Calculus is the rock on which math built its church. This course looks at Differentiation & Integration, First & Second Order Derivatives and Integrals.
This course covers Topic 7: Differentiation and Topic 8: Integration from the Pure Mathematics section of Edexcel AS Level Maths. This will be examined on Paper 1 of AS Level Edexel Maths. You will build on these concepts at A-Level.
What is differentiation? The derivative of a function is another function which represents the slope or gradient of that function. Differentiation by first principles is also defined here.
The second order derivative is the derivative of the derivative. The second derivative gives the rate of change of the derivative, or the gradient of the curve, with respect to x.
Differentiation can be represented graphically in a number of ways. Gradients & tangents, normals, and maxima, minima & stationary points can be used as an illustrator.
Integration is the reverse of differentiation. If you take a function, differentiate it and then integrate the resulting expression, you will be left with the original function.
Integration does have uses other than just reversing differentiation. Sometimes when calculating a definite integral, you may end up with an answer that is a negative number.
Differentiate from first and second principles. Calculate the derivative of these functions. Revise your knowledge of Differentiation and Integration in this quiz.
