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Niveau débutant

Knowledge of single variable calculus.

Approx. 27 heures pour terminer
Anglais
Sous-titres : Anglais

Ce que vous allez apprendre

  • First-order differential equations

  • Second-order differential equations

  • The Laplace transform and series solution methods

  • Systems of differential equations and partial differential equations

Compétences que vous acquerrez

Ordinary Differential EquationPartial Differential Equation (PDE)Engineering Mathematics
Certificat partageable
Obtenez un Certificat lorsque vous terminez
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
Niveau débutant

Knowledge of single variable calculus.

Approx. 27 heures pour terminer
Anglais
Sous-titres : Anglais

Offert par

Logo Université des sciences et technologies de Hong Kong

Université des sciences et technologies de Hong Kong

Programme du cours : ce que vous apprendrez dans ce cours

Évaluation du contenuThumbs Up97%(2,717 notes)Info
Semaine
1

Semaine 1

5 heures pour terminer

First-Order Differential Equations

5 heures pour terminer
15 vidéos (Total 126 min), 12 lectures, 6 quiz
15 vidéos
Course Overview2 min
Introduction to Differential Equations | Lecture 19 min
Week One Introduction59s
Euler Method | Lecture 29 min
Separable First-order Equations | Lecture 38 min
Separable First-order Equation: Example | Lecture 46 min
Linear First-order Equations | Lecture 513 min
Linear First-order Equation: Example | Lecture 65 min
Application: Compound Interest | Lecture 713 min
Application: Terminal Velocity | Lecture 811 min
Application: RC Circuit | Lecture 911 min
The SIR Model16 min
The Basic Reproductive Ratio7 min
Solution of the SIR Model4 min
12 lectures
Welcome and Course Information1 min
How to Write Math in the Discussions Using MathJax1 min
Runge-Kutta Methods10 min
Separable First-order Equations10 min
Separable First-order Equation Examples10 min
Linear First-order Equations5 min
Change of Variables Transforms a Nonlinear to a Linear Equation10 min
Linear First-order Equation: Examples10 min
Saving for Retirement10 min
Borrowing for a Mortgage10 min
Terminal Velocity of a Skydiver10 min
The Current in an RC Circuit10 min
6 exercices pour s'entraîner
Diagnostic Quiz 10 min
Classify Differential Equations5 min
Separable First-order ODEs10 min
Linear First-order ODEs10 min
Applications10 min
Week One Assessment30 min
Semaine
2

Semaine 2

4 heures pour terminer

Homogeneous Linear Differential Equations

4 heures pour terminer
11 vidéos (Total 93 min), 11 lectures, 3 quiz
11 vidéos
Euler Method for Higher-order ODEs | Lecture 109 min
The Principle of Superposition | Lecture 116 min
The Wronskian | Lecture 128 min
Homogeneous Second-order ODE with Constant Coefficients| Lecture 139 min
Case 1: Distinct Real Roots | Lecture 147 min
Case 2: Complex-Conjugate Roots (Part A) | Lecture 157 min
Case 2: Complex-Conjugate Roots (Part B) | Lecture 168 min
Case 3: Repeated Roots (Part A) | Lecture 1712 min
Case 3: Repeated Roots (Part B) | Lecture 184 min
Complex Numbers17 min
11 lectures
Second-order Equation as System of First-order Equations5 min
Second-order Runge-Kutta Method10 min
Linear Superposition for Inhomogeneous ODEs10 min
Wronskian of Exponential Function5 min
Roots of the Characteristic Equation10 min
Distinct Real Roots10 min
Hyperbolic Sine and Cosine Functions10 min
Do You Know Complex Numbers?
Complex-Conjugate Roots10 min
Sine and Cosine Functions10 min
Repeated Roots10 min
3 exercices pour s'entraîner
Superposition, the Wronskian, and the Characteristic Equation10 min
Homogeneous Equations15 min
Week Two Assessment30 min
Semaine
3

Semaine 3

5 heures pour terminer

Inhomogeneous Linear Differential Equations

5 heures pour terminer
12 vidéos (Total 127 min), 9 lectures, 4 quiz
12 vidéos
Inhomogeneous Second-order ODE | Lecture 199 min
Inhomogeneous Term: Exponential Function | Lecture 2011 min
Inhomogeneous Term: Sine or Cosine (Part A) | Lecture 219 min
Inhomogeneous Term: Sine or Cosine (Part B) | Lecture 228 min
Inhomogeneous Term: Polynomials | Lecture 237 min
Resonance | Lecture 2413 min
RLC Circuit | Lecture 2511 min
Mass on a Spring | Lecture 269 min
Pendulum | Lecture 2712 min
Damped Resonance | Lecture 2814 min
Nondimensionalization17 min
9 lectures
Multiple Inhomogeneous Terms5 min
Exponential Inhomogeneous Term10 min
Sine or Cosine Inhomogeneous Term10 min
Polynomial Inhomogeneous Term5 min
When the Inhomogeneous Term is a Solution of the Homogeneous Equation10 min
Do You Know Dimensional Analysis?
Another Nondimensionalization of the RLC Circuit Equation10 min
Another Nondimensionalization of the Mass on a Spring Equation5 min
Find the Amplitude of Oscillation10 min
4 exercices pour s'entraîner
Solving Inhomogeneous Equations15 min
Particular Solutions15 min
Applications and Resonance15 min
Week Three Assessment40 min
Semaine
4

Semaine 4

4 heures pour terminer

The Laplace Transform and Series Solution Methods

4 heures pour terminer
11 vidéos (Total 123 min), 10 lectures, 4 quiz
11 vidéos
Definition of the Laplace Transform | Lecture 2913 min
Laplace Transform of a Constant Coefficient ODE | Lecture 3011 min
Solution of an Initial Value Problem | Lecture 3113 min
The Heaviside Step Function | Lecture 3210 min
The Dirac Delta Function | Lecture 3312 min
Solution of a Discontinuous Inhomogeneous Term | Lecture 3413 min
Solution of an Impulsive Inhomogeneous Term | Lecture 357 min
The Series Solution Method | Lecture 3617 min
Series Solution of the Airy's Equation (Part A) | Lecture 3714 min
Series Solution of the Airy's Equation (Part B) | Lecture 387 min
10 lectures
The Laplace Transform of Sine10 min
Laplace Transform of an ODE10 min
Solution of an Initial Value Problem10 min
Heaviside Step Function10 min
The Dirac Delta Function5 min
Discontinuous Inhomogeneous Term5 min
Impulsive Inhomogeneous Term5 min
Series Solution Method5 min
Series Solution of a Nonconstant Coefficient ODE5 min
Solution of the Airy's Equation5 min
4 exercices pour s'entraîner
The Laplace Transform Method15 min
Discontinuous and Impulsive Inhomogeneous Terms15 min
Series Solutions15 min
Week Four Assessment30 min

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