lecture 2 1.computing 101 2.developing a solution 3.problem solving

Lecture 2

1. Computing 1012. Developing a Solution3. Problem Solving

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Recommendation on taking notes in EGR115

• Notebook– slide number in margin. comments on the right.– write down vocabulary words– write down overall ideas– write down things that we repeat 4 or 5 times!– write down possible errors

• Printout of Slides*– print 2 or 3 slides per page– draw arrows, add your comments– Highlight

*We will do our best to have the slides posted by the night before, but no guarantees.

Computer Hardware• 1946 – ENIAC (Electronic Numerical Integrator And

Computer) – First general purpose electronic computer.• The Von Neumann computer architecture is mostly what

we use today. The architecture separates a computer in 3 major parts:– The Central Processing Unit (CPU)– The computer memory– The Input/Output (I/O) devices

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CPU + memoryScreen=output

Speakers=output Mouse=input

Keyboard=input

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The important pieces

• Computing (as a whole) can be broken into 4 main categories:– Hardware

• What people generally think of as the computer. You can touch it. (Normally limited to electronic components)

– Software• Applications, games, programs you run.

– Data• The stuff applications use and produce – Word documents, saved game

files, Excel Spreadsheets, etc.– Media

• Where things get stored. Hard disks, USB thumb drives, CD/DVD disks, 3.5” floppy disks, magnetic tape.

Programming?

• You will generally be using hardware to write software that uses data and is saved on media.

• Programming is the act of writing logical instructions that the computer will execute when the software is used.

• Writing a program can be as difficult as learning to speak a foreign language, since the programmer is constrained to the vocabulary (specific terminology or keywords), grammar (exact syntax), and punctuation (symbols) of programming.

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Categories of software

• Software contains the instructions the CPU uses to run programs.

• There are several categories, including:– Operating systems (OS) – manager of the computer system as a whole– Software applications – commercial programs that have been written

to solve specific problems– Language compilers - to ‘translate’ programs written by people into

something understandable by the machine (sometimes not needed)

Generations of Languages used to write software

1) Machine language – also called binary language. Sequence of 0’s and 1’s.

(rarely written by hand)

2) Assembly language – each line of code produces a single machine instruction (add, subtract…)(Used by specialty professionals)

3) High-level language – slightly closer to spoken languages.(How most programmersprogram)

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add b,cadd a,b

a = a + b + c;

This line does the same as the two above.

Finally… MATLAB

• Is both a software application and a language interpreter.

• Is an interpreted language – does not require compilation, but it does have a conversion step hidden from the user.

• Has an interactive environment –– “In the MATLAB environment, you can develop and execute programs

that contain MATLAB commands. You can execute a MATLAB command, observe the results, and then execute another MATLAB command that interacts with the information in memory, observe its results and so on.”

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Generating a Solution

• Computers make very fast, very accurate mistakes.

• They do exactly what you tell them to, not what you mean for them to do.

• You are looking to design a technique for solving a problem. If the inputs change, then the technique should still work.

• If the goal is to solve a problem, you have to know how to solve the problem before you can tell the computer how to solve it.

• The set and order of steps you (and the computer) take to solve a problem is called an algorithm.

General Idea of This Lesson

• Provide you with a method (i.e. a recipe) for solving problems

Example problems:• “Find the optimum nozzle dimensions for …”• “Solve for the optimum path for the robot …”• “Find the range of temperatures adequate for …”

• In EGR115, most tasks will be:“Develop a program that ……”

General Terms

• Keep in mind there are 2 sides to software– The person who writes software: the programmer– The person who uses software: the user (i.e. client)

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General Terms

• Keep in mind there are 2 sides to software– The person who writes software: the programmer– The person who uses software: the user (i.e. client)

• As you (the student) develop software, you will constantly jump back and forth between the two roles.

• Your goal:“The programmer should make the user’s life easy.”- Clear directions- Clear units- Examples of answers- Clean presentation

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Where do I even start?

ME408 Clean Thermal

Power Systems

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Scientific Problem-Solving Method

1. Problem Statementa. Diagramb. Assumptions

2. Solution Steps (manual solution)a. Theory / limitationsb. Itemize specific steps (in order) as you solve the problemc. Identify results & verify accuracy

3. Computerize the solutiona. Express the algorithm as steps general to any instance of the problemb. Translate the algorithm to lines of codec. Test and verify result

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2. Solution Stepsa. Theory / limitationsb. Itemize specific steps (in order) as you solve the problemc. Identify results & verify accuracy

3. Computerize the solutiona. Express the algorithm as steps general to any instance of the problemb. Translate the algorithm to lines of codec. Test and verify results

• Create a program to “solve” many instances => Create a program to re-use the solution for other sets of givens.

• Coding is very late in the process.

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1. Problem Statement– Summarize the given information– Must contain all essential information, units included!

• GET RID OF useless information!– State what is to be determined

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Example – Aerospace Engineering

• Problem:– Givens

• Temperature (Kelvin)• Volume (meters cubed)• n : chemical amount of gas (moles)• R : gas constant R = 8.3144 Joules/(moles*Kelvin)

– Solve for• The pressure (Pascals)

http://www.epa.gov/eogapti1/bces/module2/idealgas/idealgas.htm

NOTE: There is no full sentence here!!!

Do not rewrite the problem. Separate the GIVENS from the SOLVE FOR.

(Might use the Ideal Gas Law)

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Example – Mechanical Engineering

• Problem: Stress on a beam

– Givens• Load 1: R1 = 10lb• Load 2: R2 = 60lb• Load 3: R3 = 20lb• Load 4: R4 = 50lb• Distances from start of beam to load2: 5ft• Distance between load2 and 3: 15ft• Distance between load3 and end of beam: 7ft

– Solve for• shear diagram• moment diagram

square beam

R1 = 10lb

R2 = 60lb R3 = 20lb

R4 = 50lb

5ft 15ft 7ft

NOTE: There is no full sentence here!!!

Do not rewrite the problem. Separate the GIVENS from the SOLVE FOR.

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Example – Civil Engineering

• Problem: Elongation of rod

– Givens• diameter of rod: 0.5in• length of rod: 6ft• weight of load: 2000lbs• material: steel

– Solve for• normal stress in rod (psi)• strain (elongation for 1 unit) in the rod (inches/in)• elongation of rod (inches)

2000 lbs

6ft

AGAIN…No full sentences


• Sometimes it is helpful to think about the problem this way:– What am I trying to get to (e.g., the output)?– What are the constants given in the problem?– What are the things the user will provide (either from the keyboard or

a file)– What are the constants I think I will need but that aren’t given (e.g.,

gravity, pi, etc.)– What things can I calculate with that information? Note, this may be

something where you know how to calculate (e.g., area or circumference) or that you know a formula exists for and you just need to find that formula. (e.g., solving for unknown parts of a triangle)

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Example – Aerospace Engineering

http://txchnologist.com/post/31532018204/txchnical-improvements-combining-rockets-and-jets-for

http://www.universetoday.com/29317/how-to-keep-asteroids-away-tie-them-up/

http://hsc.csu.edu.au/engineering_studies/focus/aero/3057/Graphics.html

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Example – Civil Engineering

http://map.ua.edu/resources/

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Example – Electrical Engineering

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For example…

• Assume no friction• Assume wall thickness is negligible• Assume initial speed is zero• Assume mass of object is negligible

• Aerodynamics: Assume laminar flow (i.e. no turbulence)

• Thermodynamics: Assume geometry of a turkey is that of an American football

• Solids: assume system is in equilibrium

Assumptions

• ASSUMPTIONS ARE NOT FACTS!

• Assume “Area of a Circle” = π * radius2

• That isn’t an assumption – it’s a fact. Assumptions are things that MIGHT not be true (or that you know AREN’T true).

• Assuming π = 3.14 is an assumption because you know it isn’t true.

• They may be necessary to solve the problem, or they may just make the problem easier to solve.

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Example – General Equations

• Volume of a sphereV = 4/3*∏*R^3

• Volume of a cubeV = L^3

• Newton’s second law of motionF = m*a

• Equation of a liney = m*x + b

• Slopem = Δy/Δx = (y2-y1)/(x2-x1)

• WeightW = mass * g

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Example – ME/AE Engineering

• If the system is in equilibrium,ΣF = 0 (“sum of all forces equals zero”)

• Bernoulli’s Principle (fluid dynamic)

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Example – Electrical/Civil Engineering

• Ohm’s lawV = R*I (V=voltage (V), R=resistance (Ω), I=current (A))

• Electrical Power (i.e. Work)P = V * I (P = power, in Watts)

• Potential EnergyPenergy = w * h (W=weight (Newtons), h=height (m), P (Joules))

• Kinetic EnergyKenergy = ½*m * v2

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Identify Results

• Make sure the solutions are clearly identified– example: boxed, circled, colored, underlined, centered…

© FrigginPhysics.com

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Verify

• Do the values match/verify the diagram?

• Common sense– Time cannot be negative– (Scalar) distance cannot be negative

• Visually– If you drew a scaled diagram, verify that the results are close to the drawing?

• Is it realistic? Drive Time = 394,242,305,932 seconds?Vrunner = 217.5 miles/hr

When turning in homework, always work on fixing errors, but if you fail, at least indicate “something wrong, this is unrealistic”… before turning it in..

http://www.hardenedshelters.com/underground.asp

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Last but not least!!! Presenting the data

• Paper, or machine

• Either way:– Clearly present the

information– Words and sentences

must explain what’s going on each step

– Skip lines, space things out!• not everything has to fit

on the top left corner!!!!

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Bad Presentations

• inadequate paper size, incomplete (missing data, and units), change of orientation, no breathing room…where are the results?!

http://www.math.mcgill.ca/rags/JAC/ddb121.htmlSemester 2012 Fall

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HORRIBLE HANDWRITING!

• You can feel it in your guts…

How you can feel “OK” turning this in????- See this as a draft, & start over!!

What is this?

• Lower case b?• Lower case c?• Lower case e?• Capitol G?

• If we can’t clearly identify it, it is wrong.





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b. and c. is what will be learned all this semester!

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3a. Deduce the algorithm

• In mathematics and computer science, an algorithm is a step-by-step procedure for calculation. (Wikipedia)

• More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. (Wikipedia)

• Algorithms – must not be complex!– should be detailed/organized– must be general enough for different values of inputs

– Simple problem = simple algorithm– Complex problem = detailed algorithm

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Example

The problem The algorithmDefine base and heightCalculate areaDisplay result

OR

Define side1 and 2’s lengthDefine angle between the two

sidesCalculate areaDisplay result

height=6m

base=3m

side 1=25m

side 2 = 45m

angle = 26.5deg

“detailed yet general”

NOTE: There is neither full sentence here, nor detailed equations!!!

lecture 2 1.computing 101 2.developing a solution 3.problem solving

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