Notes from Chapter 5, Thinking Like an Engineer

For this assignment, we were asked to read Chapter 5 and summarize what we learned about the following topics:

1. Sample Fermi Problems
   I learned that Fermi problems require a person to solve a variety of real life issues without all the information needed to find an accurate answer.
   Fermi problems are used to estimate reasonable answers.
   Ex) How many feet of steel were used to construct the Eiffel Tower?
   
   
2. General Hints for Estimation
   -Determine accuracy required (orders of magnitude; factors of 10)
   -Ballpark is usually good enough
   -Is it comparably better to err on the high or low side?
   -Do not worry about minor effects.
   Estimation is used to find unknown, hard to measure, and inconvenient-to-obtain values.
   
   
3. Estimation by Analogy
   Analogies are based on comparison measures.
   Ex) My chicken pot pie is the size of a softball.
   
   
4. Estimation by Aggregation
   In order to estimate by aggregation, I have to add up the sum of an item's parts.
   Ex) The area of an oddly shaped garden. Divide the garden into easily calculated portions and then add up the sums.
   
   
5. Estimation by Upper & Lower Bounds
   This is based on determining "conservative estimates" or "worst-case scenarios."
   Ex) Estimating the amount of food for a party. Estimate the highest number of people that could come and base your food purchase of of that number (Upper bound).
   
   
6. Estimation by Modeling
   Used to calculate and grasp the meaning of mathematical models and statistics.
   Ex from the book) "Given a large sample, its average and standard deviation can be calculated. Assuming that the length of sunflower seeds is normally distributed, the one-in-a-billion largest sunflower seed would be expected to be six standard deviations greater than the sample average."
   Personal reaction: I don't really understand this example or the concept, at least not as fully as I would like to. I was hoping to ask some questions about estimation by modeling.
   
   
7. Significant Figures
   Significant figures are composed of digits that can be thought of as reliable in a calculation.
   All non-zero digits are considered significant and zeroes are considered significant in different conditions.
   Don't round while calculating or you will diminish the reliability of your final answer.
   
   
8. Reasonableness
   Two types:

   Physical

   -Answer needs to make sense in the physical world

   -Convert your solution to familiar units

   Ex) decigrams/gallons to grams/liters 

   -Consider models in very large/small values to test they're applications compared to the sense of the problem

   
   

   Reasonably Precise

   -Accuracy: How close is the measured value to the actual value?

   
   

   -Error: Difference between measured value and actual value; due to inadequate equipment, improper techniques, and environmental conditions

   -Repeatability: how close a variety of measurements are to one another without respect to the actual value

   - Precision combines accuracy and repeatability

   -The more sig. figs, the more precise a measurement is if the value is accurate

   Ex:

   
   
   

   

   Source: http://blog.robotiq.com/?Tag=robotic+industrial+application

   
   Note: "You should report values in engineering calculations in a way that does not imply a higher level of accuracy than is know."
   Basically, 2-4 significant figures is sufficient for most calculations.
9. Precision vs. Accuracy (summarized above)
10. Engineering Notation vs. Scientific Notation
    Scientific Notation
             Typically expressed: #.### x 10^N
             N= how many places away from the decimal the first significant figure is
    Used to simplify a number whose first significant digit is far from the decimal point
    
    

    Engineering Notation

                      Typically expressed: ###.### x 10^M
                      M= a multiple of 3
    
    
11. Calculator E-Notation
    Letter “E” used to represent scientific/engineering notation on a calculator
    Means “times 10 raised to the ____”
    Ex) 3.7 E 9 = 3700000000 = 3.7 x 10^9
    Use exponential notation for numbers greater than 10,000 and less than 0.0001
    
    
12. Fractions vs. Constants
    Preferred format for answers in engineering: constants/decimals (including symbols)
    Two reasons:
             -It is difficult to instantly recognize the value of a
             fraction      Ex) 689/4
             -Precision is usually kept to 3-4 digits

    
    

    
    

    Overall, I learned the different methods of estimation account for the various situations and the desired accuracy. I also learned how to write solutions following the rules of significant figures; scientific, engineering, and calculator notation; and fractions vs. constants. I look forward to applying this information in future tasks. I am a little nervous about my ability to understand and solve Fermi problems, but practice makes perfect!