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        "intro": "In this Section we show how a periodic function can be expressed as a series of sines and cosines.\nWe begin by obtaining some standard integrals involving sinusoids. We then <b>assume<\/b> that if \\(f(t)\\) is a periodic function, of period \\(2\\pi\\), then the Fourier series expansion takes the form:\n\\[ f(t) = \\dfrac{a_0}{2} + \\sum_{n=1}^\\infty (a_n \\cos nt + b_n \\sin nt)\\]\nOur main purpose here is to show how the constants in this expansion, \\(a_n\\) (for \\(n = 0, 1, 2, 3, \\dots\\)) and\n\\(b_n\\) (for \\(n = 1, 2, 3, \\dots\\)), may be determined for any given function \\(f(t)\\).",
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            "heading": "Functions of period 2pi",
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            "heading": "Orthogonality",
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            "heading": "Calculation of Fourier coefficients",
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            "heading": "Examples of Fourier series",
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            "heading": "Fourier series for functions of general period",
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