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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.

### 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.

The result $$f(x)=f(0)+x\,f'(0)+x^2/2!\,f''(0)+\dots$$.

Points where a curve is locally horizontal; how to find and classify them.

Lesson
Lesson

Finding points where a curve changes its direction of curvature.

Lesson
Lesson
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