Acerca de este Curso
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Comienza de inmediato y aprende a tu propio ritmo.

Fechas límite flexibles

Restablece las fechas límite en función de tus horarios.

Nivel principiante

Knowledge of single variable calculus.

Aprox. 14 horas para completar

Sugerido: 5 hours per week...

Inglés (English)

Subtítulos: Inglés (English)

Qué aprenderás

  • Check

    First-order differential equations

  • Check

    Second-order differential equations

  • Check

    The Laplace transform and series solution methods

  • Check

    Systems of differential equations and partial differential equations

Habilidades que obtendrás

Differential EquationsOrdinary Differential EquationPartial Differential Equation (PDE)Engineering Mathematics

100 % en línea

Comienza de inmediato y aprende a tu propio ritmo.

Fechas límite flexibles

Restablece las fechas límite en función de tus horarios.

Nivel principiante

Knowledge of single variable calculus.

Aprox. 14 horas para completar

Sugerido: 5 hours per week...

Inglés (English)

Subtítulos: Inglés (English)

Programa - Qué aprenderás en este curso

Semana
1
6 horas para completar

First-Order Differential Equations

12 videos (Total 97 minutos), 11 lecturas, 6 cuestionarios
12 videos
Course Overview2m
Introduction to Differential Equations9m
Week 1 Introduction47s
Euler Method9m
Separable First-order Equations8m
Separable First-order Equation: Example6m
Linear First-order Equations13m
Linear First-order Equation: Example5m
Application: Compound Interest13m
Application: Terminal Velocity11m
Application: RC Circuit11m
11 lecturas
Welcome and Course Information2m
Get to Know Your Classmates10m
Practice: Runge-Kutta Methods10m
Practice: Separable First-order Equations10m
Practice: Separable First-order Equation Examples10m
Practice: Linear First-order Equations5m
Change of Variables Transforms a Nonlinear to a Linear Equation10m
Practice: Linear First-order Equation: Examples10m
Practice: Compound Interest10m
Practice: Terminal Velocity10m
Practice: RC Circuit10m
6 ejercicios de práctica
Diagnostic Quiz15m
Classify Differential Equations10m
Separable First-order ODEs15m
Linear First-order ODEs15m
Applications20m
Week One1h
Semana
2
8 horas para completar

Second-Order Differential Equations

22 videos (Total 218 minutos), 20 lecturas, 3 cuestionarios
22 videos
Euler Method for Higher-order ODEs9m
The Principle of Superposition6m
The Wronskian8m
Homogeneous Second-order ODE with Constant Coefficients9m
Case 1: Distinct Real Roots7m
Case 2: Complex-Conjugate Roots (Part A)7m
Case 2: Complex-Conjugate Roots (Part B)8m
Case 3: Repeated Roots (Part A)12m
Case 3: Repeated Roots (Part B)4m
Inhomogeneous Second-order ODE9m
Inhomogeneous Term: Exponential Function11m
Inhomogeneous Term: Sine or Cosine (Part A)9m
Inhomogeneous Term: Sine or Cosine (Part B)8m
Inhomogeneous Term: Polynomials7m
Resonance13m
RLC Circuit11m
Mass on a Spring9m
Pendulum12m
Damped Resonance14m
Complex Numbers17m
Nondimensionalization17m
20 lecturas
Practice: Second-order Equation as System of First-order Equations10m
Practice: Second-order Runge-Kutta Method10m
Practice: Linear Superposition for Inhomogeneous ODEs10m
Practice: Wronskian of Exponential Function10m
Do You Know Complex Numbers?
Practice: Roots of the Characteristic Equation10m
Practice: Distinct Real Roots10m
Practice: Hyperbolic Sine and Cosine Functions10m
Practice: Complex-Conjugate Roots10m
Practice: Sine and Cosine Functions10m
Practice: Repeated Roots10m
Practice: Multiple Inhomogeneous Terms10m
Practice: Exponential Inhomogeneous Term10m
Practice: Sine or Cosine Inhomogeneous Term10m
Practice: Polynomial Inhomogeneous Term10m
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 Equation10m
Find the Amplitude of Oscillation10m
3 ejercicios de práctica
Homogeneous Equations20m
Inhomogeneous Equations20m
Week Two1h
Semana
3
6 horas para completar

The Laplace Transform and Series Solution Methods

11 videos (Total 123 minutos), 10 lecturas, 4 cuestionarios
11 videos
Definition of the Laplace Transform13m
Laplace Transform of a Constant Coefficient ODE11m
Solution of an Initial Value Problem13m
The Heaviside Step Function10m
The Dirac Delta Function12m
Solution of a Discontinuous Inhomogeneous Term13m
Solution of an Impulsive Inhomogeneous Term7m
The Series Solution Method17m
Series Solution of the Airy's Equation (Part A)14m
Series Solution of the Airy's Equation (Part B)7m
10 lecturas
Practice: The Laplace Transform of Sine10m
Practice: Laplace Transform of an ODE10m
Practice: Solution of an Initial Value Problem10m
Practice: Heaviside Step Function10m
Practice: The Dirac Delta Function15m
Practice: Discontinuous Inhomogeneous Term20m
Practice: Impulsive Inhomogeneous Term10m
Practice: Series Solution Method10m
Practice: Series Solution of a Nonconstant Coefficient ODE1m
Practice: Solution of the Airy's Equation10m
4 ejercicios de práctica
The Laplace Transform Method30m
Discontinuous and Impulsive Inhomogeneous Terms20m
Series Solutions20m
Week Three1h
Semana
4
8 horas para completar

Systems of Differential Equations and Partial Differential Equations

19 videos (Total 177 minutos), 17 lecturas, 6 cuestionarios
19 videos
Systems of Homogeneous Linear First-order ODEs8m
Distinct Real Eigenvalues9m
Complex-Conjugate Eigenvalues12m
Coupled Oscillators9m
Normal Modes (Eigenvalues)10m
Normal Modes (Eigenvectors)9m
Fourier Series12m
Fourier Sine and Cosine Series5m
Fourier Series: Example11m
The Diffusion Equation9m
Solution of the Diffusion Equation: Separation of Variables11m
Solution of the Diffusion Equation: Eigenvalues10m
Solution of the Diffusion Equation: Fourier Series9m
Diffusion Equation: Example10m
Matrices and Determinants13m
Eigenvalues and Eigenvectors10m
Partial Derivatives9m
Concluding Remarks2m
17 lecturas
Do You Know Matrix Algebra?
Practice: Eigenvalues of a Symmetric Matrix10m
Practice: Distinct Real Eigenvalues10m
Practice: Complex-Conjugate Eigenvalues10m
Practice: Coupled Oscillators10m
Practice: Normal Modes of Coupled Oscillators10m
Practice: Fourier Series10m
Practice: Fourier series at x=010m
Practice: Fourier Series of a Square Wave10m
Do You Know Partial Derivatives?10m
Practice: Nondimensionalization of the Diffusion Equation10m
Practice: Boundary Conditions with Closed Pipe Ends10m
Practice: ODE Eigenvalue Problems10m
Practice: Solution of the Diffusion Equation with Closed Pipe Ends10m
Practice: Concentration of a Dye in a Pipe with Closed Ends10m
Please Rate this Course5m
Acknowledgements
6 ejercicios de práctica
Systems of Differential Equations20m
Normal Modes30m
Fourier Series30m
Separable Partial Differential Equations20m
The Diffusion Equation20m
Week Four1h
4.8
35 revisionesChevron Right

Principales revisiones sobre 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.

Instructor

Avatar

Jeffrey R. Chasnov

Professor
Department of Mathematics

Acerca de Universidad Científica y Tecnológica 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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