This course is about differential equations and covers material that all engineers should know. Both basic theory and applications are taught. In the first five weeks we will learn about ordinary differential equations, and in the final week, partial differential equations.
ofrecido por
Differential Equations for Engineers
Universidad Científica y Tecnológica de Hong Kong
Acerca de este Curso
72,238 vistas recientes
Qué aprenderás
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 obtendrás
Ordinary Differential EquationPartial Differential Equation (PDE)Engineering Mathematics
Certificado para compartir
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Nivel principiante
Knowledge of single variable calculus.
Aprox. 17 horas para completar
Sugerido: 6 weeks of study, 4 hours/week
Inglés (English)
Subtítulos: Inglés (English)
ofrecido por
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.
Programa - Qué aprenderás en este curso
5 horas para completar
First-Order Differential Equations
A differential equation is an equation for a function with one or more of its derivatives. We introduce differential equations and classify them. We then learn about the Euler method for numerically solving a first-order ordinary differential equation (ode). Then we learn analytical methods for solving separable and linear first-order odes. An explanation of the theory is followed by illustrative solutions of some simple odes. Finally, we learn about three real-world examples of first-order odes: compound interest, terminal velocity of a falling mass, and the resistor-capacitor electrical circuit.
5 horas para completar
15 videos (Total 126 minutos), 11 lecturas, 6 cuestionarios
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
11 lecturas
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
Compound Interest10m
Terminal Velocity10m
RC Circuit10m
6 ejercicios de práctica
Diagnostic Quiz10m
Classify Differential Equations5m
Separable First-order ODEs10m
Linear First-order ODEs10m
Applications10m
Week One Assessment30m
4 horas para completar
Homogeneous Linear Differential Equations
We generalize the Euler numerical method to a second-order ode. We then develop two theoretical concepts used for linear equations: the principle of superposition, and the Wronskian. Armed with these concepts, we can find analytical solutions to a homogeneous second-order ode with constant coefficients. We make use of an exponential ansatz, and transform the constant-coefficient ode to a second-order polynomial equation called the characteristic equation of the ode. The characteristic equation may have real or complex roots and we learn solution methods for the different cases.
4 horas para completar
11 videos (Total 93 minutos), 11 lecturas, 3 cuestionarios
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
11 lecturas
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 ejercicios de práctica
Superposition, the Wronskian, and the Characteristic Equation10m
Homogeneous Equations15m
Week Two Assessment30m
4 horas para completar
Inhomogeneous Linear Differential Equations
We now add an inhomogeneous term to the constant-coefficient ode. The inhomogeneous term may be an exponential, a sine or cosine, or a polynomial. We also study the phenomena of resonance, when the forcing frequency is equal to the natural frequency of the oscillator. Finally, we learn about three important applications: the RLC electrical circuit, a mass on a spring, and the pendulum.
4 horas para completar
12 videos (Total 127 minutos), 9 lecturas, 4 cuestionarios
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
9 lecturas
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 ejercicios de práctica
Solving Inhomogeneous Equations15m
Particular Solutions15m
Applications and Resonance15m
Week Three Assessment30m
4 horas para completar
The Laplace Transform and Series Solution Methods
We present two new analytical solution methods for solving linear odes. The first is the Laplace transform method, which is used to solve the constant-coefficient ode with a discontinuous or impulsive inhomogeneous term. The Laplace transform is a good vehicle in general for introducing sophisticated integral transform techniques within an easily understandable context. We also introduce the solution of a linear ode by a series solution. Although we do not go deeply here, an introduction to this technique may be useful to students that encounter it again in more advanced courses.
4 horas para completar
11 videos (Total 123 minutos), 10 lecturas, 4 cuestionarios
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
10 lecturas
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 ejercicios de práctica
The Laplace Transform Method15m
Discontinuous and Impulsive Inhomogeneous Terms15m
Series Solutions15m
Week Four Assessment30m
Revisiones
Principales revisiones sobre DIFFERENTIAL EQUATIONS FOR ENGINEERS
por AAFeb 6, 2020
Very good course if you want to start using differential equations without any rigorous details. Thanks to professor`s explanation everything is very clear. Good basis to continue to dive deeper.
por AZFeb 11, 2020
The instructor and materials were excellent. The quizzes at the end of each section were non-trivial and it's a great course to jumpstart your ability to work with ODEs and PDEs.
por ABAug 31, 2019
Excellent course. I would recommend it very highly! The professor starts from the very basics and goes on to tackle highly intricate and interesting problems.
por AKSep 7, 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 NApr 2, 2020
This is how a refresher course must be executed. Simple yet informative lectures coupled with sufficiently challenging exercises.\n\nThank you for this.
por YHApr 2, 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.
por VKFeb 17, 2020
Really good course. Well organized. Applications to physical systems might be difficult to grasp for non physics students. But you can do well.
por MPMar 17, 2020
A very genuine course which provided me with the knowledge in depth for the differential calculus required by a engineer.
por PHJul 14, 2019
A really great course. The work is very challenging, but rewarding. Thank you Professor Chasnov for an excellent course!
por SKNov 23, 2019
I have learned a lot from this course. This is very helpful for every engineer. Thank you so much, Sir.
por TNMar 19, 2020
It's really good. The lecture makes me more understanding of Differential Equations. All the best.
por MMOct 31, 2019
A good refresher to the differential equations and solutions to first and second order problems
por SFMay 22, 2019
I can't be thankful enough for this course. It was a life changing for me. Thank you VERY much!
por ABJun 28, 2019
Great course to learn how to use Differential Equations in real life. Highly recommended!
por MKAug 21, 2019
I have just started. I find it an awesome course. Thanks to the instructor for hard work.
por RSJul 22, 2019
Very friendly for beginners. Very useful concepts for engineers. Really helpful for me.
por SAMar 11, 2020
great course all the video lectures are great and wholesome.thank you for the content
por GCApr 2, 2019
Was amazing learning something new in this course under our beloved professor.
por RMAug 5, 2019
That is a very good course. And it related to real-time applications also.
por SHOct 14, 2019
IT is very good course for learning differential equations for engineers
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