Solutions to Penrose's ‘Road To Reality’
Chapter 6: Real-number calculus

§6.1 What makes an honest function?
6.1 * The Heaviside function
§6.3 Higher derivatives; C∞-smooth functions
6.2 *** A smoothness proof
§6.4 The ‘Eulerian’ notion of a function?
6.3 * Maclaurin's series
§6.5 The rules of differentiation
6.4 *** An arbitrary smooth but not analytic function
6.5 * The derivative of the exponential function
6.6 ** An application of the product rule
6.7 * The quotient rule
6.8 * Applying the basic rules of differentiation
6.9 ** Derivatives of logarithmic functions
6.10 ** Deviratives of trigonometric functions