Section 2.2 describes a derivation of the integral expressions for the Fourier coefficients and defines the resulting Fourier series for functions of period \(2\pi\). Two worked examples are used to explore convergence by plotting the partial sums of the Fourier series.



Section 2.3 describes the Fourier cosine and sine series that are generated by even and odd \(2\pi\)-periodic functions.



Section 2.4 describes six useful tips for the efficient calculation of Fourier coefficients.



Section 2.5 introduces piecewise continuity which is the only new concept needed to state a powerful pointwise convergence theorem for Fourier series. The hypotheses, convergence result, non-examinable proof and implications for differentiability and integrability of Fourier series are briefly discussed. The convergence theorem is applied to the two earlier worked examples.