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Differentiation (Metric)
Class Details
Tom Baker
Learn, or revise, differentiation from first principles, techniques of differentiation and using differentiation to sketch curves and solve problems.
Units
Principles
The gradient of a curve as the limit of the gradient of a secant or chord. This is an A-level topic, but sometimes a bit neglected at that level.
Techniques
Differentiating key functions, and sums, products, quotients and composites. This is an A-level topic, which Science and Engineering courses at Imperial will assume you know.
Differentiating functions of the form \(a\,f(x)+b\,g(x)\).
Differentiating functions of the form \(f(g(x))\).
Putting the rules of differentiation to use.
Differentiating functions given implicitly, in equations of the form \(f(x,\,y)=0\).
Applications
Using differentiation to find stationary points and points of inflexion on curves, and to solve problems involving velocity and acceleration. This is an A-level topic, which Science and Engineering courses at Imperial will assume you know.