This course is all about differential equations. 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.
Этот курс входит в специализацию ''Специализация Mathematics for Engineers'
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Об этом курсе
Knowledge of single variable calculus.
Чему вы научитесь
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.
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Гонконгский университет науки и технологий
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.
Программа курса: что вы изучите
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.
Рецензии
- 5 stars88,58 %
- 4 stars9,79 %
- 3 stars1,19 %
- 2 stars0,05 %
- 1 star0,37 %
Лучшие отзывы о курсе DIFFERENTIAL EQUATIONS FOR ENGINEERS
I don't have a math or engineering background but this course has a great balance of simplicity and challenging problems that I can confidently take to higher level mathematics
Best course. have explained the theoratical and practical aspects of differential equations and at the same time covered a substantial chunk of the subject in a very easy and didactic manner.
Loved the course. The content is to the point and explains the practical applications where differential equations are used which made the course more interesting.
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.
Специализация Mathematics for Engineers: общие сведения
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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