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Physics with hidden calculus

Crossing campus this afternoon, a student whose exam is later this week asked me “when you ask a real-world question on the exam and you want us to solve an ODE, can we just do it using formula we memorised from A-level physics?” Like what? “Like with one of the distance questions we might just use $v^2 = u^2 + 2as$.” I said that if they were relying on a result we didn’t use in the module and that they hadn’t proven, this would be a problem.

In the latest Taking Maths Further podcast (Episode 19: Computer games and mechanics), we had a puzzle that we say could be answered roughly, but the precise answer 23.53 (2 d.p.) required a little calculus. On Twitter, @NickJTaylor said

Help a dude write an open-source calculus textbook (or use one of the many great ones already available)

A chap called Dixon Crews has posted to reddit’s maths section asking for help with a writing project.