebraic rules addition, subtraction, multiplication, division caveat: beware of arithmetic signs 7

8 powers & roots (exponentiation) root = 1/power (inverse operations) examples: area = length squared volume = length cubed Rules of exponents a 0 = 1 a x a y = a x+y a x a y = a x y a x = 1 a x a x y = a xx a x y b z = axx b zz y a x = ax y 8

9 Algebraic logic/operator hierarchy Please Excuse My Dear Aunt Sally means: Parenthesis, Exponents, Multiplication / Division, Addition / Subtraction Operator Precedence (...) x y, +, - vernier dial caliper example: X (mean / average) Σ (sigma) = summation significant digits median (middle value) 9

10 more convenient method of expressing wide range of numeric values calculator shows E for 10, /. notation is reversed in other countries! x million x hundred thousand x ten thousand x thousand 100 1x hundred 10 1x ten 1 1x10 0 (unity) 0.1 1x tenth x hundredth x thousandth x ten-thousandth x hundred-thousandth x millionth 10

11 works the same way as scientific notation except: 1. significant digits of the number is shown as a value between 1 and exponent is a multiple of 3 commonly used with engineering measurement units 10 n symbol prefix English 10 9 G giga billion 10 6 M mega million 10 3 k kilo thousand 10 0 one 10-3 m milli thousandth 10-6 µ micro millionth 10-9 n nano billionth K is used for Kelvin see 11

12 Just as we have seen with Excel, data graphing is important to human visualization Calculators with large LCDs are ideal for displaying (crude but effective) graphs the TI-89 features advanced graphing features visualization window/zoom plot tracing math calculations (i.e. statistics) 12

13 Fundamental Units Based on real-world physical phenomena: Phenomena SI (metric) Unit English Unit length meter foot mass kilogram slug (/pound) time second second temperature Kelvin Rankine electric current ampere ampere luminous intensity candela candela molecular mass mole pound mole SI = Système International vs. English/USCS = U.S. Customary System 13

14 Length from speed of light in a vacuum: 299,792,458 m/s (~3x10 8 m/s) Mass from a cylinder of platinum-iridium alloy in France Time duration of 9,192,631,770 radiation cycles of cesium-133 is 1 second cycles/second is expressed in Hertz (Hz) 14

15 Temperature that water freezes (32ºF or 0ºC) absolute zero is lowest theoretical temperature (-273ºC) Kelvin scale starts at this point (0ºK = -273ºC) Rankine is English version (0ºR = -460ºF) 15

16 ºC ºK ºR ºF Conversions: water boils water freezes C = K 273 F = R 460 C = 5 ( F 32) 9 F = 9 C absolute zero

17 Electric current Ohm s law: V=I R or I=V/R 1 Ampere (A) is the resulting current when 1 Volt (V) is applied across a 1 Ohm (Ω) resistance Luminous intensity amount of power of yellow light source per steradian Molecular mass amount of substance 1 mole = number of atoms in kg of carbon-12 used in chemical engineering 17

18 Derived from fundamental units Plane (2D) angles: radian (rad) 1 radian = circumferential (arc) length of a circle s radius (57.3º) full circumference of circle = 2π rad see Solid (3D) angles: steradian (sr) see 18