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Author Gander, Walter. author Solving Problems in Scientific Computing Using Maple and MATLABยฎ [electronic resource] / by Walter Gander, Jiล{153}รญ Hล{153}ebรญฤ{141}ek Berlin, Heidelberg : Springer Berlin Heidelberg, 1995 Second, Expanded Edition http://dx.doi.org/10.1007/978-3-642-97619-3 XV, 318 p. 15 illus. online resource

SUMMARY

Modern computing tools like Maple (symbolic computation) and MATLAB (a numeric computation and visualization program) make it possible to easily solve realistic nontrivial problems in scientific computing. In education, traditionally, complicated problems were avoided, since the amount of work for obtaining the solutions was not feasible for students. This situation has changed now, and students can be taught real-life problems that they can actually solve using the new powerful software. The reader will improve his knowledge through learning by examples and he will learn how both systems, MATLAB and Maple, may be used to solve problems interactively in an elegant way. This second edition has been expanded by two new chapters. All programs can be obtained from a server at ETH Zurich

CONTENT

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{128}{148} 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

Mathematics Programming languages (Electronic computers) Algebra System theory Algorithms Numerical analysis Statistical physics Dynamical systems Mathematics Numerical Analysis Algebra Programming Languages Compilers Interpreters Algorithms Statistical Physics Dynamical Systems and Complexity Systems Theory Control

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