## Take the Next Step

Finding the right college means finding the right fit. See all that the College of Engineering and Computer Science has to offer by visiting campus.

EGR 1010 is an applied mathematics course taught by the College of Engineering and Computer Science faculty, consisting of lecture, lab, and recitation. All topics are driven by engineering applications taken directly from core engineering courses. The lectures are motivated by hands-on laboratory exercises including a thorough integration with Matlab.

- Basic Algebraic Manipulations (1.0 weeks)
- Trigonometry (1.0 weeks)
- 2-D Vectors (1.0 weeks)
- Complex Numbers (1.0 weeks)
- Sinusoids & Harmonic Signals (1.0 weeks)
- Matrices & Systems of Equations (1.0 weeks)
- Basics of Differentiation (3.0 weeks)
- Basics of Integration (3.0 weeks)
- Differential Equations (3.0 weeks)

- Introductory Mathematics for Engineering Application, 2nd Edition
- MATLAB: An Introduction with Applications, 6th Edition

(Updated 09/13/2023)

- Straight Lines in Engineering (PDF)
- Quadratic Equations in Engineering (PDF)
- Algebra and Geometry Handout (PDF)

**Videos**

- Introduction
- Vehicle During Braking - pt. 1 (Intro, Slope Only)
- Vehicle During Braking - pt. 2 (y-intercept, Plotting)
- Electric Circuits - pt. 1 (Intro, Slope Only)
- Electric Circuits - pt. 2 (y-intercept)
- Electric Circuits - pt. 3 (Inverse Problem)
- Pre-loaded Tension Spring - pt. 1
- Pre-loaded Tension Spring - pt. 2 (Inverse Problem)
- Projectile Motion - pt. 1
- Projectile Motion - pt. 2
- Quadratic Example - Series Circuit Containing a Lamp
- Quadratic Example - Resistors in Parallel

**Videos**

- One Link Robot - pt. 1 (Intro)
- One Link Robot - pt. 2 (Identities, Definitions)
- One Link Robot - pt. 3 (On Axis Examples)
- One Link Robot - pt. 4 (Off Axis Examples, Ref Angle)
- One Link Robot - pt. 5 (Summary)
- One Link Robot - pt. 6 (Exact Angle Examples)
- One Link Robot - pt. 7 (Large Angle Examples)
- One Link Robot - pt. 8 (Inverse Problem)
- One Link Robot - pt. 9 (atan2)
- One Link Robot - pt. 10 (atan2 Example)
- Two Link Robot - pt. 1 (Intro, Examples)
- Two Link Robot - pt. 2 (Inverse Problem to Theta2, Law of Sin/Cos)
- Two Link Robot - pt. 3 (Inverse Problem to Theta1, Elbow up/down)

**Videos**

- Introduction and Definitions
- Polar/Rectangular Examples
- Statics - Vacuum Example
- Vector Addition - Position Vectors of the Two Link Robot
- 2D Vectors - Ship Positioning
- 2D Vectors - Airplane Relative Velocity Example
- Airplane Relative Velocity Using Law of Sines/Cosines
- 2D Vectors - Cable Tension Example
- 2D Vectors - Television on a Ramp

**Videos**

- Complex Number Notation
- Comparison to Vector Math
- Impedance - pt. 1 (Resistor)
- Impedance - pt. 2 (Inductor)
- Impedance - pt. 3 (Capacitor)
- Impedance - pt. 4 (Circuit Components in Series)
- Complex Number Calculations (Multiplication)
- Complex Number Calculations (Division)
- Complex Number Calculations (Complex Conjugate)

**Videos**

- Plotting of One Link Robot Components w.r.t Theta
- Plotting of One Link Robot Components w.r.t Time (No Phase Angle)
- Plotting of One Link Robot Components w.r.t Time (Phase Angle)
- Oscillating Spring-Mass Example 1
- Oscillating Spring-Mass Example 2 (Eqn. to Picture)
- Oscillating Spring-Mass Example 3 (Picture to Eqn.)
- Addition of Sinusoids - pt. 1 (One Phase Angle into Sine)
- Addition of Sinusoids - pt. 2 (One Phase Angle into Cosine)
- Addition of Sinusoids - pt. 3 (Complex Number Method)
- Addition of Sinusoids - pt. 4 (Two Phase Angles into Sine)

**Videos**

- The Two Loop Circuit - pt. 1 (Substitution)
- The Two Loop Circuit - pt. 2 (Graphing)
- The Two Loop Circuit - pt. 3 (Matrix Method)
- The Two Loop Circuit - pt. 4 (Cramer's Rule)
- Static Equilibrium Example (Intro)
- Static Equilibrium Example (Substitution)
- Static Equilibrium Example (Matrix Method)
- Static Equilibrium Example (Cramer's Rule)

- Introduction to Derivatives in Engineering (PDF)
- Derivatives in Dynamics (PDF)
- Derivatives Handout (PDF)

**Videos**

- Introduction to the Derivative (Freefall Example 1st Half)
- The Derivative Handout
- Introduction to the Derivative (Freefall Example 2nd Half)
- Derivatives - pt. 1 (Projectile Motion)
- Derivatives - pt. 2 (Concavity)
- Derivatives - pt. 3 (Dynamics & Equation Practice)
- Derivatives - pt. 4 (Particle Motion - Position, Velocity, and Acceleration)
- Derivatives - pt. 5 (Particle Motion - Sketching)
- Derivatives and Plotting - pt. 1 (Sketching the Velocity)
- Derivatives and Plotting - pt. 2 (Sketching the Position)
- Beam Dynamics - pt. 1 (Intro)
- Beam Dynamics - pt. 2 (Velocity & Acceleration)

**Videos**

- Introduction and Definitions
- Example 1 - Charge and Power - pt. 1 (Current)
- Example 1 - Charge and Power - pt. 2 (Power)
- Example 1 - Charge and Power - pt. 3 (Maximum Power)
- Example 2 - Inductor - pt. 1 (Voltage Calculation)
- Example 2 - Inductor - pt. 2 (Location of Maximum and Sketch)
- Example 3 - Inductor Plotting - pt. 1 (Current)
- Example 3 - Inductor Plotting - pt. 2 (Power)
- Example 4 - Current Across a Capacitor (Addition of Sinusoids Review)
- Example 5 - Capacitor Plotting - pt. 1 (Charge)
- Example 5 - Capacitor Plotting - pt. 2 (Voltage)

**Videos**

**Videos**

- The Asphalt Problem - pt. 1 (Intro & Inscribed Rectangles)
- The Asphalt Problem - pt. 2 (Integration)
- The Integral Handout
- Back to the Asphalt Problem
- Integration - Concept of Work (Integration Practice)
- Introduction to Centroids
- Centroid of a Triangle w.r.t. "x"
- Centroid of a Triangle w.r.t. "y"
- Centroids of Solid Bodies (1st Moment of Area of a Rectangle)
- Distributed Load on a Dam - Resultant Force
- Distributed Load on a Beam - Location of the Resultant Force
- Distributed Load on a Beam - Example

**Videos**

**Videos**

- Example 1 - Capacitor - pt. 1 (Voltage)
- Example 1 - Capacitor - pt. 2 (Stored Energy)
- Extra Example - Inductor - pt. 1 (Current)
- Extra Example - Inductor - pt. 2 (Sketch)
- Extra Example - Inductor - pt. 3 (Power)
- Extra Example - Inductor - pt. 4 (Stored Energy)
- Example 3 - Capacitor Plotting
- Example 4 - Capacitor Plotting (curves)
- Example 5 - Inductor Plotting
- Example 5 - Inductor Plotting - pt. 2 (Shifted Waveform)

**Videos**

**Videos**

- The Spring Mass System (Introduction)
- The Spring Mass System (Unforced Response - Transient & Steady State)
- The Spring Mass System (Unforced Response - Initial Conditions)
- The Spring Mass System (Forced Response - Transient & Steady State)
- The Spring Mass System (Forced Response - Initial Conditions)
- The Spring Mass System (Approaching Resonance)

**Videos**

- Intro to an RC Circuit
- RC Circuit (Transient Solution)
- RC Circuit (Steady State and Total Solution with Zero Input)
- RC Circuit (Steady State and Total Solution with Constant Input)
- RC Circuit - pt. 1 (Sinusoidal Input Through Total Solution)
- RC Circuit - pt. 2 (Applying Initial Conditions and Low Pass Filter)
- Intro to an LC Circuit
- LC Circuit (Transient Solution)
- LC Circuit (Steady State Solution and Total Solution with Zero Input)
- LC Circuit (Steady State Solution and Total Solution with Constant Input)
- LC Circuit (Steady State Solution and Total Solution with Sinusoidal Input)
- LC Circuit Resonance

Homework is assigned on a weekly basis from the course textbook (5-6 problems) and the course programming book (3-4 problems).

The following topics are covered in this class:

- Matlab: Introduction (Video)
- Matlab: Vector Math (Video)
- Matlab: Plotting (Video)
- Matlab: Matrix Operations(Video)
- Matlab: If...Else Statements (Video)
- Matlab: Function Files (Video)
- Matlab: Symbolics (Video)
- Matlab: Additional Functions (Video)

There are 8 hands-on lab assignments that supplement the course material. Additionally, there are 4 self guided Matlab supplemental assignments that illustrate a more application-based approach to coding. The labs below are written as if students are in the lab with equipment. The virtual labs mimic what is done in-person and can be used in lieu of the hands-on labs. As such, while the lab requirements remain unchanged between both the hands-on and virtual labs, the procedures may differ. The included videos below outline the step-by-step process for the virtual labs.

Sinusoids in Engineering - Measurement and Analysis of Harmonic Signals

- Matlab Supplemental #1: Flight Control System Analysis (PDF)
- Matlab Supplemental #2: Deflection of Truss Analysis (PDF)
- Matlab Supplemental #3: Derivative Visualization - Slope at a Point (PDF)
- Matlab Supplemental #4: Airplane Wing Loads - Bending and Shear Stress (PDF)

Finding the right college means finding the right fit. See all that the College of Engineering and Computer Science has to offer by visiting campus.