Informações sobre o curso

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Knowledge of single variable calculus.

Aprox. 27 horas para completar
Inglês

O que você vai aprender

  • First-order differential equations

  • Second-order differential equations

  • The Laplace transform and series solution methods

  • Systems of differential equations and partial differential equations

Habilidades que você terá

Ordinary Differential EquationPartial Differential Equation (PDE)Engineering Mathematics
Certificados compartilháveis
Tenha o certificado após a conclusão
100% on-line
Comece imediatamente e aprenda em seu próprio cronograma.
Prazos flexíveis
Redefinir os prazos de acordo com sua programação.
Nível iniciante

Knowledge of single variable calculus.

Aprox. 27 horas para completar
Inglês

Instrutores

oferecido por

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Universidade de Ciência e Tecnologia de Hong Kong

Programa - O que você aprenderá com este curso

Classificação do conteúdoThumbs Up98%(5,348 classificações)Info
Semana
1

Semana 1

5 horas para concluir

First-Order Differential Equations

5 horas para concluir
15 vídeos (Total 126 mín.), 12 leituras, 6 testes
15 videos
Course Overview2min
Introduction to Differential Equations | Lecture 19min
Week One Introduction59s
Euler Method | Lecture 29min
Separable First-order Equations | Lecture 38min
Separable First-order Equation: Example | Lecture 46min
Linear First-order Equations | Lecture 513min
Linear First-order Equation: Example | Lecture 65min
Application: Compound Interest | Lecture 713min
Application: Terminal Velocity | Lecture 811min
Application: RC Circuit | Lecture 911min
The SIR Model16min
The Basic Reproductive Ratio7min
Solution of the SIR Model4min
12 leituras
Welcome and Course Information1min
How to Write Math in the Discussions Using MathJax1min
Runge-Kutta Methods10min
Separable First-order Equations10min
Separable First-order Equation Examples10min
Linear First-order Equations5min
Change of Variables Transforms a Nonlinear to a Linear Equation10min
Linear First-order Equation: Examples10min
Saving for Retirement10min
Borrowing for a Mortgage10min
Terminal Velocity of a Skydiver10min
The Current in an RC Circuit10min
6 exercícios práticos
Diagnostic Quiz 10min
Classify Differential Equations5min
Separable First-order ODEs10min
Linear First-order ODEs10min
Applications10min
Week One Assessment30min
Semana
2

Semana 2

4 horas para concluir

Homogeneous Linear Differential Equations

4 horas para concluir
11 vídeos (Total 93 mín.), 11 leituras, 3 testes
11 videos
Euler Method for Higher-order ODEs | Lecture 109min
The Principle of Superposition | Lecture 116min
The Wronskian | Lecture 128min
Homogeneous Second-order ODE with Constant Coefficients| Lecture 139min
Case 1: Distinct Real Roots | Lecture 147min
Case 2: Complex-Conjugate Roots (Part A) | Lecture 157min
Case 2: Complex-Conjugate Roots (Part B) | Lecture 168min
Case 3: Repeated Roots (Part A) | Lecture 1712min
Case 3: Repeated Roots (Part B) | Lecture 184min
Complex Numbers17min
11 leituras
Second-order Equation as System of First-order Equations5min
Second-order Runge-Kutta Method10min
Linear Superposition for Inhomogeneous ODEs10min
Wronskian of Exponential Function5min
Roots of the Characteristic Equation10min
Distinct Real Roots10min
Hyperbolic Sine and Cosine Functions10min
Do You Know Complex Numbers?
Complex-Conjugate Roots10min
Sine and Cosine Functions10min
Repeated Roots10min
3 exercícios práticos
Superposition, the Wronskian, and the Characteristic Equation10min
Homogeneous Equations15min
Week Two Assessment30min
Semana
3

Semana 3

5 horas para concluir

Inhomogeneous Linear Differential Equations

5 horas para concluir
12 vídeos (Total 127 mín.), 9 leituras, 4 testes
12 videos
Inhomogeneous Second-order ODE | Lecture 199min
Inhomogeneous Term: Exponential Function | Lecture 2011min
Inhomogeneous Term: Sine or Cosine (Part A) | Lecture 219min
Inhomogeneous Term: Sine or Cosine (Part B) | Lecture 228min
Inhomogeneous Term: Polynomials | Lecture 237min
Resonance | Lecture 2413min
RLC Circuit | Lecture 2511min
Mass on a Spring | Lecture 269min
Pendulum | Lecture 2712min
Damped Resonance | Lecture 2814min
Nondimensionalization17min
9 leituras
Multiple Inhomogeneous Terms5min
Exponential Inhomogeneous Term10min
Sine or Cosine Inhomogeneous Term10min
Polynomial Inhomogeneous Term5min
When the Inhomogeneous Term is a Solution of the Homogeneous Equation10min
Do You Know Dimensional Analysis?
Another Nondimensionalization of the RLC Circuit Equation10min
Another Nondimensionalization of the Mass on a Spring Equation5min
Find the Amplitude of Oscillation10min
4 exercícios práticos
Solving Inhomogeneous Equations15min
Particular Solutions15min
Applications and Resonance15min
Week Three Assessment40min
Semana
4

Semana 4

4 horas para concluir

The Laplace Transform and Series Solution Methods

4 horas para concluir
11 vídeos (Total 123 mín.), 10 leituras, 4 testes
11 videos
Definition of the Laplace Transform | Lecture 2913min
Laplace Transform of a Constant Coefficient ODE | Lecture 3011min
Solution of an Initial Value Problem | Lecture 3113min
The Heaviside Step Function | Lecture 3210min
The Dirac Delta Function | Lecture 3312min
Solution of a Discontinuous Inhomogeneous Term | Lecture 3413min
Solution of an Impulsive Inhomogeneous Term | Lecture 357min
The Series Solution Method | Lecture 3617min
Series Solution of the Airy's Equation (Part A) | Lecture 3714min
Series Solution of the Airy's Equation (Part B) | Lecture 387min
10 leituras
The Laplace Transform of Sine10min
Laplace Transform of an ODE10min
Solution of an Initial Value Problem10min
Heaviside Step Function10min
The Dirac Delta Function5min
Discontinuous Inhomogeneous Term5min
Impulsive Inhomogeneous Term5min
Series Solution Method5min
Series Solution of a Nonconstant Coefficient ODE5min
Solution of the Airy's Equation5min
4 exercícios práticos
The Laplace Transform Method15min
Discontinuous and Impulsive Inhomogeneous Terms15min
Series Solutions15min
Week Four Assessment30min

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