problem solving

1. Chapter 3
Problem Solving Methods

2. Engineers Solve Problems
 Problem solving is a powerful human activity.
 Computers are useful tools in problem solving,
but it is the human who actually solves the
problem.
 It is impossible to teach specific facts that will
always lead to a solution.
 The ability to solve problem comes from doing it.
 Many things must pull together to solve a
problem.

3. Problem Solving
 Problem solving is a combination of
experience, knowledge, process, and
art
 Design process is a series of logical
steps that when followed produce an
optimal solution given time and
resources as two constraints

4. Problem Solving; cont’
A problem is a situation, quantitative or
otherwise, that confronts an individual
or group of individuals, that requires
resolution, and for which the individual
sees no apparent path to the solution.

5. Problem Solving; cont’
Problem solving is a process, an
activity whereby a best value is
determined for an unknown, subject to
a specific set of conditions. It is a
means by which an individual uses
previously acquired knowledge, skills
and understanding to satisfy the
demands of an unfamiliar situation.

6. What skills must be used when
solving a problem?
Knowledge
Motivation
Experience
Communication Skills
Learning Skills
Group Skills

7. Problem Analysis
 A distinguishing characteristic of a qualified
engineer is the ability to solve technical
problems; both art and science
 Science; knowledge of mathematics,
chemistry, physics, etc
 Art; proper judgment, experience, common
sense, and know-how; to know when and
how rigorously science should be applied
and whether the resulting answer
reasonably satisfies the original problem
is an art

8. Techniques for Error Free
Problem Solving
Always draw a picture of the physical
situation,if possible.
State any assumptions made.
Indicate all given properties on the
diagram with their units.
Convert units to a given unit system.
Label unknown quantities with a
question mark.

9. Techniques for Error Free
Problem Solving
From the text, write the main equation
which contains the unknown quantity.
Or
derive the desire algebraic equation by
solving integral or differential equations.
Algebraically manipulate the equation to
isolate the desired quantity.

10. Techniques for Error Free
Problem Solving
Write subordinate equations for the unknown
quantities in the main equation. Indent to
indicate that the equation is subordinate. It
may be necessary to go through several
levels of subordinate equations before all the
quantities in the main equation are known.
Once all algebraic manipulations and
substitutions are made, insert numerical
values with their units.

11. Techniques for Error Free
Problem Solving
Insure that all units cancel.
Check one last time for sign error. Compute
the answer.
Clearly mark the final answer. Indicate
units!
Insure that the final answer makes physical
sense!
Insure that all questions have been
answered.

12. Skills used in Implementing
Problem Solving Strategies
Analysis
Use logic to:
Identify the system to be analyzed
Identify the objective Identify relationships
Divide the system into parts

13. Skills used in Implementing
Problem Solving Strategies
Synthesis
Use creativity to:
Develop ideas via brainstorming
Evaluate the ideas by analysis when
enough ideas have been generated

14. Skills used in Implementing
Problem Solving Strategies
Decision Making
Use logic to
compare the various ideas and
select the “best” one(s)
Generalization - Going from the
specific to the broad use abstraction to:
Aid in analysis, synthesis, and decision
making

15. 3.1 Types of Problems
 Research Problems
 Knowledge Problems
 Troubleshooting Problems
 Mathematics Problems
 Resource Problems
 Social Problems
 Design Problems

16. Types of Problems; cont’
 Research Problems
 A hypothesis be proven or disproved
 Example; CFC may destroy the earth’s
ozone layer is a hypothesis. Design an
experiment that either proves or disproves
the hypothesis

17. Types of Problems;
cont’
 Knowledge Problems
 When a person encounters a situation that
he doesn’t understand
 Example;
 A chemical engineer noticed that the
chemical plant produces more product
when it rains
 Further study showed that heat exchanger
cooled by rain increasing product

18. Types of Problems;
cont’
 Troubleshooting Problems
 When equipment or software behaves in
unexpected or improper ways
 Example
 During vibration test of an aluminum
beam, the amplitude of the response is
higher at all exciting frequencies
 Troubleshooting shows that 60 cps of AC
current was close to the natural frequency
of the beam

19. Types of Problems; cont’
 Troubleshooting Problems; cont’
 e.g. an electronic amplifier has a loud
“hum” when it is in a room with
fluorescent lights.

20. Types of Problems;
cont’
 Mathematics Problems
 Describe physical phenomena with
mathematical models
 Engineers can unleash the extraordinary
power of mathematics, with the rigorously
proven theorems and algorithms
 Example; Isaac Newton’s sine square law
can be applied to hypersonic flow

e.g. find x such that 4x + 5 = 0.

21. Types of Problems; cont’
 Resource Problems
 There is never enough time, money, or
equipment to accomplish the task
 Engineers who can get the job done in
spite of resource limitations are highly
prized and awarded
e.g. how will we get the money to build our
new factory?

22. Types of Problems; cont’
 Social Problems
 For example, if a factory is relocated to
where there is shortage of skilled worker,
engineers should set up training program
for employees
e.g. how can we improve education?

23. Types of Problems; cont’
 Design Problems
 Require creativity, teamwork, and broad
knowledge
 Example; design a new car
 Economy car? SUV?
 Design goal and parameters

24. Team Exercise
 If you have enough money to buy a car,
what kind of car do you like to buy?
 If you are a car design engineer, identify
design goal and design parameters
from your team’s preference

25. Team Exercise
 Well Posed Design Problem: Design a
new car that can:
 1. Go from 0 - 60 mph in 6 seconds
 2. Gets 50 miles/gal
 3. Costs less than $10,000 to the
consumer
 4. Does not exceed government pollution
standards
 5. Appeals to aesthetic tastes

26. Team Exercise
 1. Identify Problem e.g. we need to
build a new car since we are losing
market share
 2. Synthesis (integrating parts to for a
whole) e.g. we can combine an
aerodynamic body with a fuel efficient
engine to make a new car with very
high fuel efficiency

27. Team Exercise
3. Analysis
 identify relationships,
 distinguish fact from opinion,
 detect logic information,
 make conclusions from evidence,
 select relevant information,
 TRANSLATE REAL-WORLD PROBLEM
INTO MATHEMATICAL MODEL
 e.g. compare the drag of different body
types and determine if engine can fit
under the hood

28. Team Exercise
4. Application (identify the pertinent
information) e.g. What force is required
to allow the car to go 60 mph knowing
the car has a 30ft2
projected area and a
0.35 drag coefficient based on wind
tunnel data?

29. Team Exercise
 5. Comprehension (use the data and
explicit theory to solve the problem)
 F = 1/2 Cd ρ A V2
 F=force
 Cd=drag coef. ρ=air density A=protected
frontal area V=speed

30. Difficulties in Problem Solving
 Most common difficulty: failure to use known
information.
 To avoid this problem:
 Write the problem in primitive form and
sketch an accurate picture of the setup (where
applicable).
 Transform the primitive statements to simpler
language.
 Translate verbal problems to more abstract
mathematical statement(s) and figures,
diagrams, charts, etc.

31. General Problem Solving
Method
Define and understand problem
1. Sketch the problem
2. Gather information
3. Generate and evaluate potential
solutions
 Use applicable theories and assumptions
4. Refine and implement solution
5. Verify and test solution

32. Define and Understand
 Understand what is being asked
 Describe input/output (I/O)
 what are you given
 knowns
 what are you trying to find
 unknowns
 Sketch the problem

33. Gather Information
 Collect necessary data
 List relevant equations/theories
 State all assumptions

34. Generate Solution Methods
 Apply theories and assumptions.
 Typically, there is more than one approach
to solving a problem
 Work problem by hand using the potential
solution methods
 Break problem into parts; scale it down; etc.
 e.g., if the problem was to calculate the average
of 1000 numbers, work the problem by hand
using, say, 10 numbers, in order to establish a
method

35. Refine and Implement
 Evaluate solution methods.
 accuracy
 ease of implementation
 etc.
 Implement “best” solution.

36. Verify and Test
 Compare solution to the problem statement
 Is this what you were looking for?
 Does your answer make sense?
 Clearly identify the solution
 Sketch if appropriate

37. CHECK YOUR WORK!!
 Don’t stop at getting an answer!!
 Think about whether the answer makes
physical sense.
 you are the instructor and you have to turn in
final grades. In your haste, you calculate the
average of Susie’s grades (100, 70, 90) to be
78 and give Susie a C...

38. Getting It Right
 The problem solving process may be an
iterative process.
 If at first you don’t succeed (i.e., the
algorithm test fails), try again…
 The more thorough you are at each
step of the problem solving process, the
more likely you are to get it right the first
time!!

39. Team Exercise
 Given: A student is in a stationary hot-
air balloon that is momentarily fixed at
1325 ft above a piece of land. This pilot
looks down 60o
(from horizontal) and
turns laterally 360o
.
Note: 1 acre = 43,560 ft2

40. Team Exercise; cont’
 Required:
 a) Sketch the problem
 b) How many acres of land are
contained by the cone created by her
line of site?
 c) How high would the balloon be if,
using the same procedure, an area
four times greater is encompassed?

41. Creative Problem Solving
 The nine dots shown
are arranged in equally
spaced rows and
columns. Connect all
nine points with four
straight lines without
lifting the pencil from
the paper and without
retracing any line.
• • •
• • •
• • •
Individual Exercise (3 minutes)

42. Creative Problem Solving
• • •
• • •
• • •

43. Creative Problem Solving
 If you enjoy solving puzzles, you will enjoy
engineering
 Crick and Watson figured DNA when they
were young
 Engineers create from nature what did not
exist before
 In this creative process, the engineer
marshals skills in mathematics, materials, and
other engineering discipline and from these
resources create a new solution for a human
need

44. Creative Problem Solving
 Engineering is not dull or stifling; send
people to moon, communication from
battlefield, etc
 Creative artists spent many years
perfecting their skills
 Engineers need patience, practice, and
gaining problem-solving techniques by
training

45. Self-Questions for Problem Solving
 How important is the answer to a given
problem?
 Would a rough, preliminary estimate be
satisfactory or high degree accuracy
demanded?
 How much time do you have and what
resources are at your disposal?
 Data available or should be collected,
equipments and personnel, etc

46. Self-Questions for Problem Solving
 What about the theory you intend to use?
Can you use it now or must learn to use it? Is
it state of the art?
 Can you make assumptions that simplify
without sacrificing needed accuracy?
 Are other assumptions valid and applicable?
 Optimize time and resources vs reliability

47. Engineering Method
1. Recognize and understand the
problem (most difficult part)
2. Accumulate data and verify accuracy
3. Select the appropriate theory or
principles
4. Make necessary assumptions
5. Solve the problem
6. Verify and check results

48. Engineering Method
 Perfect solutions to real problems do
not exist. Simplify the problem to solve
it; steady state, rigid body, adiabatic,
isentropic, static etc
 To solve a problem, use mathematical
model; direct methods, trial-and-error,
graphic methods, etc.

49. Problem Presentation
 Problem statement
 Diagram
 Theory
 Assumptions
 Solution steps
 Identify results and verify accuracy

50. Standards of Problem Presentation
 Engineers should have ability to present
information with great clarity in a neat,
careful manner
 Poor engineering documents can be
legal problems in courts
 Follow standard forms such as shown
in the textbooks

51. Team Assignment
 Page 141 Problem 3.20

52. Algorithms
 Algorithm: “a step-by-step procedure
for solving a problem or accomplishing
an end” (Webster)
 Algorithms can be described by
 Pseudocode
 Flowcharts

53. Pseudocode
 English-like description of each step of
algorithm
 Not computer code
 Example - take out trash barrels
while there are more barrels
take barrel to street
return to garage
end

54. Flowcharts
 Graphical description of algorithm
 Standard symbols used for specific
operations
Input/Output
Start/Stop
Branch Test
Process Step
Process Flow

55. Flowchart Example
Define the
problem
Read
input
Solve the
problem
Can I
solve this?
Output
results
What do I need
to know?
Ask for
more input
Begin
Can I
solve this?
End
yes
no
yes
no

56. Top Down Design
 State problem clearly
 Sketch problem
 Describe input/output (I/O)
 Work problem by hand
 Algorithm: pseudocode or flowchart
 Decomposition - break problem into steps
 Stepwise refinement - solve each step
 Test the algorithm/check your work!!

57. Example (Team exercise, 15
min)
 State problem clearly:
 Given ax2
+ bx + c = 0, find x.
 Describe I/O:
 Input: a, b, c
 Output: x

58. Example (cont.)
 Hand example:
 a=1, b=4, c=4
 equation? (See Chapter 6, Mathematics
Supplement)
 x=?

59. Example (cont.)
 Algorithm development
 write an algorithm in pseudocode to take
any set of coefficients (i.e., a, b, c) and
give the value of x for each set
 Test your algorithm
 a,b,c = 1,4,4
 a,b,c = 1,1,-6
 a,b,c = 1,0,1
 other good test cases?