ENGR 112 Exam 1

dimensions vs. units
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dimensions vs. units
dimensions: used to describe physical quantities
examples- length, time, mass
units: describe the specific measure of a particular dimension
examples- meters, yards, grams, seconds
fundamental dimensions
a dimension that can conveniently and usefully be manipulated when expressing all physical quantities of a particular field
examples- length (L), mass (M), Time (T), amount of a substance (N), light intensity (J), electric current (A)
derived dimension
a dimension that results from the combination of fundamental dimension
example- m/s, m/s^2, hertz, newton, pascal, joule, watt, volt, ohm, newton meter
absolute system
has dimensions that are not affected by gravity. L, T, and M are typical fundamental dimensions and Force [F] is a derived quantity determined from Newton's second law.
gravitational systems
force, length, and time are defined units while mass is a derived quantity, which is determined from Newton's law of Gravitation
dimensional homogeneity
for an equation to be valid, it must be dimensionally homogeneous, that is the dimensions on the left-hand side must equal the dimensions on the right-hand side
5 step conversion procedure
1. term to be converted
2. conversion formula
3. set up fraction
4. multiply
5. calculate
weight vs. mass
Mass is a measurement of the amount of matter something contains, while Weight is the measurement of the pull of gravity on an object
mathematical rules governing dimensions
addition/subtraction: all terms that are added must have the same dimensions
multiplication/division: the dimensions in multiplication/division are treated as though they were variables and cancel accordingly
import data files into matlab
xlsread()
load()
save()
formatting plotslinespec xlabel(), ylabel() title() grid() legend()multiple plots on matlabhold on subplot()how to use mesh and meshgridmesh(a,b,c)histogram in matlabhistogram(x, # of bins)descriptive statisticssummarizes or describes important features of a set of data without attempting to infer conclusions that go beyond the data derived from observationstatistical inferencestatistical generalizations made about the data may be used to predict future outcomespopulationdata set contains ALL members or eventssamplea subset of a given populationmeasures of central tendency: meanthe average of all of the datameasures of central tendency: medianthe middle value for an ordered set of datameasures of central tendency: modethe data value that appears in the set with the greatest frequencymeasures of variation: minimumsmallest data valuemeasures of variation: maximumlargest data valuemeasures of variation: rangethe spread of the data, from the min to the maxmeasures of variation: variancepopulation variance: find the mean of the residual values-sum of the errors squared mu = 1/n * sum from 1 to n (x) sigma^2 = 1/n * the sum of (x-mu)^2measures of variation: sample variancesmall sample: s^2 = 1/(n-1) * the sum of (x-xbar)^2 large sample: s^2 = 1/n * the sum of (x-xbar)^2measures of variation: standard deviationpopulation standard deviation: sigma = sqrt(sigma^2) = [1/n * the sum of (x-mu)^2]^1/2measures of variation: sample standard deviations = sqrt(s^2)histogramsillustrate how values are distributed within a given range (includes the min and max) -first you must subdivide the range of values into equally spaced intervals called "bins" -once the intervals have been determined, the values found in each respective range must be accounted for -bins on the x axis and the frequency of values in each interval on the y axishistograms: probabilityrelative frequency = frequency / total number probability = relative frequency * 100%frequency tables-no less than 6 and no more than 15 classes -the square root of n, where n is the number of data points, provides an approximate number of classes to consider -select classes that will accommodate all of the data points -make sure that each data point fits into only one class -whenever possible, make the class intervals equal lengthnormal distributionf(x) = 1/ (sigma*sqrt(2pi)) * e^((x-mu)^2/2sigma^2)normal probability distribution: z valuesthe z value for a particular x value is the distance from the mean measured in number of standard deviationsnormal probability distribution: z-tablestable from 0 to infinity: since the standard normal distribution is symmetric about the mean value, the values in the table represent numerical integrals for values of z starting at the mean value. YOU HAVE TO ADD .5 TO THE TABLE VALUE TO GET THE TOTAL CUMULATIVE PROBABILITY table from -infinity to infinity: the z value equals the cumulative probability how to read: if you computed a z value of .13, find .1 in the first column and .03 in the first row and then find their intersection pointnormal probability distribution: z-table calculations to compute probability within a given rangethe value you find on the z table using the z value, is the probability. Depending on which z table you use, you may or may not need to add .5 to the probabilitynormal probability distribution: normalize a data set into a z-formmean while using z = 0 standard deviation while using z = 1 z = (x-mu)/ sigmanormal probability distribution: be able to switch from z-form to non-normalized x-formx-scale: mu, mu + sigma, mu - sigma z-scale: 0, 1, -1 z=(x-mu)/sigmanormal probability distribution: test for normality or log-normality using a probability plotnormpdf(x,mu,sigma) normcdf(x,mu,sigma) norminv(p,mu,sigma) probplot('normal', x) probplot('lognormal', x)z-table calculations to compute a confidence interval on the mean of specified probability given the population standard and test dataalpha = region not in ci (ex: 95% ci -> alpha = .05) large sample size: sample mean is approximately normal with mean mu sub xbar = mu and std sigma sub xbar = sigma / sqrt(N) z = (xbar - mu sub xbar) / sigma sub xbar = (xbar - mu) / (sigma/sqrt(N)) ci of mu with known sigma: xbar - z sub z/2*sigma/sqrt(N) < mu <xbar + z sub a/2*sigma/sqrt(N)five major steps in the design process: identify the needsomething that doesn't already exist anyone can indentifyfive major steps in the design process: understanding the needwhat does the solution need to do? how well does it need to be done? effort increases quality inputs: stakeholders wantsfive major steps in the design process: ideate possible solutionscreative portion of the design process generate many solutions evaluate best solution select best solution inputs: engineering specificationsfive major steps in the design process: define a solutionchosen concept testing ->modeling -> prototyping -> analysis -> have we met specs yet: if yes, document final design, if no, go back to testing inputs: viable conceptfive major steps in the design process: implement solutionusually involves a handoff to other engineersengineering specificationsquantitative, measurable criteria that the product is designed to satisfy metric: characteristic of the product that will be measured numerical range: range of the metric that is acceptable units: a definite amount of a physical quantity defined and adopted by convention and or law, that is used as a standard for measurement of the same physical quantity of any amount.algorithmsa compact and reliable method of communicating the underlying logic of a solution or process -inputs/outputs -definiteness -effectiveness -finiteness -not uniqueness -proper format for the intended performerslope and intercept for linear regression for a set of data is given the summation formula used in classy = b1x + b0 + E E = some error b1 = (n*sum(x*y)-sum(x)*sum(y)) / (n*sum(x^2) - (sum(x))^2) b0 = (1/n)*sum(y)-(b1/n)*sum(x)significance of R^2it measures the correlation coefficient. An r^2 close to 1 is good and shows that x and y are strongly related. If it's close 0 it shows that x and y have little relationshipsignificance of Mean Square Errorsmaller mse means its a good regressions model MSE = (1/n)*sum from 1 to n error^2 sum from 1 to n error^2 = sum from 1 to n (y-b1x-b0)^2significance of Sum Square Errorsum of the squared differences between each observation and its group's mean. It can be used as a measure of variation within a cluster. If all cases within a cluster are identical the SSE would then be equal to 0.functions to be provided by the prototype of final projectread bar code from four cards and determine the pellet mix specified by those receive and sort a mixture of 75 pellets won't dispense if 75 pellets haven't been provided won't dispense chemical stabilization pellets solar poweredinitial specifications of final projectpellets: color/transparency, size (14mm or 18-20mm), material card reader: 3.5 x 11 inch long size, >75, pellets color sensor: distance, >= 1, lego unit