Course Materials 

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The main text for this course consist of a set of notes written by Dr. Herman: Fourier and Complex Analysis. We will also use resources from the web.

• Review #1, Practice Exam #1 - Answers
• Review #2, Practice Exam #2 - Answers
• Exam Topics, 2006 Final Exam - Answers
• See Fourier Series on YouTube and Gibbs Phenomena
  or Videos on Fourier Series - Donny Lee
• Mobius Transformations Revealed on YouTube

Overview

• Prelude for Strings - The Origin of Spectral Theory

• Fourier Analysis - Short Overview

• Sound Generator

• The Physics of Sound

• Listen to Fourier Series

• MiniSpectroscopy Applet

• Specta of Elements - A Clickable Periodic Table

• Speech Analysis Tutorial

• Examples of Audio Spectrum Analysis

• Spectral Analysis of an ECG

Sequences and Infinite Series

• Class Toolbook Presentation (Needs Neuron Plugin ) series.tbk
• Tutorial on Sequences and Series from Visual Calculus
• Sequences and Series in Maple
• Overview of sequences and series - See additional material, problems and videos
• SOSMath - Sequences, Series, Geometric Series, Power Series, 

• Convergence Tests - Harvey Mudd College

• Power Series Applets

Fourier Series

• Fourier Series and Waves

• Listen to Fourier Series

• Fourier Series Applet

• Special Trigonometric Bases - Harvey Mudd College

• Products of Trigonometric Functions, also at ThinkQuest

• Fourier Series - Eric Weinstein's World of Math

• SOS Math - Fourier Series

• Fourier Series and Convergence

• Maple Worksheet - fseries.mws, EvenOdd.mws

• The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet ...- Google Books Result

• Note on Gibbs Phenomenon, 1925

• Gibbs Phenomena Applets 1, 2

Orthogonal Functions

• Orthogonal Functions - Introduction

• Special Functions

Complex Variables

• Notes on Complex Anaylsis

  • Complex Analysis - George Cain

  • Complex Analysis Notes - Harold V. McIntosh

  • Complex Analysis - The Complex Analysis Project

  • W L Chen's Notes

• The Origin of Complex Numbers

• A Short History of Complex Numbers

• Short Course on Complex Numbers

• Visualizing Complex Functions

  • Complex Function Plots - Maple

  • ComplexGrid.m, plotcomplex.m, domcol2.m - Matlab

  • Visual Complex Function Links

  • Complex Function Grapher

  • f(z) Demo

  • Fractal Explorer

• Residue Theorem and examples

• The Residue Theorem and its Applications

Dirac Delta Function

• MathWorld

• K. Bryan's The Delta Function

Fourier Transforms

• Maple File for Fourier Transforms

• Fourier Transform, Fourier Series, Discrete Fourier Transform - Eric Weinstein's World of Math

• Wikipedia Entry

• Fourier Analysis Tutorial

• An Intuitive Explanation of Fourier Theory

• MIT Opencourseware notes

• Diffraction Theory by Fourier Transforms

Laplace Transforms

• Laplace Transform Table - MS Word

• Practice Laplace Transform Problems

• Introduction to Laplace Transforms for Engineers
• Mathworld
• Tables
  • Collections of Worksheets! http://www.equationsheet.com/ 
  • http://www.vibrationdata.com/Laplace.htm 
  • eFunda: Laplace Transform Table
  • http://cnyack.homestead.com/files/alaplace/laptre.htm 
  • http://www.sosmath.com/tables/laplace/laplace.html 

Signal Analysis

• An Introduction to the Sampling Theorem

• Culling's DSP Dictionary

• Aliasing Applet

Discrete Transforms

• Mathematics of the Discrete Fourier Transform

• The Fast Fourier Transform

• DFT PDF Notes with Matlab

• Comparison of Fourier Transform, Fourier Series and DFT - Maple File

• Sampling Effects - Maple File

• Signals Talk

• Software
  • Spectrum Lab 
  • Cool Edit
  • Gold Wave
  • Audacity

MATLAB

• Basic Matlab

• Matlab TiddlyWiki - Herman

• A Matlab Tutorial

• Octave - Open Source Software that recognizes many Matlab functions

• Matlab Educational Demos

• Introduction to Computer Programming with MATLAB

• Online Tutorial

• Creating a GUI in Matlab 5

• Matlab Training Sessions

MAPLE

• Basic Maple

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