EGR 1101

Introductory Mathematics for Engineering Applications

Professor Nick Reeder

Reminders

Please turn off cell phones.

No food or soft drinks in the classroom.

Stow water bottles at floor level.

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.

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)

Weekly Assignments

1. Homework (From book by Rattan & Klingbeil)

2. MATLAB Homework (From book by Gilat)3. Lab report (including 200-word abstract)

Need to spend a lot of time outside of class!

EGR 1101 Unit 1

Linear Equations in Engineering

(Chapter 1 of Rattan/Klingbeil text)

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

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.

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

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

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.

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

Fixed Voltage Source:

Variable Voltage Source:

Resistor:

A Simple Circuit

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.

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.

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

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 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

You must memorize these prefixes. To practice, play the Metric Prefix

matching game on my Games page.

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 0.00000133 s,write 1.33 s (pronounced “1.33 microseconds”).

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.

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.