MATLAB Mathematics - SERC - Index of
MATLAB Mathematics - SERC - Index of MATLAB Mathematics - SERC - Index of
2 Polynomials and Interpolation Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Polynomial Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Representing Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 Polynomial Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 Characteristic Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4 Polynomial Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4 Convolution and Deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 Polynomial Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 Polynomial Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6 Partial Fraction Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9 Interpolation Function Summary . . . . . . . . . . . . . . . . . . . . . . . . 2-9 One-Dimensional Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . 2-10 Two-Dimensional Interpolation . . . . . . . . . . . . . . . . . . . . . . . . 2-12 Comparing Interpolation Methods . . . . . . . . . . . . . . . . . . . . . . 2-13 Interpolation and Multidimensional Arrays . . . . . . . . . . . . . . 2-15 Triangulation and Interpolation of Scattered Data . . . . . . . . . 2-18 Tessellation and Interpolation of Scattered Data in Higher Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26 Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-37 3 Fast Fourier Transform (FFT) Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2 Finding an FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2 Example: Using FFT to Calculate Sunspot Periodicity . . . . . . . 3-3 Magnitude and Phase of Transformed Data . . . . . . . . . . . . . 3-7 FFT Length Versus Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9 ii Contents
Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10 4 Function Functions Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2 Representing Functions in MATLAB . . . . . . . . . . . . . . . . . . . . 4-3 Plotting Mathematical Functions . . . . . . . . . . . . . . . . . . . . . . . 4-5 Minimizing Functions and Finding Zeros . . . . . . . . . . . . . . . 4-8 Minimizing Functions of One Variable . . . . . . . . . . . . . . . . . . . . 4-8 Minimizing Functions of Several Variables . . . . . . . . . . . . . . . . 4-9 Fitting a Curve to Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10 Setting Minimization Options . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13 Output Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14 Finding Zeros of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21 Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-25 Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26 Numerical Integration (Quadrature) . . . . . . . . . . . . . . . . . . . 4-27 Example: Computing the Length of a Curve . . . . . . . . . . . . . . 4-27 Example: Double Integration . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28 Parameterizing Functions Called by Function Functions 4-30 Providing Parameter Values Using Nested Functions . . . . . . 4-30 Providing Parameter Values to Anonymous Functions . . . . . . 4-31 5 Differential Equations Initial Value Problems for ODEs and DAEs . . . . . . . . . . . . . . 5-2 ODE Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 iii
- Page 1 and 2: MATLAB® The Language of Technical
- Page 3: Revision History June 2004 First pr
- Page 8 and 9: Introduction to Initial Value ODE P
- Page 10 and 11: vi Contents
- Page 12 and 13: 1 Matrices and Linear Algebra Funct
- Page 14 and 15: 1 Matrices and Linear Algebra Matri
- Page 16 and 17: 1 Matrices and Linear Algebra Addin
- Page 18 and 19: 1 Matrices and Linear Algebra If x
- Page 20 and 21: 1 Matrices and Linear Algebra y = v
- Page 22 and 23: 1 Matrices and Linear Algebra Vecto
- Page 24 and 25: 1 Matrices and Linear Algebra backs
- Page 26 and 27: 1 Matrices and Linear Algebra If A
- Page 28 and 29: 1 Matrices and Linear Algebra You c
- Page 30 and 31: 1 Matrices and Linear Algebra 0.9 0
- Page 32 and 33: 1 Matrices and Linear Algebra Inver
- Page 34 and 35: 1 Matrices and Linear Algebra X = p
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- Page 42 and 43: 1 Matrices and Linear Algebra In co
- Page 44 and 45: 1 Matrices and Linear Algebra Matri
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Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10<br />
4<br />
Function Functions<br />
Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2<br />
Representing Functions in <strong>MATLAB</strong> . . . . . . . . . . . . . . . . . . . . 4-3<br />
Plotting Mathematical Functions . . . . . . . . . . . . . . . . . . . . . . . 4-5<br />
Minimizing Functions and Finding Zeros . . . . . . . . . . . . . . . 4-8<br />
Minimizing Functions <strong>of</strong> One Variable . . . . . . . . . . . . . . . . . . . . 4-8<br />
Minimizing Functions <strong>of</strong> Several Variables . . . . . . . . . . . . . . . . 4-9<br />
Fitting a Curve to Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10<br />
Setting Minimization Options . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13<br />
Output Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14<br />
Finding Zeros <strong>of</strong> Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21<br />
Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-25<br />
Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26<br />
Numerical Integration (Quadrature) . . . . . . . . . . . . . . . . . . . 4-27<br />
Example: Computing the Length <strong>of</strong> a Curve . . . . . . . . . . . . . . 4-27<br />
Example: Double Integration . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28<br />
Parameterizing Functions Called by Function Functions 4-30<br />
Providing Parameter Values Using Nested Functions . . . . . . 4-30<br />
Providing Parameter Values to Anonymous Functions . . . . . . 4-31<br />
5<br />
Differential Equations<br />
Initial Value Problems for ODEs and DAEs . . . . . . . . . . . . . . 5-2<br />
ODE Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2<br />
iii
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