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Differentiation I

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About this Course

About the Course

In this course, Professor Samir Siksek (University of Warwick) gives an introduction to differentiation for AS and A-Level students in the first of his three-course series on this topic. In the first mini-lecture, we recall the equation of a straight line and discuss gradient. In the second mini-lecture, we determine the equation for a tangent line to a curve. In the third mini-lecture, we use our work from the previous mini-lecture to define the derivative at a point on a curve as the equation for the gradient of the tangent at that point on the curve. In the fourth mini-lecture, we calculate the derivative of various basic functions from first principles. In the fifth mini-lecture, we introduce the derivatives of common functions including f(x) = c, f(x) = xn, f(x) = sin(kx), f(x) = cos(kx), f(x) = ekx, and f(x) = ln(kx).

About the Lecturer

Samir Siksek is a Professor of Mathematics at the University of Warwick. His research interests include Galois representations, modularity, explicit arithmetic geometry, arithmetic of curves and surfaces, Diophantine equations (the generalized Fermat equation in particular), and Waring's problem. In 2012, he appeared on BBC Radio 4’s In Our Time program discussing Fermat’s Last Theorem.