1. Introductory Mathematics for Engineering Applications
EGR 1101
Introductory Mathematics for Engineering Applications
Professor Nick Reeder

2. Reminders Please turn off cell phones.
No food or soft drinks in the classroom.
Stow water bottles at floor level.

3. Course Overview
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.

4. Weekly Schedule Monday 2:00 – 3:50 Lecture (Reeder)
Wednesday 2:00 – 3:50 Lab/MATLAB projects (Thompson)
Friday 2:00 – 3:50 Lecture (Reeder)

5. Weekly Assignments Homework (From book by Rattan & Klingbeil)
MATLAB Homework (From book by Gilat)
Lab report (including 200-word abstract)
Need to spend a lot of time outside of class!

6. Linear Equations in Engineering (Chapter 1 of Rattan/Klingbeil text)
EGR 1101 Unit 1
Linear Equations in Engineering
(Chapter 1 of Rattan/Klingbeil text)

7. Mathematical Review
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

8. Graphical Interpretation
A line’s y-intercept (b) tells you where the line crosses the y-axis.
The line’s slope (m) tells you how steep the line is.

9. Two Common Questions Involving Lines
Given a line’s slope (m) and y-intercept (b), find the value of y for a particular value of x.
Given two points (x1, y1) and (x2, y2), find the slope and y-intercept of the line containing those points.

10. This Week’s Examples A braking vehicle
Voltage and current in a circuit
Deflection of a pre-loaded spring

11. Electric Circuits: Water Analogy
Electric circuit: An arrangement of components through which electrons flow. Can compare it to a plumbing system through which water flows.

12. Some Electrical Terminology
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.

13. 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):

14. Some Symbols Used in Electrical Drawings
Fixed Voltage Source:
Variable Voltage Source:
Resistor:
In symbol for fixed voltage source, the longer line is the positive terminal.

15. 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.

16. Two Basic Electrical Laws
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
Ohm’s Law: For a resistor, voltage equals current times resistance: V = IR

17. Review: Large and Small Numbers
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 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.

19. Engineering Prefix Game
You must memorize these prefixes.
To practice, play the Metric Prefix matching game on my Games page.

20. Using Engineering Prefixes
Whenever you have a number that’s greater than 1000 or less than 1, you should use these prefixes.
Examples:
Instead of writing 750,000 Hz, write 750 kHz (pronounced “750 kilohertz”).
Instead of writing s, write 1.33 s (pronounced “1.33 microseconds”).

21. Calculator’s Exponent Key
Scientific calculators have an exponent key (usually labeled EE, EXP, or E) that lets you easily enter numbers with engineering prefixes.
Examples:
To enter 750 k, press 750 EE 3.
To enter 1.33 , press 1.33 EE −6.

22. Calculator Modes
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.
Do engineering prefix practice sheet