Transcript EET 159 PowerPoint Slides - Sinclair Community College

EGR 1101
Introductory Mathematics for
Engineering Applications
Professor Nick Reeder
Reminders
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Please turn off cell phones.
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No food or soft drinks in the classroom.
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Stow water bottles at floor level.
Course Overview
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Based on innovative Wright State
University course, EGR 1010.
Goal is to show lots of engineering
applications of math.
Covers math topics from algebra
through differential equations.
Only Sinclair course (?) with a teaching
assistant. Our TA is Mr. John
Thompson, a Wright State mechanical
engineering grad student.
Weekly Schedule
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Monday 2:00 – 3:50
Lecture (Reeder)
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Wednesday 2:00 – 3:50
Lab/MATLAB projects (Thompson)
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Friday 2:00 – 3:50
Lecture (Reeder)
Weekly Assignments
3.
Homework (From book by Rattan &
Klingbeil)
MATLAB Homework (From book by Gilat)
Lab report (including 200-word abstract)
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Need to spend a lot of time outside of class!
1.
2.
EGR 1101 Unit 1
Linear Equations in Engineering
(Chapter 1 of Rattan/Klingbeil text)
Mathematical Review
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Slope-intercept equation for a line in
the x-y plane:
y = mx + b
For a given line, m (the slope) and b
(the y-intercept) are constants.
But x (the independent variable) and y
(the dependent variable) are variables.
Example:
y = 5x + 10
Graphical Interpretation
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A line’s y-intercept (b) tells you
where the line crosses the y-axis.
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The line’s slope (m) tells you how
steep the line is.
Two Common Questions Involving
Lines
1.
Given a line’s slope (m) and y-intercept
(b), find the value of y for a particular
value of x.
2. Given two points (x1, y1) and (x2, y2),
find the slope and y-intercept of the
line containing those points.
This Week’s Examples
1.
A braking vehicle
2.
Voltage and current in a circuit
3.
Deflection of a pre-loaded spring
Electric Circuits: Water Analogy
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Electric circuit: An arrangement of
components through which electrons
flow. Can compare it to a plumbing
system through which water flows.
Some Electrical Terminology
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Voltage (measured in volts): Similar to
water pressure.
•
Current (measured in amperes):
Similar to the amount of water flowing.
•
Resistance (measured in ohms):
Similar to an obstruction in a pipe that
limits water flow.
Some Electrical Components
Fixed voltage source (like a pump
whose pressure is constant):
Variable voltage source (like a
pump whose pressure you
can adjust):
Resistor (like an obstruction
in a pipe):
Some Symbols Used in Electrical
Drawings
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Fixed Voltage Source:
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Variable Voltage Source:
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Resistor:
A Simple Circuit
A wire is like a water pipe. The amount of
electricity flowing through a wire is called
current, which is measured in amperes.
The voltage
(pressure)
at this point
is greater than
the voltage
at this point.
A voltage source is like
a water pump. Its
voltage rating (in volts)
tells you how strong it is.
Resistors are like partial blockages
in the pipe. They reduce the amount
of current that flows through the circuit.
Two Basic Electrical Laws
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Kirchhoff’s Voltage Law (KVL): Around
any closed loop in a circuit, the sum of the
voltage rises is equal to the sum of the
voltage drops.
∑ Voltage rises = ∑ Voltage drops
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Ohm’s Law: For a resistor, voltage equals
current times resistance:
V = IR
Review: Large and Small
Numbers
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Engineers often deal with very large or
very small numbers.
Example: a system’s clock signal
might have a frequency of 750,000 Hz
and a period of 0.00000133 s.
It’s not convenient to write or discuss
numbers using so many zeroes.
Instead we use engineering
prefixes, which are abbreviations for
certain powers of 10.
Engineering Prefix Game
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You must memorize these prefixes.
To practice, play the Metric Prefix
matching game on my Games page.
Using Engineering Prefixes
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Whenever you have a number that’s
greater than 1000 or less than 1,
you should use these prefixes.
Examples:
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Instead of writing 750,000 Hz,
write 750 kHz
(pronounced “750 kilohertz”).
Instead of writing 0.00000133 s,
write 1.33 s
(pronounced “1.33 microseconds”).
Calculator’s Exponent Key
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Scientific calculators have an
exponent key (usually labeled EE,
EXP, or E) that lets you easily enter
numbers with engineering prefixes.
Examples:
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To enter 750 k, press 750 EE 3.
To enter 1.33 , press 1.33 EE −6.
Calculator Modes
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Most scientific calculators also have
an engineering mode, which forces
the answer always to be displayed
with one of the engineering powers
of 10.
Learn how to use this feature of
your calculator. It will save you
from making mistakes.