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.
Este curso forma parte de Programa especializado: Mathematics for Engineers
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Acerca de este Curso
Knowledge of single variable calculus.
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
Knowledge of single variable calculus.
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
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.
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 quadratic 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.
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.
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 discuss the series solution of a linear ode. 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.
Reseñas
- 5 stars88,66 %
- 4 stars9,74 %
- 3 stars1,20 %
- 2 stars0,05 %
- 1 star0,32 %
Principales reseñas sobre DIFFERENTIAL EQUATIONS FOR ENGINEERS
Professor Jeff Chasnov has a very good understanding of ode's which makes it very useful for this course. The course was very efficient and was easy to grasp.
I think this course is very suitable for any curious mind. You can learn very important and necessary concepts with this course. The courses taught by Professor Dr. Chasnov are excellent.
This was a very nice course! I used it to brush up my knowledge rather than learning from scratch, but I think it is well-paced and the lecture notes are superb! Thank you very much!
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.
Acerca de Programa especializado: Mathematics for Engineers
This specialization was developed for engineering students to self-study engineering mathematics. We expect students are already familiar with single variable calculus and computer programming. Students will learn matrix algebra, differential equations, vector calculus and numerical methods. MATLAB programming will be taught. Watch the promotional video!

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