Informações sobre o curso
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Nível iniciante

Knowledge of single variable calculus.

Aprox. 14 horas para completar

Sugerido: 5 hours per week...

Inglês

Legendas: Inglês

O que você vai aprender

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    First-order differential equations

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    Second-order differential equations

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    The Laplace transform and series solution methods

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    Systems of differential equations and partial differential equations

Habilidades que você terá

Differential EquationsOrdinary Differential EquationPartial Differential Equation (PDE)Engineering Mathematics

100% online

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. 14 horas para completar

Sugerido: 5 hours per week...

Inglês

Legendas: Inglês

Programa - O que você aprenderá com este curso

Semana
1
6 horas para concluir

First-Order Differential Equations

12 vídeos (Total 97 mín.), 11 leituras, 6 testes
12 videos
Course Overview2min
Introduction to Differential Equations9min
Week 1 Introduction47s
Euler Method9min
Separable First-order Equations8min
Separable First-order Equation: Example6min
Linear First-order Equations13min
Linear First-order Equation: Example5min
Application: Compound Interest13min
Application: Terminal Velocity11min
Application: RC Circuit11min
11 leituras
Welcome and Course Information2min
Get to Know Your Classmates10min
Practice: Runge-Kutta Methods10min
Practice: Separable First-order Equations10min
Practice: Separable First-order Equation Examples10min
Practice: Linear First-order Equations5min
Change of Variables Transforms a Nonlinear to a Linear Equation10min
Practice: Linear First-order Equation: Examples10min
Practice: Compound Interest10min
Practice: Terminal Velocity10min
Practice: RC Circuit10min
6 exercícios práticos
Diagnostic Quiz15min
Classify Differential Equations10min
Separable First-order ODEs15min
Linear First-order ODEs15min
Applications20min
Week One1h
Semana
2
8 horas para concluir

Second-Order Differential Equations

22 vídeos (Total 218 mín.), 20 leituras, 3 testes
22 videos
Euler Method for Higher-order ODEs9min
The Principle of Superposition6min
The Wronskian8min
Homogeneous Second-order ODE with Constant Coefficients9min
Case 1: Distinct Real Roots7min
Case 2: Complex-Conjugate Roots (Part A)7min
Case 2: Complex-Conjugate Roots (Part B)8min
Case 3: Repeated Roots (Part A)12min
Case 3: Repeated Roots (Part B)4min
Inhomogeneous Second-order ODE9min
Inhomogeneous Term: Exponential Function11min
Inhomogeneous Term: Sine or Cosine (Part A)9min
Inhomogeneous Term: Sine or Cosine (Part B)8min
Inhomogeneous Term: Polynomials7min
Resonance13min
RLC Circuit11min
Mass on a Spring9min
Pendulum12min
Damped Resonance14min
Complex Numbers17min
Nondimensionalization17min
20 leituras
Practice: Second-order Equation as System of First-order Equations10min
Practice: Second-order Runge-Kutta Method10min
Practice: Linear Superposition for Inhomogeneous ODEs10min
Practice: Wronskian of Exponential Function10min
Do You Know Complex Numbers?
Practice: Roots of the Characteristic Equation10min
Practice: Distinct Real Roots10min
Practice: Hyperbolic Sine and Cosine Functions10min
Practice: Complex-Conjugate Roots10min
Practice: Sine and Cosine Functions10min
Practice: Repeated Roots10min
Practice: Multiple Inhomogeneous Terms10min
Practice: Exponential Inhomogeneous Term10min
Practice: Sine or Cosine Inhomogeneous Term10min
Practice: Polynomial Inhomogeneous Term10min
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 Equation10min
Find the Amplitude of Oscillation10min
3 exercícios práticos
Homogeneous Equations20min
Inhomogeneous Equations20min
Week Two1h
Semana
3
6 horas para concluir

The Laplace Transform and Series Solution Methods

11 vídeos (Total 123 mín.), 10 leituras, 4 testes
11 videos
Definition of the Laplace Transform13min
Laplace Transform of a Constant Coefficient ODE11min
Solution of an Initial Value Problem13min
The Heaviside Step Function10min
The Dirac Delta Function12min
Solution of a Discontinuous Inhomogeneous Term13min
Solution of an Impulsive Inhomogeneous Term7min
The Series Solution Method17min
Series Solution of the Airy's Equation (Part A)14min
Series Solution of the Airy's Equation (Part B)7min
10 leituras
Practice: The Laplace Transform of Sine10min
Practice: Laplace Transform of an ODE10min
Practice: Solution of an Initial Value Problem10min
Practice: Heaviside Step Function10min
Practice: The Dirac Delta Function15min
Practice: Discontinuous Inhomogeneous Term20min
Practice: Impulsive Inhomogeneous Term10min
Practice: Series Solution Method10min
Practice: Series Solution of a Nonconstant Coefficient ODE1min
Practice: Solution of the Airy's Equation10min
4 exercícios práticos
The Laplace Transform Method30min
Discontinuous and Impulsive Inhomogeneous Terms20min
Series Solutions20min
Week Three1h
Semana
4
8 horas para concluir

Systems of Differential Equations and Partial Differential Equations

19 vídeos (Total 177 mín.), 17 leituras, 6 testes
19 videos
Systems of Homogeneous Linear First-order ODEs8min
Distinct Real Eigenvalues9min
Complex-Conjugate Eigenvalues12min
Coupled Oscillators9min
Normal Modes (Eigenvalues)10min
Normal Modes (Eigenvectors)9min
Fourier Series12min
Fourier Sine and Cosine Series5min
Fourier Series: Example11min
The Diffusion Equation9min
Solution of the Diffusion Equation: Separation of Variables11min
Solution of the Diffusion Equation: Eigenvalues10min
Solution of the Diffusion Equation: Fourier Series9min
Diffusion Equation: Example10min
Matrices and Determinants13min
Eigenvalues and Eigenvectors10min
Partial Derivatives9min
Concluding Remarks2min
17 leituras
Do You Know Matrix Algebra?
Practice: Eigenvalues of a Symmetric Matrix10min
Practice: Distinct Real Eigenvalues10min
Practice: Complex-Conjugate Eigenvalues10min
Practice: Coupled Oscillators10min
Practice: Normal Modes of Coupled Oscillators10min
Practice: Fourier Series10min
Practice: Fourier series at x=010min
Practice: Fourier Series of a Square Wave10min
Do You Know Partial Derivatives?10min
Practice: Nondimensionalization of the Diffusion Equation10min
Practice: Boundary Conditions with Closed Pipe Ends10min
Practice: ODE Eigenvalue Problems10min
Practice: Solution of the Diffusion Equation with Closed Pipe Ends10min
Practice: Concentration of a Dye in a Pipe with Closed Ends10min
Please Rate this Course5min
Acknowledgements
6 exercícios práticos
Systems of Differential Equations20min
Normal Modes30min
Fourier Series30min
Separable Partial Differential Equations20min
The Diffusion Equation20min
Week Four1h
4.8
34 avaliaçõesChevron Right

Principais avaliações do Differential Equations for Engineers

por AKSep 8th 2019

It was a great journey to go through this course. Prof. Jeffery explains the concepts very well. I hope this course will help me greatly in my other courses.

por YHApr 3rd 2019

Thank you Prof. Chasnov. The lectures are really impressive and explain derivations throughly. I cannot enjoy more on a math course than this one.

Instrutores

Avatar

Jeffrey R. Chasnov

Professor
Department of Mathematics

Sobre Universidade de Ciência e Tecnologia de Hong Kong

HKUST - A dynamic, international research university, in relentless pursuit of excellence, leading the advance of science and technology, and educating the new generation of front-runners for Asia and the world....

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