Lecture Notes on Chapter 10

Page 1 Review of Even and Odd Functions
Page 2 Some integral Formulas
Page 3 Definition of Fourier Series
Page 4 Finding a₀
Page 5 Finding a₇
Page 6 Finding b₄
Page 7 f(x) odd => a_n=0; f(x) even => b_n = 0
Page 8 Square Wave Example
Page 9 Graphs for Square Wave Example
Page 10 Triangle Wave Example
Page 11 Homework Set #9
Page 12a Application.
Page 12b continued
Page 12c graph
Page 13 Even and odd periodic extensions
Page 14 Fourier series of the even extension
Page 15 continued
Page 16 continued
Page 17 Graphs
Page 18 Graphs continued
Page 19 Graphs continued
Page 20 Wave equation
Page 21 continued
Page 22 continued
Page 23 continued
Page 24 continued
Page 25 Maple animation of vibrating string
Page 25a Maple animation of vibrating string (HTML)
Page 26 Homework Set #10
Page 27 continued
Page 28 Heat Equation (Both end points held at zero)
Page 29 Example
Page 30 Graphs
Page 30a Animation
Page 31 Heat Equation (End points held at nonzero temperatures)
Page 32 Example
Page 33 continued
Page 34 Animation of example
Page 35 Heat Equation (Insulated ends)
Page 36 continued
Page 37 continued
Page 38 Example
Page 39 continued
Page 40 Rough graphs.
Page 41 Summary of Heat Equation Problems
Page 42 Ring Problem (Optional Homework)
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