Grade 12 Calculus and Vectors
Comprehensive list of FREE video tutorials for Canada and North America's grade 12 Calculus and Vectors

Calculus was developed by German mathematician and philosopher Gottfried Wilhelm Leibniz and English mathematician and physicist Sir Isaac Newton (concurrently, but from different parts of the world).

Calculus has two main parts: Derivatives and Integrals. Derivatives, the component of Calculus that is taught in Calculus and Vectors, mainly assist with solving problems that involves rates of changes and curve sketching. Meanwhile, integration is used to find areas and volumes made by the most complicated curves and shapes. Thus, Calculus is most useful in solving problems that presents itself in a state of continuum.

There are many different notations used in Calculus to indicate derivative of a function. Leibniz introduced the df(x)/dx or dy/dx notation (read as ‘d’ ‘y’ by ‘d’ ‘x’ or ‘derivative of ‘y’ with respect to ‘x’), while Newton came up with the ‘dot notation’ (ė or ë) which is now primarily used to indicate derivatives with respect to time. Leonhard Euler’s notation uses a prefix ‘D’ as a differential operator with the function ‘f(x)’ following it (i.e. Df and D²f, D³f...Dⁿf used for higher order of differentials). He also introduced the D_xf(x) or D_xy notation which reads exactly as Leibniz’s notation, above. Most popular notation to date belongs to Joseph Louis Lagrange, as he coined the ‘prime notation’ such as f’(x) (read as "f" "prime of" "x"), and f’’(x), f’’’(x)...fⁿ(x) for higher order of differentiation.

Please refer to high school math prerequisite tree to see the recommended courses and materials one should be familiar with prior to taking up Calculus and Vectors.

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