Differential Equations for Engineers
The Hong Kong University of Science and Technology
By highlighting both theories and applications in practice, this amazing course might be your excellent choice to grasp the differential equations in shortest time. You are actually learning math and physics at the same time, building your own mapping between the 2 disciplines. I find this method of learning is quite effective and efficient.
The course started from the simplest case: linear first-order differential equations. Don’t be surprised that they are just around you: compound interest rate, velocity of running, and resistor-capacitor circuit in your windshield wipers.
Next is the homogeneous linear second-order differential equations, the complex numbers come into play. You now need to pay attention to complex conjugate roots and degenerated roots.
You will learn how to solve the inhomogeneous equations like this x” + p(t) x’ + q(t) x = g(t), how to explain the resonance phenomenon, mass on the spring, pendulum and applications like resistor-capacitor-inductor circuits.
The course is getting harder, but taking you to a different perspective. With the Laplace transform you can convert a differential equation into another space where the equation is easier to solve. And do not forget the series solution method, which is another technique of solving linear differential equations.
In the week 5, matrix is gonna take your adventure to the next level – systems of differential equations! If you have not heard eigenvalue or eigenvectors first. You probably need to check out the course ‘Matrix Algebra for Engineers’ first. The final week is a taste of partial differential equation. I enjoyed very much the elegancy of Fourier series and the diffusion equation of a dye in a pipe.
The entire course was taught on a lightboard, the derivation of equations are neat and beautiful. This course deserves your attention, you shouldn’t miss out.
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