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Differential Equations (Metric)
Class Details
Tom Baker
Learn, or revise, solving first order differential equations by various methods, solving second order differential equations with constant coefficients, and classifying the critical points of systems.
Units
First Order
Solving differential equations of the form \(dy/dx=f(x,\,y)\). Part of this topic is found on A-level courses, and the rest is Further Maths.
Second Order
Solving differential equations of the form \(a\,d^2y/dx^2+b\,dy/dx+c\,y=f(x)\). This is a Further Maths topic; courses that require Further Maths may assume it.
Solving differential equations of the form \(a\,d^2y/dx^2+b\,dy/dx+c\,y=0\); oscillatory and exponential solutions.
Solving differential equations of the form \(a\,d^2y/dx^2+b\,dy/dx+c\,y=f(x)\) using a complementary function and a particular integral.
Qualitative Methods
Classifying the critical points of systems of the form \(dx/dt = f_1(x,\,y)\), \(dy/dt = f_2(x,\,y)\). This is part of the First Year content of some Science and Engineering courses at Imperial.