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Differential Equations for Engineers
  • Level Foundation
  • Duration 27 hours
  • Course by The Hong Kong University of Science and Technology
  • Offered by

About

This course is all about differential equations and covers both theory and applications. In the first five weeks, students will learn about ordinary differential equations, while the sixth week is an introduction to partial differential equations. The course includes 56 concise lecture videos, with a few problems to solve after each lecture. After each major topic, there is a short practice quiz. At the end of each week, there is an assessed quiz. Solutions to the problems and practice quizzes can be found in the instructor-provided lecture notes. Download the lecture notes from the link https://www.math.hkust.edu.hk/~machas/differential-equations-for-engineers.pdf Watch the promotional video from the link https://youtu.be/eSty7oo09ZI

Modules

Welcome to Differential Equations for Engineers

    • 2 Videos
    • 3 Readings
    • 1 Quiz
    • 1 Assignment
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1 Assignment

  • Classify Differential Equations

2 Videos

  • Course Overview
  • Introduction to Differential Equations | Lecture 1

3 Readings

  • Welcome and Course Information
  • Certificate or Audit?
  • How to Write Math in the Discussion Forums Using MathJax

1 Quiz

  • Diagnostic Quiz

Introduction to Week One

    • 1 Videos
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1 Videos

  • Week One Introduction

Numerical Methods

    • 1 Videos
    • 1 Readings
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1 Videos

  • Euler Method | Lecture 2

1 Readings

  • Runge-Kutta Methods

Separable Equations

    • 2 Videos
    • 2 Readings
    • 1 Quiz
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2 Videos

  • Separable First-order Equations | Lecture 3
  • Separable First-order Equation: Example | Lecture 4

2 Readings

  • Separable First-order Equations
  • Separable First-order Equation Examples

1 Quiz

  • Separable First-order ODEs

Linear Equations

    • 2 Videos
    • 3 Readings
    • 1 Quiz
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2 Videos

  • Linear First-order Equations | Lecture 5
  • Linear First-order Equation: Example | Lecture 6

3 Readings

  • Linear First-order Equations
  • Change of Variables Transforms a Nonlinear to a Linear Equation
  • Linear First-order Equation: Examples

1 Quiz

  • Linear First-order ODEs

Applications

    • 3 Videos
    • 5 Readings
    • 1 Quiz
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3 Videos

  • Application: Compound Interest | Lecture 7
  • Application: Terminal Velocity | Lecture 8
  • Application: RC Circuit | Lecture 9

5 Readings

  • Saving for Retirement
  • Borrowing for a Mortgage
  • Terminal Velocity of a Skydiver
  • How Fast Can You Skydive?
  • The Current in an RC Circuit

1 Quiz

  • Applications

Quiz

    • 2 Quiz
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2 Quiz

  • Week One Assessment (audit)
  • Week One Assessment

Additional Videos: The SIR Epidemic Model of Infectious Disease

    • 3 Videos
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3 Videos

  • The SIR Model
  • The Basic Reproductive Ratio
  • Solution of the SIR Model

Introduction to Week Two

    • 1 Videos
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1 Videos

  • Week Two Introduction

Numerical Methods

    • 1 Videos
    • 2 Readings
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1 Videos

  • Euler Method for Higher-order ODEs | Lecture 10

2 Readings

  • Second-order Equation as System of First-order Equations
  • Second-order Runge-Kutta Method

Theory

    • 3 Videos
    • 3 Readings
    • 1 Quiz
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3 Videos

  • The Principle of Superposition | Lecture 11
  • The Wronskian | Lecture 12
  • Homogeneous Second-order ODE with Constant Coefficients| Lecture 13

3 Readings

  • Linear Superposition for Inhomogeneous ODEs
  • Wronskian of Exponential Function
  • Roots of the Characteristic Equation

1 Quiz

  • Theory of ODE

Distinct Real Roots

    • 1 Videos
    • 2 Readings
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1 Videos

  • Case 1: Distinct Real Roots | Lecture 14

2 Readings

  • Distinct Real Roots
  • Hyperbolic Sine and Cosine Functions

Complex-Conjugate Roots

    • 2 Videos
    • 3 Readings
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2 Videos

  • Case 2: Complex-Conjugate Roots (Part A) | Lecture 15
  • Case 2: Complex-Conjugate Roots (Part B) | Lecture 16

3 Readings

  • Do You Know Complex Numbers?
  • Complex-Conjugate Roots
  • Sine and Cosine Functions

Repeated Roots

    • 2 Videos
    • 1 Readings
    • 1 Quiz
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2 Videos

  • Case 3: Repeated Roots (Part A) | Lecture 17
  • Case 3: Repeated Roots (Part B) | Lecture 18

1 Readings

  • Repeated Roots

1 Quiz

  • Homogeneous Equations

The Amazing Equation y' = y

    • 1 Plugin
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Supplemental Videos

    • 1 Videos
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1 Videos

  • Complex Numbers

Quiz

    • 2 Quiz
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2 Quiz

  • Week Two Assessment (audit)
  • Week Two Assessment

Introduction to Week Three

    • 1 Videos
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1 Videos

  • Week Three Introduction

Theory and Exponential Inhomogeneous Terms

    • 2 Videos
    • 2 Readings
    • 1 Quiz
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2 Videos

  • Inhomogeneous Second-order ODE | Lecture 19
  • Inhomogeneous Term: Exponential Function | Lecture 20

2 Readings

  • Multiple Inhomogeneous Terms
  • Exponential Inhomogeneous Term

1 Quiz

  • Solving Inhomogeneous Equations

Particular Solutions for Sine/Cosine and Polynomials

    • 3 Videos
    • 2 Readings
    • 1 Quiz
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3 Videos

  • Inhomogeneous Term: Sine or Cosine (Part A) | Lecture 21
  • Inhomogeneous Term: Sine or Cosine (Part B) | Lecture 22
  • Inhomogeneous Term: Polynomials | Lecture 23

2 Readings

  • Sine or Cosine Inhomogeneous Term
  • Polynomial Inhomogeneous Term

1 Quiz

  • Particular Solutions

Resonance

    • 1 Videos
    • 1 Readings
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1 Videos

  • Resonance | Lecture 24

1 Readings

  • When the Inhomogeneous Term is a Solution of the Homogeneous Equation

Applications and Damped Resonance

    • 4 Videos
    • 4 Readings
    • 1 Quiz
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4 Videos

  • RLC Circuit | Lecture 25
  • Mass on a Spring | Lecture 26
  • Pendulum | Lecture 27
  • Damped Resonance | Lecture 28

4 Readings

  • Do You Know Dimensional Analysis?
  • Another Nondimensionalization of the RLC Circuit Equation
  • Another Nondimensionalization of the Mass on a Spring Equation
  • Find the Amplitude of Oscillation

1 Quiz

  • Applications and Resonance

Supplemental Videos

    • 1 Videos
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1 Videos

  • Nondimensionalization

Quiz

    • 2 Quiz
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2 Quiz

  • Week Three Assessment (audit)
  • Week Three Assessment

Introduction to Week Four

    • 1 Videos
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1 Videos

  • Week Four Introduction

The Laplace Transform Method

    • 3 Videos
    • 3 Readings
    • 1 Assignment
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1 Assignment

  • The Laplace Transform Method

3 Videos

  • Definition of the Laplace Transform | Lecture 29
  • Laplace Transform of a Constant Coefficient ODE | Lecture 30
  • Solution of an Initial Value Problem | Lecture 31

3 Readings

  • The Laplace Transform of Sine
  • Laplace Transform of an ODE
  • Solution of an Initial Value Problem

Heaviside Step Function and Dirac Delta function

    • 4 Videos
    • 4 Readings
    • 1 Quiz
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4 Videos

  • The Heaviside Step Function | Lecture 32
  • The Dirac Delta Function | Lecture 33
  • Solution of a Discontinuous Inhomogeneous Term | Lecture 34
  • Solution of an Impulsive Inhomogeneous Term | Lecture 35

4 Readings

  • Heaviside Step Function
  • The Dirac Delta Function
  • Discontinuous Inhomogeneous Term
  • Impulsive Inhomogeneous Term

1 Quiz

  • Discontinuous and Impulsive Inhomogeneous Terms

Series Solution Method

    • 3 Videos
    • 3 Readings
    • 1 Quiz
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3 Videos

  • The Series Solution Method | Lecture 36
  • Series Solution of the Airy's Equation (Part A) | Lecture 37
  • Series Solution of the Airy's Equation (Part B) | Lecture 38

3 Readings

  • Series Solution Method
  • Series Solution of a Nonconstant Coefficient ODE
  • Solution of the Airy's Equation

1 Quiz

  • Series Solutions

Quiz

    • 2 Quiz
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2 Quiz

  • Week Four Assessment (audit)
  • Week Four Assessment

Introduction to Week Five

    • 1 Videos
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1 Videos

  • Week Five Introduction

Systems of First-order Linear Differential Equations

    • 3 Videos
    • 4 Readings
    • 1 Quiz
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3 Videos

  • Systems of Homogeneous Linear First-Order ODEs | Lecture 39
  • Distinct Real Eigenvalues | Lecture 40
  • Complex-Conjugate Eigenvalues | Lecture 41

4 Readings

  • Do You Know Matrix Algebra?
  • Eigenvalues of a Symmetric Matrix
  • Distinct Real Eigenvalues
  • Complex-Conjugate Eigenvalues

1 Quiz

  • Systems of Differential Equations

Phase Portraits

    • 4 Videos
    • 4 Readings
    • 1 Quiz
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4 Videos

  • Phase Portraits | Lecture 42
  • Stable and Unstable Nodes | Lecture 43
  • Saddle points | Lecture 44
  • Spirals | Lecture 45

4 Readings

  • Phase Portraits
  • Nodes
  • Saddle Points
  • Spirals

1 Quiz

  • Phase portraits

Normal Modes

    • 3 Videos
    • 2 Readings
    • 1 Assignment
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1 Assignment

  • Normal Modes

3 Videos

  • Coupled Oscillators | Lecture 46
  • Normal Modes (Eigenvalues) | Lecture 47
  • Normal Modes (Eigenvectors) | Lecture 48

2 Readings

  • Coupled Oscillators
  • Normal Modes of Coupled Oscillators

Supplemental Videos

    • 2 Videos
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2 Videos

  • Matrices and Determinants
  • Eigenvalues and Eigenvectors

Quiz

    • 2 Quiz
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2 Quiz

  • Week Five Assessment (audit)
  • Week Five Assessment

Introduction to Week Six

    • 1 Videos
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1 Videos

  • Week Six Introduction

Fourier Series

    • 3 Videos
    • 3 Readings
    • 1 Quiz
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3 Videos

  • Fourier Series | Lecture 49
  • Fourier Sine and Cosine Series |Lecture 50
  • Fourier Series: Example | Lecture 51

3 Readings

  • Fourier Series
  • Fourier series at x=0
  • Fourier Series of a Square Wave

1 Quiz

  • Fourier Series

The Diffusion Equation

    • 1 Videos
    • 2 Readings
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1 Videos

  • The Diffusion Equation | Lecture 52

2 Readings

  • Do You Know Partial Derivatives?
  • Nondimensionalization of the Diffusion Equation

Separation of Variables

    • 2 Videos
    • 2 Readings
    • 1 Quiz
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2 Videos

  • Solution of the Diffusion Equation: Separation of Variables | Lecture 53
  • Solution of the Diffusion Equation: Eigenvalues | Lecture 54

2 Readings

  • Boundary Conditions with Closed Pipe Ends
  • ODE Eigenvalue Problems

1 Quiz

  • Separable Partial Differential Equations

Diffusion of a Dye

    • 2 Videos
    • 2 Readings
    • 1 Quiz
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2 Videos

  • Solution of the Diffusion Equation: Fourier Series | Lecture 55
  • Diffusion Equation: Example | Lecture 56

2 Readings

  • Solution of the Diffusion Equation with Closed Pipe Ends
  • Concentration of a Dye in a Pipe with Closed Ends

1 Quiz

  • The Diffusion Equation

Supplemental Videos

    • 1 Videos
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1 Videos

  • Partial Derivatives

Quiz

    • 2 Quiz
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2 Quiz

  • Week Six Assessment (audit)
  • Week Six Assessment

Farewell

    • 1 Videos
    • 2 Readings
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1 Videos

  • Concluding Remarks

2 Readings

  • Please Rate this Course
  • Acknowledgements

Auto Summary

"Differential Equations for Engineers" is a foundational course in the Data Science & AI domain, led by an expert instructor. Over six weeks, learners explore both ordinary and partial differential equations through 56 concise lectures, practice problems, and quizzes. Ideal for engineers, the course offers comprehensive lecture notes and various subscription options to suit different learning needs.

Jeffrey R. Chasnov
Instructor

Jeffrey R. Chasnov