# [Maxima] Maxima by Example: Ch. 7, 8, 9, 10, and 11 posted

Edwin Woollett woollett at charter.net
Wed Apr 29 18:48:22 CDT 2009

```The old chapter seven has been split into 7 plus 10 for ease of maintenance.
However, all (7 - 11) have been updated with a fancy verbatim environment
plus the latex color package to make the maxima code stand out better.
(ch. 1 - 6 remain to be updated with this style.)

New material is:
ch. 8: numerical integration,
ch. 9: bigfloats and arbitrary precision quadrature,
ch. 11 fast fourier transforms
=============
some details:

Chapter 7: Symbolic Integration

1. --mbe7sint.pdf : Apr. 29, 2009, Maxima 5.18.1, 35 pages
2. --mbe7code.txt : Copy and Paste Code: Apr. 29, 2009, Maxima 5.18.1

Chapter 7 Topics:
1. Examples of Use of Integrate,
2. Piecewise Defined Functions,
3. Area Between Curves Examples,
4. Arc Length of an Ellipse,
5. Double Integrals : Area and Moment of Inertia of an Elliptical Laminate,
6. Triple Integrals: Volume and Moment of Inertia of a Solid Ellipsoid,
7. Derivative of a Definite Integral with respect to a Parameter,
8. Integration by Parts,
9. Change of Variables

Chapter 8: Numerical Integration

1. --mbe8nint.pdf : Apr. 29, 2009, Maxima 5.18.1, 20 pages
2. --mbe8code.txt : Copy and Paste Code: Apr. 29, 2009, Maxima 5.18.1

Chapter 8 Topics:
3. Numerical Integration Decision Trees

Chapter 9: Bigfloats and Arbitrary Precision Quadrature
(A valuable feature of a computer algebra system is the ability to easily
do arithmetic to "arbitrary" precision. This chapter presents three
powerful methods of arbitrary precision quadrature, including examples
and test integrals.)

1. --mbe9bfloat.pdf : Apr. 29, 2009, Maxima 5.18.1, 31 pages
2. --mbe9code.txt : Copy and Paste Code: Apr. 29, 2009, Maxima 5.18.1
3. --fdf.mac : Apr. 29, 2009, Maxima 5.18.1
4. --qbromberg.mac : Apr. 29, 2009, Maxima 5.18.1
5. --quad_de.mac : Apr. 29, 2009, Maxima 5.18.1
6. --quad_ts.mac : Apr. 29, 2009, Maxima 5.18.1
7. --quad_gs.mac : Apr. 29, 2009, Maxima 5.18.1

Chapter 9 Topics:
1. The Use of Bigfloat Numbers in Maxima,
1.1 Bigfloat Numbers Using bfloat, fpprec, and fpprintprec.
1.2 Using print and printf with Bigfloats,
1.3 Adding Bigfloats having Differing Precision,
1.4 Polynomial Roots Using bfallroots,
1.5 Bigfloat Number Gaps and Binary Arithmetic,
1.6 Effect of Floating Point Precision on Function Evaluation,
2. Arbitrary Precision Quadrature with Maxima,
2.1 Using bromberg for Arbitrary Precision Quadrature,
2.2 A Double Exponential Quadrature Method for a <= x < inf,
2.3 The tanh-sinh Quadrature Method for a <= x <= b,
2.4 The Gauss-Legendre Quadrature Method for a <= x <= b

Chapter 10: Fourier Series, Fourier and Laplace Transforms.
(This material, which has been updated, was originally located in the
old chapter 7)

1. --mbe10fltrans.pdf : Apr. 29, 2009, Maxima 5.18.1, 38 pages
2. --mbe10code.txt : Copy and Paste Code: Apr. 29, 2009, Maxima 5.18.1

Chapter 10 Topics:
1. Fourier Series Expansion Examples,
2. Fourier Integral Transform Pair Examples,
3. Dirac Delta (Unit Impulse) Function Examples,
4. Laplace Transform Integral Examples,
5. Inverse Laplace Transform Examples and Residues

Chapter 11: The Fast Fourier Transform.
(Our Maxima package qfft.mac provides a list-based interface to Maxima's
fft.lisp.
Of particular interest is flines(...) which goes from a signal sample list
to a FFT
spectrum histogram in one step.)

1. --mbe11fft.pdf : Apr. 29, 2009, Maxima 5.18.1, 33 pages
2. --mbe11code.txt : Copy and Paste Code: Apr. 29, 2009, Maxima 5.18.1
3. --qfft.mac : Apr. 29, 2009, Maxima 5.18.1

Chapter 11 Topics:
1. FFT Spectrum of a Monochromatic Signal,
2. FFT Spectrum of a Sum of Two Monochromatic Signals,
3. FFT Spectrum of a Rectangular Wave,
4. FFT Spectrum Sidebands of a Tone Burst Before and After Filtering,
5. Fast Fourier Transforms using qfft.mac,
6. Cleaning a Noisy Signal using FFT Methods
-------------------

Ted Woollett
http://www.csulb.edu/~woollett/

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