engineering maths assignment

Engineering Mathematics

Looking for free Engineering Math help? We have a collection of free Engineering Mathematics Videos.

The topics covered are Chain rule, Partial Derivative, Taylor Polynomials, Critical points of functions, Lagrange multipliers, Vector Calculus, Line Integral, Double Integrals, Laplace Transform, Fourier series.

We also have free math calculators and tools to help you understand the steps and check your answers.

Math Calculators and Tools

Chain Rule Calculator This tool will help you to understand the differentiation process of a composite function. Use show steps to see possible differentiation steps.

Partial Derivative Calculator This tool will help you to understand the possible partial derivative steps.

Double Integral Calculator This tool allows you to calculate double integrals in f(x, y)

Laplace Transform Calculator This tool allows you the calculate the Laplace Transform of the given function.

Fourier Series Calculator This tool allows you to calculate the Fourier series of a function.

Calculus Calculator with step by step solutions Functions, Operations on Functions, Polynomial and Rational Functions, Exponential and Logarithmic Functions, Sequences and Series, Evaluating Limits, Derivatives, Applications of Differentiation, Integrals, Applications of Integration, Techniques of Integration, Parametric Equations and Polar Coordinates

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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

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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, practice final exam.

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