CMPS 1371 Introduction to Computing for Engineers

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CMPS 1371Introduction to Computing for Engineers

• PRINCIPLES OF PROBLEM SOLVING

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Problem Solving

• Define the Problem
• Identify given information.
• Identify other available information.
• Design and implement your solution to the
  problem.
• Verify your solution.
• Reflect on your solution.

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Example

• Suppose you work for a company that produces
  packaging. You are told that a new material is
  available to protect the package if dropped,
  provided the package hits the ground at less than
  25 ft/sec. The average package weight is 20
  pounds with rectangular dimensions of 12 by 12 by
  8 inches.

• You must determine whether the packaging material
  provides enough protection when carried by a
  delivery person.

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Problem Solving

• Define the Problem
• What problem are you trying to solve?
• "What would success look like?"
• What should the program output? Computed values?
  A plot or series of plots?
• The implication is that the package is to be
  protected from an accidental drop while being
  carried (not falling off the delivery truck)

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Problem Solving

• Identify given information.
• What constants or data are supplied?
• What theory, principles, models and equations
  have you been given?
• The known information is the packages weight,
  dimensions, and the maximum allowed impact speed.

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Problem Solving

• Identify other available information.
• What theory, principles, models and equations can
  you find in other sources (text books, lecture
  notes, etc.)?
• Although not explicitly stated, you need to know
  the maximum height from which the package can be
  dropped without damage.
• You need to find a relationship between the
  speed of impact and the height of the dropped
  package

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Problem Solving

• Basic assumptions
• The package is dropped from rest with no vertical
  or horizontal velocity
• The package does not tumble
• The effect of air drag is negligible
• Assume maximum height of 6 feet (ignore those 8ft
  delivery men)
• The acceleration, g, due to gravity is constant
  since only a 6 ft drop

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Problem Solving

• Design and implement your solution to the
  problem.
• How can you break the larger problem into smaller
  problems?
• Can you sketch the problem?
• Look at the problem from the top down or bottom
  up?
• What programming techniques might you use to
  convert input to output?
• What variables do you need? Vectors? Arrays?
• What principles and equations apply to convert
  input to output?

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Problem Solving

• Since the problem involves mass in motion, we can
  apply Newtons Laws
• Height vs time to impact
• h ½ g t2
• Impact speed vs time to impact
• v g t
• Conservation of mechanical energy
• m g h ½ m v2

m
g
v
h
ground
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Problem Solving

• We could solve for any three of the equations,
  but notice the 3rd equation does not involve the
  impact time
• m g h ½ m v2
• h ½ v2 / g
• Notice the mass cancelled out hence, weight of
  the package does not affect the relation between
  the impact speed and the height dropped

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Problem Solving

• Solution
• h ½ v2 / g
• v 25 ft/sec, g 32.2 ft/sec2
• h ½ (25)2 / 32.2 9.7 ft
• gtgtv 25
• gtgtg 32.2
• gtgth v.2./(2.g)
• h
• 9.7050

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Problem Solving

• Verify your solution.
• How do you know your solution is correct?
• If the computed height was negative, we would
  know we did something wrong.
• If the height was very large, we might be
  suspicious
• Computed height of 9.7 ft seems reasonable
• To be conservative, we would report that the
  protective packaging works for heights less than
  9 ft when dropped.

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Problem Solving

• Reflect on your solution.
• What worked?
• What didn't?

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Fundamental Operations

• List of possible operations we may expect to
  perform on collections
• Build / Insert - Create a collection of elements
• Traverse - Create a new collection by operating
• on an existing collection
• Map - Transform a collection with same length
• Filter - Remove items with specified criteria
• Fold - Collection is summarized
• Search - Locate specified element
• Sort - Re-ordering of elements