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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.
Solving differential equations of the form \(dy/dx = f(x)\,g(y)\), by separating the variables.
Solving differential equations that can be written in the form \(d/dx(f(x,\,y))=0\).
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.
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.