Fourier analysis & transforms
Undergraduate · Math
Syllabus focus
Standard syllabus · STEM / applied
Pricing calculator
Choose materials, tutoring, or both — or book a single session as needed. Customize your plan on the subscribe page.
$1,162 · Fourier analysis & transforms · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.
Topics typically covered
Standard syllabus
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)
STEM / applied
Signal and image processing
- Filtering: low-pass, high-pass, and band-pass filters
- Modulation, demodulation, and AM/FM (mathematical view)
- Sampling theorem and aliasing
- Implementation of FFT in MATLAB/Python
- Applications in acoustics, optics, and communications
Engineering applications
- Vibrations and modal analysis via Fourier methods
- Transfer functions and frequency response
- Correlation and power spectral density
- Solving PDEs with boundary conditions using transform methods
- Numerical approximation of continuous transforms
Notes
Topics reflect common Fourier analysis syllabi at US colleges and universities. Some programs teach this material within differential equations or applied analysis courses.