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Beginner Level

Knowledge of single variable calculus.

Approx. 27 hours to complete
English

### What you will learn

• First-order differential equations

• Second-order differential equations

• The Laplace transform and series solution methods

• Systems of differential equations and partial differential equations

### Skills you will gain

Ordinary Differential EquationPartial Differential Equation (PDE)Engineering Mathematics
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Beginner Level

Knowledge of single variable calculus.

Approx. 27 hours to complete
English

### Offered by ## Syllabus - What you will learn from this course

Content Rating98%(5,838 ratings)
Week
1

## Week 1

5 hours to complete

## First-Order Differential Equations

5 hours to complete
15 videos (Total 126 min), 12 readings, 6 quizzes
15 videos
Course Overview2m
Introduction to Differential Equations | Lecture 19m
Week One Introduction59s
Euler Method | Lecture 29m
Separable First-order Equations | Lecture 38m
Separable First-order Equation: Example | Lecture 46m
Linear First-order Equations | Lecture 513m
Linear First-order Equation: Example | Lecture 65m
Application: Compound Interest | Lecture 713m
Application: Terminal Velocity | Lecture 811m
Application: RC Circuit | Lecture 911m
The SIR Model16m
The Basic Reproductive Ratio7m
Solution of the SIR Model4m
Welcome and Course Information1m
How to Write Math in the Discussions Using MathJax1m
Runge-Kutta Methods10m
Separable First-order Equations10m
Separable First-order Equation Examples10m
Linear First-order Equations5m
Change of Variables Transforms a Nonlinear to a Linear Equation10m
Linear First-order Equation: Examples10m
Saving for Retirement10m
Borrowing for a Mortgage10m
Terminal Velocity of a Skydiver10m
The Current in an RC Circuit10m
6 practice exercises
Diagnostic Quiz 10m
Classify Differential Equations5m
Separable First-order ODEs10m
Linear First-order ODEs10m
Applications10m
Week One Assessment30m
Week
2

## Week 2

4 hours to complete

## Homogeneous Linear Differential Equations

4 hours to complete
11 videos (Total 93 min), 11 readings, 3 quizzes
11 videos
Euler Method for Higher-order ODEs | Lecture 109m
The Principle of Superposition | Lecture 116m
The Wronskian | Lecture 128m
Homogeneous Second-order ODE with Constant Coefficients| Lecture 139m
Case 1: Distinct Real Roots | Lecture 147m
Case 2: Complex-Conjugate Roots (Part A) | Lecture 157m
Case 2: Complex-Conjugate Roots (Part B) | Lecture 168m
Case 3: Repeated Roots (Part A) | Lecture 1712m
Case 3: Repeated Roots (Part B) | Lecture 184m
Complex Numbers17m
Second-order Equation as System of First-order Equations5m
Second-order Runge-Kutta Method10m
Linear Superposition for Inhomogeneous ODEs10m
Wronskian of Exponential Function5m
Roots of the Characteristic Equation10m
Distinct Real Roots10m
Hyperbolic Sine and Cosine Functions10m
Do You Know Complex Numbers?
Complex-Conjugate Roots10m
Sine and Cosine Functions10m
Repeated Roots10m
3 practice exercises
Superposition, the Wronskian, and the Characteristic Equation10m
Homogeneous Equations15m
Week Two Assessment30m
Week
3

## Week 3

5 hours to complete

## Inhomogeneous Linear Differential Equations

5 hours to complete
12 videos (Total 127 min), 9 readings, 4 quizzes
12 videos
Inhomogeneous Second-order ODE | Lecture 199m
Inhomogeneous Term: Exponential Function | Lecture 2011m
Inhomogeneous Term: Sine or Cosine (Part A) | Lecture 219m
Inhomogeneous Term: Sine or Cosine (Part B) | Lecture 228m
Inhomogeneous Term: Polynomials | Lecture 237m
Resonance | Lecture 2413m
RLC Circuit | Lecture 2511m
Mass on a Spring | Lecture 269m
Pendulum | Lecture 2712m
Damped Resonance | Lecture 2814m
Nondimensionalization17m
Multiple Inhomogeneous Terms5m
Exponential Inhomogeneous Term10m
Sine or Cosine Inhomogeneous Term10m
Polynomial Inhomogeneous Term5m
When the Inhomogeneous Term is a Solution of the Homogeneous Equation10m
Do You Know Dimensional Analysis?
Another Nondimensionalization of the RLC Circuit Equation10m
Another Nondimensionalization of the Mass on a Spring Equation5m
Find the Amplitude of Oscillation10m
4 practice exercises
Solving Inhomogeneous Equations15m
Particular Solutions15m
Applications and Resonance15m
Week Three Assessment40m
Week
4

## Week 4

4 hours to complete

## The Laplace Transform and Series Solution Methods

4 hours to complete
11 videos (Total 123 min), 10 readings, 4 quizzes
11 videos
Definition of the Laplace Transform | Lecture 2913m
Laplace Transform of a Constant Coefficient ODE | Lecture 3011m
Solution of an Initial Value Problem | Lecture 3113m
The Heaviside Step Function | Lecture 3210m
The Dirac Delta Function | Lecture 3312m
Solution of a Discontinuous Inhomogeneous Term | Lecture 3413m
Solution of an Impulsive Inhomogeneous Term | Lecture 357m
The Series Solution Method | Lecture 3617m
Series Solution of the Airy's Equation (Part A) | Lecture 3714m
Series Solution of the Airy's Equation (Part B) | Lecture 387m
The Laplace Transform of Sine10m
Laplace Transform of an ODE10m
Solution of an Initial Value Problem10m
Heaviside Step Function10m
The Dirac Delta Function5m
Discontinuous Inhomogeneous Term5m
Impulsive Inhomogeneous Term5m
Series Solution Method5m
Series Solution of a Nonconstant Coefficient ODE5m
Solution of the Airy's Equation5m
4 practice exercises
The Laplace Transform Method15m
Discontinuous and Impulsive Inhomogeneous Terms15m
Series Solutions15m
Week Four Assessment30m