Standard syllabus
Fourier analysis & transforms · Undergraduate · Math
Topics
Fourier series
- Orthogonality of sine and cosine functions on intervals
- Fourier series for periodic functions; coefficients and convergence
- Even and odd extensions; sine and cosine series
- Parseval's theorem and energy interpretation
- Gibbs phenomenon and convergence at discontinuities
Fourier and Laplace transforms
- Definition and properties of the Fourier transform
- Convolution theorem and filtering
- Discrete Fourier transform (DFT) and sampling
- Laplace transform review and connection to frequency domain
- Inverse transforms and transform pairs (table methods)
Applications and generalizations
- Heat equation and PDE solutions via Fourier series
- Signal decomposition and frequency content
- Window functions and leakage (introduction)
- Fast Fourier transform (FFT) algorithm overview
- Introduction to wavelets (optional topic)
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$1,162 · Fourier analysis & transforms · 18 tutoring hrs
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