Series of Functions

Power series and Fourier series are very powerful tools in analysis. But before we get to them, we need to build a firm foundation by understanding the behavior of general sequences and series of functions.
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• Sequences of functions: pointwise convergence, uniform convergence, properties.
• Series of functions: pointwise convergence, uniform convergence, properties.
• Basic systems of functions.
• Power series and their properties.
• Taylor series, expanding functions in power series and summing up series.
• Fourier series (trigonometric series).
• Properties of Fourier series (differentiability etc, amplitude-phase angle form, complex form).
• Applications of series.