Page 9 - Numerical Analysis Using MATLAB and Excel

5.13 Exercises............................................................................................................... 5−47
5.14 Solutions to End−of−Chapter Exercises............................................................... 5−49

MATLAB Computations: Pages 5−11, 5−13 through 5−14, 5−16 through 5−17,
5−19, 5−23, 5−33 through 5−35, 5−37,
5−49 through 5−53, 5−55

6 Fourier, Taylor, and Maclaurin Series 6−1
6.1 Wave Analysis ........................................................................................................6−1
6.2 Evaluation of the Coefficients ...............................................................................6−2
6.3 Symmetry ...............................................................................................................6−7
6.4 Waveforms in Trigonometric Form of Fourier Series .........................................6−12
6.5 Alternate Forms of the Trigonometric Fourier Series .........................................6−25
6.6 The Exponential Form of the Fourier Series .......................................................6−29
6.7 Line Spectra .........................................................................................................6−33
6.8 Numerical Evaluation of Fourier Coefficients .....................................................6−36
6.9 Power Series Expansion of Functions ..................................................................6−40
6.10 Taylor and Maclaurin Series ................................................................................6−41
6.11 Summary ..............................................................................................................6−48
6.12 Exercises ..............................................................................................................6−51
6.13 Solutions to End−of−Chapter Exercises ..............................................................6−53
MATLAB Computations: Pages 6−35, 6−45, 6−58 through 6−61
Excel Computations: Pages 6−37 through 6−39

7 Finite Differences and Interpolation 7−1

7.1 Divided Differences ...............................................................................................7−1
7.2 Factorial Polynomials .............................................................................................7−6
7.3 Antidifferences ...................................................................................................7−12
7.4 Newton’s Divided Difference Interpolation Method .........................................7−15
7.5 Lagrange’s Interpolation Method ........................................................................7−17
7.6 Gregory−Newton Forward Interpolation Method ..............................................7−19
7.7 Gregory−Newton Backward Interpolation Method ...........................................7−21
7.8 Interpolation with MATLAB .............................................................................7−24
7.9 Summary .............................................................................................................7−39
7.10 Exercises .............................................................................................................7−44
7.11 Solutions to End−of−Chapter Exercises .............................................................7−45
MATLAB Computations: Pages 7−8 through 7−9, 7−13 through 7−15,
7−26 through 7−38, 7−45 through 7−46,
7−48, 7−50, 7−52
Excel Computations: Pages 7−17 through 7−19, 7−22 through 7−25, 7−49, 7−52

Numerical Analysis Using MATLAB® and Excel®, Third Edition iii
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