Even and odd parts of a function

How to write an arbitrary function as the sum of an even function and an odd function. We derive expressions for the even and odd parts by forming a pair of simultaneous equations based on the desired symmetry properties. The thumbnail shows the graph of f(x) = e^x, along with its even and odd parts, the hyperbolic trigonometric functions.

About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.

#mathematics #symmetry #functions #graphs #parity #calculus #integration #simultaneousequations #maths #math #science #education

[mikip]

Never thought that you could do this with any function! This is great for integrals that have symetric limits around the zero.

[anmoldeepsingh]

Please make a video on intuition behind internal flux linkage of an infinite cylinderical wire whenever you get the time. I am unable to wrap my head behind the idea of multiplying flux by x^2/r^2 to get the flux linkage.