Engineering Mathematics with Examples and Solutions
Applications of mathematics to engineering systems, including electric circuits, are presented with examples and solutions.
Math for Engineers
Ac circuits.
- Current and Voltages Computations in Series RLC circuit
- Series and Parallel Impedances Computations
- Calculate Equivalent Impedance in AC Circuits . Examples with detailed solution.
- Use Complex Numbers in AC circuits
AC Circuits Calculators
- Current and Voltages Calculator for Series RLC circuits
- Parallel RLC circuit Impedance Calculator
- Series RLC circuit Impedance Calculator
MATH Engineering PAGES IN DIFFERENT LANGUAGES
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Engineering Mathematics (EGR 1010) Topics and Materials
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.
Class Materials
- Course Information
Lecture Notes
Laboratory assignments.
- 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
Sample Materials
(Updated 09/13/2023)
Course Info
- Syllabus - Fall 2023 (PDF)
- Schedule - Fall 2023 (PDF)
- Straight Lines in Engineering (PDF)
- Quadratic Equations in Engineering (PDF)
- Algebra and Geometry Handout (PDF)
- 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
- Trigonometry in Engineering (PDF)
- Trigonometry Handout (PDF)
- 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)
- 2D Vectors in Engineering (PDF)
- 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
- Complex Numbers in Engineering (PDF)
- 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)
- Sinusoids in Engineering (PDF)
- 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)
- Systems of Equations in Engineering (PDF)
- 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)
- 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)
- Derivatives in Electric Circuits (PDF)
- 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)
- Derivatives in Strength of Materials (PDF)
- Introduction to Beams
- Cantilever Beam Example
- Simply Supported Beam Example (Point Load)
- Simply Supported Beam Example (Sinusoidal Load)
- Axially Loaded Bar - pt. 1 (Normal and Shear Stress on Oblique Plane)
- Axially Loaded Bar - pt. 2 (Maximum Stresses)
- Introduction to Integrals in Engineering (PDF)
- Integrals in Statics (PDF)
- Integrals Handout (PDF)
- 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
- Integrals in Dynamics (PDF)
- Integration - Pt. 1 (Position, Velocity, & Acceleration)
- Integration - Pt. 2 (Freefall Example)
- Integration - Pt. 3 (Projectile Example)
- Integration - Pt. 4 (Graphical Interpretation)
- Integrals and Plotting Example
- Integrals in Electric Circuits (PDF)
- 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)
- Introduction to Differential Equations in Engineering (PDF)
- Differential Equations Handout (PDF)
- The Leaky Bucket (Introduction)
- The Differential Equation Handout
- The Leaky Bucket (Transient Solution)
- The Leaky Bucket (Steady State Solution)
- The Leaky Bucket (Total Soln and Plotting)
- Total Solution for the Leaky Bucket Lab
- Differential Equations in Mechanical Systems (PDF)
- 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)
- Differential Equations in Electric Systems (PDF)
- 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
Download all Sample Lecture Notes (Zip)
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.
Application of Algebra in Engineering - The One Loop Circuit
- Virtual Lab
Trigonometry Relationships - One and Two Link Planar Robots
Sinusoids in Engineering - Measurement and Analysis of Harmonic Signals
Systems of Engineering - The Two Loop Circuit
Derivatives in Engineering - Velocity and Acceleration in Free Fall
Integrals in Engineering - Work and Stored Energy in a Spring
Differential Equations in Engineering - The Leaking Bucket
Differential Equations in Engineering - Spring Mass Vibration
- 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)
- Sample Exam #1 (PDF)
- Sample Exam #2 (PDF)
- Sample Final Exam (PDF)
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Browse Course Material
Course info, instructors.
- Prof. Daniel Frey
- Prof. Gilbert Strang
Departments
- Mechanical Engineering
As Taught In
- Applied Mathematics
- Differential Equations
- Linear Algebra
Learning Resource Types
Engineering math: differential equations and linear algebra, 2.087 engineering math, homework 1.
This file contains the information regarding 2.087 Engineering Math, Homework 1.
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This course is about the mathematics that is most widely used in the mechanical ... Engineering Math: Differential Equations and Linear Algebra. Menu. ... down with its engines off. After five seconds, it deploys its speedbrakes. This is a graph of its velocity. See Homework 1 Problem 9 for the full problem and a MATLAB script modeling the ...
Engineering Math: Differential Equations and Linear Algebra. Menu. More Info Syllabus Calendar Lecture Videos Assignments MATLAB Scripts Exams Related Resources Assignments. HOMEWORK ASSIGNMENTS Homework 1 (PDF) MATLAB Script for Problem 9 (M) Homework 2 (PDF) Homework 3 (PDF) Homework 4 (PDF) Homework 5 (PDF) MATLAB Script for Problem 4 (M) ...
Homework #1. Date Issued: Wednesday 3 September, 2014. Date Due: Wednesday 10 September, 2014, 9:30AM (bring hard copy to lecture ) As described in the course policies document, this is one of 5 homeworks you will complete in this course. Each of these count as 6% of your total grade. Full credit can generally only be earned by showing your ...
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Applications of mathematics to engineering systems, including electric circuits, are presented with examples and solutions. Math for Engineers. Multivariable Calculus ; Multiple Integrals Calculations and Applications; Laplace Transform with Examples and Solutions; Mathematical Formulas and Identities; Math Calculators and Solvers
Specialization - 5 course series. This specialization was developed for engineering students to self-study engineering mathematics. We expect students to already be familiar with single variable calculus and computer programming. Through this specialization, students will learn matrix algebra, differential equations, vector calculus, numerical ...
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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.
Now, with expert-verified solutions from Engineering Mathematics 5th Edition, you'll learn how to solve your toughest homework problems. Our resource for Engineering Mathematics includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice ...
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MATH 171 designed to be a more demanding version of this course. Only one of the following will satisfy the requirements for a degree: MATH 131, MATH 142, MATH 147, MATH 151 or MATH 171. Prerequisite: Grade of C or better in MATH 150 or equivalent or acceptable score on TAMU Math Placement Exam; also taught at Galveston and Qatar campuses.
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The University of Idaho's College of Engineering annual events include the Engineering Design EXPO, the Academy of Engineers and Women in Engineering Day. Additional events includes seminars, computer science colloquia, National Society of Black Engineers lecture series, grand challenge scholar program pitch, awards ceremonies, and commencement records.