Differentiation and Functions in Mathematics

In mathematics, functions are the idealization of how a varying quantity depends on another quantity, and differentiation allows you to find and show rates of change - the two work hand-in-hand. This course will give you a detailed insight to both functions and differentiation, and how to apply them for solving mathematical problems and questions.

It starts by teaching you how to plot equations from a table of values on a graph, from quadratics to exponentials. Learn about the algebra technique known as ‘completing the square’, the process of translating functions on the X and Y axes, and how to stretch them on both. Then, grapple with what the ‘discriminant’ is and how to calculate it, and what inverse and bijective functions are.

In the second module, you will be introduced to basic differentiation and how to differentiate polynomials. Learn about the equation of a tangent and a normal of a curve, what the second derivative is and how to derive it, differentiation of tangents, products and quotients. The module finishes by teaching you the chain, product and quotient rules.

Next the course teaches you about the differentiation of logarithms and how to differentiate trigonometry equations. After that, it discusses the relationship between differentiation and the rates of change, giving you two working examples. Study using differentiation to calculate the turning points on a curve, the applications of differentiation in regards to velocity, acceleration and electricity. Then the module moves on to showing you how to work out an algebraic formula from just two measurements, and exploring the relationship between different types of functions, their differential, and second derivative.

In the last topic you are introduced to integration, the reverse of differentiation. You will learn about what it is at a basic level, integrating different types of formulas, and how to deal with powers, indices and fractions for integration. You will be shown what definite integration is and integration with trigonometry and exponential equations.