Author | Gander, Walter. author |
---|---|
Title | Solving Problems in Scientific Computing Using Maple and MATLABยฎ [electronic resource] / by Walter Gander, Jiลรญ Hลebรญฤek |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1995 |
Edition | Second, Expanded Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-97619-3 |
Descript | XV, 318 p. 15 illus. online resource |
1. The Tractrix and Similar Curves -- 1.1 Introduction -- 1.2 The Classical Tractrix -- 1.3 The Child and the Toy -- 1.4 The Jogger and the Dog -- 1.5 Showing the Motions with Matlab -- References -- 2. Trajectory of a Spinning Tennis Ball -- 2.1 Introduction -- 2.2 Maple Solution -- 2.3 Matlab Solution -- References -- 3. The Illumination Problem -- 3.1 Introduction -- 3.2 Finding the Minimal Illumination Point on a Road -- 3.3 Varying h2 to Maximize the Illumination -- 3.4 Optimal Illumination -- 3.5 Conclusion -- References -- 4. Orbits in the Planar Three-Body Problem -- 4.1 Introduction -- 4.2 Equations of Motion in Physical Coordinates -- 4.3 Global Regularization -- 4.4 The Pythagorean Three-Body Problem -- 4.5 Conclusions -- References -- 5. The Internal Field in Semiconductors -- 5.1 Introduction -- 5.2 Solving a Nonlinear Poisson Equation Using MAPLE -- 5.3 Matlab Solution -- References -- 6. Some Least Squares Problems -- 6.1 Introduction -- 6.2 Fitting Lines, Rectangles and Squares in the Plane -- 6.3 Fitting Hyperplanes -- References -- 7. The Generalized Billiard Problem -- 7.1 Introduction -- 7.2 The Generalized Reflection Method -- 7.3 The Shortest Trajectory Method -- 7.4 Examples -- 7.5 Conclusions -- References -- 8. Mirror Curves -- 8.1 The Interesting Waste -- 8.2 The Mirror Curves Created by MAPLE -- 8.3 The Inverse Problem -- 8.4 Examples -- 8.5 Conclusions -- References -- 9. Smoothing Filters -- 9.1 Introduction -- 9.2 Savitzky-Golay Filter -- 9.3 Least Squares Filter -- References -- 10. The Radar Problem -- 10.1 Introduction -- 10.2 Converting Degrees into Radians -- 10.3 Transformation of Geographical into Geocentric Coordinates -- 10.4 The Transformations -- 10.5 Final Algorithm -- 10.6 Practical Example -- References -- 11. Conformai Mapping of a Circle -- 11.1 Introduction -- 11.2 Problem Outline -- 11.3 Maple Solution -- References -- 12. The Spinning Top -- 12.1 Introduction -- 12.2 Formulation and Basic Analysis of the Solution -- 12.3 The Numerical Solution -- References -- 13. The Calibration Problem -- 13.1 Introduction -- 13.2 The Physical Model Description -- 13.3 Approximation by Splitting the Solution -- 13.4 Conclusions -- References -- 14. Heat Flow Problems -- 14.1 Introduction -- 14.2 Heat Flow through a Spherical Wall -- 14.3 Non Stationary Heat Flow through an Agriculture Field -- References -- 15. Modeling Penetration Phenomena -- 15.1 Introduction -- 15.2 Short description of the penetration theory -- 15.3 The Tate โ Alekseevskii model -- 15.4 The eroding rod penetration model -- 15.5 Numerical Example -- 15.6 Conclusions -- References -- 16. Heat Capacity of System of Bose Particles -- 16.1 Introduction -- 16.2 Maple Solution -- References -- 17. Free Metal Compression -- 17.1 Introduction -- 17.2 Disk compression -- 17.3 Compression of a metal prism -- 17.4 Conclusions -- References -- 18. Gauss Quadrature -- 18.1 Introduction -- 18.2 Orthogonal Polynomials -- 18.3 Quadrature Rule -- 18.4 Gauss Quadrature Rule -- 18.5 Gauss-Radau Quadrature Rule -- 18.6 Gauss-Lobatto Quadrature Rule -- 18.7 Weights -- 18.8 Quadrature Error -- References -- 19. Symbolic Computation of Explicit Runge-Kutta Formulas -- 19.1 Introduction -- 19.2 Derivation of the Equations for the Parameters -- 19.3 Solving the System of Equations -- 19.4 The Complete Algorithm -- 19.5 Conclusions -- References -- 20. Transient Response of a Two-Phase Half-Wave Rectifier -- 20.1 Introduction -- 20.2 Problem Outline -- 20.3 Difficulties in Applying Conventional Codes and Software Packages -- 20.4 Solution by Means of Maple -- References -- 21. Circuits in Power Electronics -- 21.1 Introduction -- 21.2 Linear Differential Equations with Piecewise Constant Coefficients -- 21.3 Periodic Solutions -- 21.4 A matlab Implementation -- 21.5 Conclusions -- References