Curated OER
Using Fourier Series
In this Fourier series worksheet, students use polynomials to approximate functions. They use trigonometric functions to approximate periodic functions. Students sketch graphs of functions and find the second degree Fourier polynomial....
Massachusetts Institute of Technology
Mit: Open Course Ware: Differential Equations
The online course consists of educational materials about differential equation. Video lectures, readings, syllabus, exams, interactive mathlets, and assignments with solutions are included.
Harvey Mudd College
Harvey Mudd College: Special Trigonometric Integrals
Proves that the cos and sin functions form an orthogonal set, as it applies to Fourier series.
Wolfram Research
Wolfram Math World: Infinite Series
The site contains information on infinite series. Includes formulas and links to related topics.
American Association of Physics Teachers
Com Padre Digital Library: Open Source Physics: Harmonics and Fourier Series
The downloadable interactive java simulation displays the sum of harmonics through a Fourier series to yield a new wave.
Other
Calculating Fourier Series
The authors provide problems involving the calculation of Fourier series and then take a stepwise approach to solving them.
Math2
Math2
This is a site for students and teachers of all grade levels. If you are looking for math tables, general information about math topics, or you would like to ask a question, this is the site to visit.
Dartmouth College
Dartmouth College: Mqed: Computer Music
The downloadable monograph investigates computer music. Topics included are the MIDI system, waves, synthesizers, coding, and computer music applications.
Texas Instruments
Texas Instruments: Fourier Analysis
Students use the TI InterActive! software to explore the connection between a function and its Fourier series.
Texas Instruments
Texas Instruments: Getting Started With the Calculus Tools App
This user-friendly application extends the build-in power of your TI-89 and TI-92 Plus by providing more specialized functionality. Use Calculus to investigate applications of differentiation, compare numerical integration techniques and...
Analyze Math
Analyze Math: Fourier Series of Periodic Functions
The tutorial investigates the Fourier series. The resource consists of an example that shows how Fourier coefficients are calculated and an interactive applet that examines the Fourier series.
Other
Old Dominion University: Geometric Series
This site explains the geometric series. There is a link to the theory of the geometric theory.
Other
Math Pages: Mean Partial Sums of Non Convergent Series
This is a wordy and comprehensive site explaining the mean partial sums of non-convergent series.
Paul Dawkins
Paul's Online Notes: Differential Equations
The tutorial explores differential equations. Topics examined are first order differential equations, second order differential equations, Laplace transforms, Fourier series, higher order differential equations, and systems of...
Math2
Math2.org: Series Expansion
A lengthy look at the rules and formulas of calculus Fourier series. Included topics: Fourier series of functions, remainders of Fourier series, Riemann's theorem, Parseval's theorem, arbitrary intervals, and Fourier transformations.
Cosmo Learning
Cosmo Learning: Computational Science and Engineering I
A collection of video lectures from a course reviewing linear algebra with applications to networks, structures, and estimation. Webpage includes thirty-six lectures from a professor at Massachusetts Institute of Technology. Lectures...
Interactive Mathematics
Interactive Mathematics: Vital Revision for Fourier Series
Begin your studies of the Fourier Series with this lesson. It contains information on all of the essentials of getting started, including trigonometric functions, continuity, periodic functions, and more.
Interactive Mathematics
Interactive Mathematics: Introduction to Infinite Series
This discussion on infinite series is a precursor to a lesson on the Fourier Series. The lesson uses graph comparison to distinguish between a series and an infinite series.
Interactive Mathematics
Interactive Mathematics: Line Spectrum
Using Fourier and Harmonic series, the line spectrums of functions are derived and represented on graphs. Several music examples show the connection between harmonics and sound.
Interactive Mathematics
Interactive Mathematics: Fourier Series Even & Odd Functions
After identifying even and odd functions, the process for finding the Fourier Series for these types of functions is demonstrated. Detailed examples and graphs are provided.
Interactive Mathematics
Interactive Mathematics: Full Range Fourier Series
This lesson presents the Dirichlet conditions that are required in order to represent a function as a Fourier Series. Examples are provided along with graphs of the waveforms that represent the functions.
Interactive Mathematics
Interactive Mathematics: Half Range Fourier Series
This presentation helps to identify when a function can be represented by only a half range Fourier series. It then shows how to find these series for even and odd functions.
Interactive Mathematics
Interactive Mathematics: Harmonic Analysis
Derived from the Fourier series, the harmonic series can be used to represent even and odd functions. Definitions of second and third harmonics are also provided.