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Maple in mathematics education and research : 4th Maple Conference, MC 2020, Waterloo, Ontario, Canada, November 2-6, 2020, Revised selected papers / / Robert M. Corless, Jurgen Gerhard, Ilias S. Kotsireas (editors)
| Maple in mathematics education and research : 4th Maple Conference, MC 2020, Waterloo, Ontario, Canada, November 2-6, 2020, Revised selected papers / / Robert M. Corless, Jurgen Gerhard, Ilias S. Kotsireas (editors) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (474 pages) |
| Disciplina | 510.285 |
| Collana | Communications in Computer and Information Science Ser. |
| Soggetto topico | Mathematics - Data processing |
| ISBN | 3-030-81698-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword -- Preface -- Organization -- Contents -- Keynote Presentation -- Bohemian Matrices: Past, Present and Future -- 1 Introduction and Terminology -- 2 The Past -- 3 The Present -- 4 The Future -- References -- Accepted Papers Alphabetically by Author -- The TruncatedSeries Package for Solving Linear Ordinary Differential Equations Having Truncated Series Coefficients -- 1 Introduction -- 2 Short Specification of the Package -- 3 LaurentSolution -- 4 RegularSolution -- 5 FormalSolution -- References -- Computation of the Observed Spectral Sequence Spectrum for Nucleotide Sequence Alignments -- 1 Phylogenetic Reconstruction -- 1.1 Introduction -- 1.2 Problem Statement -- 1.3 Definitions -- 1.4 Existence of Gaps -- 2 Procedures -- 2.1 Computation of the Observed Spectral Sequence Spectrum -- 2.2 Filling the Gaps of an Alignment -- 3 Real Application -- 3.1 Molecular Data -- 4 Conclusions -- References -- Multivariate Power Series in Maple -- 1 Introduction -- 2 Background -- 2.1 Power Series -- 2.2 Univariate Polynomials over Power Series -- 3 An Overview of the User-Interface -- 4 Design Principles -- 4.1 Lazy Evaluation -- 4.2 Maple Data Structures and Built-in Functions -- 4.3 Maple Objects -- 5 Implementation of MultivariatePowerSeries -- 5.1 PowerSeriesObject -- 5.2 UnivariatePolynomialOverPowerSeriesObject -- 6 Experimentation -- 7 Conclusions and Future Work -- References -- Bernoulli's Problem x^y=y^x and Maple -- 1 Bernoulli's Problem -- 1.1 Comparing Solutions -- 2 A Class of Simplifications -- 2.1 Limitations to Simplification -- 3 Implementation -- 3.1 The Argument -- 3.2 Testing Simplification -- 3.3 Option Parametric -- 4 Concluding Remarks -- References -- Student Satisfaction Determinants in Hybrid Learning Environments Based on MAPLE -- 1 Introduction -- 1.1 Necessities of Pre-courses in Mathematics.
1.2 Knowledge Gap and Challenges in Mathematics -- 2 Digital Bridge Course Mathematics -- 2.1 General Course Structure -- 2.2 Self-study Materials Using Möbius Courseware and MAPLE -- 2.3 Student's Experience -- 3 Acquired Experiences and Knowledge -- 3.1 Course Organization -- 3.2 Working with Möbius and MAPLE -- 4 Summary -- References -- Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs - A MAPLE Package -- 1 Introduction -- 2 Theoretical and Algorithmic Framework -- 2.1 Formal Puiseux Series Solutions -- 2.2 Algebraic Solutions -- 3 The Package FirstOrderSolve -- 3.1 Overview of the Software Structure -- 3.2 Description of the Software Components -- 3.3 Usage of the Package -- References -- Algebraic Aspects of a Rank Factorization Problem Arising in Vibration Analysis -- 1 Introduction -- 2 The Rank Factorization Problem -- 3 Characterization of P -- 4 Local and Global Studies of the Solution Space -- 4.1 Existence of a Local/Global Right Inverse E of B -- 4.2 Existence of a Local/Global Basis C of kerR(B.) -- References -- Computation of the L-norm of Finite-Dimensional Linear Systems -- 1 Introduction -- 2 Problem Description -- 3 Rational Univariate Representation Method -- 4 Roots Separation Method -- 5 Sturm-Habicht Method -- 6 Experiments -- 6.1 Practical Example -- 6.2 Experiments -- 7 Conclusion -- References -- A Maple Package to Deal with the Birationality of Curves and Surfaces Parametrizations -- 1 Introduction -- 2 Theoretical and Algorithmic Framework -- 2.1 The Curve Case -- 2.2 The Surface Case: A Partial Solution -- 3 The Package Luroth -- 3.1 General Description -- 3.2 Illustrative Examples -- 4 Approaching the General Case -- 5 Appendix -- References -- A Maple Implementation of the Finite Element Method for Solving Boundary-Value Problems for Systems of Second-Order Ordinary Differential Equations. 1 Introduction -- 2 The Problem Statement -- 2.1 The Boundary-Value Problems -- 2.2 Finite Element Scheme -- 3 Benchmark Calculations -- 3.1 ODE with Potential Calculated by Quantum Chemistry -- 3.2 ODE System with Piecewise Constant Potentials -- 4 Conclusion -- A Generation of IHPs on the Standard Interval -- B Calculation of the FEM Scheme Characteristics -- C FEM generation of Algebraic Eigenvalue Problem -- References -- Blends in Maple -- 1 Introduction -- 1.1 The Basic Formula -- 1.2 Applications -- 1.3 Initial Examples -- 2 Truncation Error and Rounding Error -- 2.1 Conditioning and the Lebesgue Function -- 3 Integration of a Blend -- 4 Horner Form -- 4.1 ``Automatic'' Differentiation -- 4.2 User Interface Considerations -- 5 Testing and Timing -- 6 Future Work -- References -- Certified Evaluations of Hölder Continuous Functions at Roots of Polynomials -- 1 Introduction -- 2 Hölder Continuous Functions -- 2.1 Polynomials -- 2.2 Rational Functions -- 3 Certification of Roots -- 4 Certified Evaluations -- 5 Implementation and Examples -- 5.1 Critical Values -- 5.2 Comparison with Ball Arithmetic -- 5.3 Extending with Custom Hölder Information Procedures -- 5.4 Benchmarking -- 6 Application to Prove Non-negativity -- 6.1 Classification of Roots -- 6.2 Certification of Non-negativity -- 7 Conclusion -- A Appendix -- References -- Maple for Distance Education in Secondary Schools During the COVID-19 Emergency -- 1 Introduction -- 2 Methodologies -- 3 Results -- 3.1 Descriptive Analysis -- 3.2 Classification of Worksheets into Five Categories -- 3.3 Representative Examples of the Various Categories of Worksheet -- 3.4 Analysis of Student Participation -- 4 Conclusion -- References -- Development of Problem Solving Skills with Maple in Higher Education -- 1 Introduction -- 1.1 Outline of the Research -- 2 State of the Art. 3 Problem Solving Inside University Modules -- 4 Methodology -- 5 Results -- 6 Examples -- 7 Conclusion -- References -- Modelling and Sensitivity Analysis of Nonlinear Firefighting Systems Using Maple -- 1 Introduction -- 2 One-at-a-Time Sensitivity Study Using Fuzzy Logic -- 3 Modelling and Sensitivity Study of Nonlinear Fire Truck Suspension Models -- 3.1 Heavy-Duty Fire Truck -- 3.2 Double Cabin Fire Truck -- 4 Conclusions and Further Research Tasks -- References -- Merging Maple and GeoGebra Automated Reasoning Tools -- 1 GeoGebra's Automated Reasoning Tools -- 2 The Symbolic Computation Background: Basic Facts -- 3 Using Maple in Automated Reasoning in Elementary Geometry -- 4 Conclusions -- References -- AGADE-A Maple Package for Computing Rational General Solutions of Parametrizable First-Order Algebraic ODEs -- 1 Introduction -- 2 Preliminaries -- 3 Algorithms for Parametrizable AODEs -- 3.1 Surface-Parametrizable AODEs -- 3.2 Curve-Parametrizable AODEs -- 3.3 Special Case for Autonomous AODEs -- 3.4 Planar Rational Systems -- 4 The Maple Package AGADE -- 5 Conclusion and Outlook -- References -- Estimation of Travel Time for Additional Metrobus Route -- 1 Introduction -- 2 Some Elements of the State of Art -- 3 Proposal of Metrobus Routes -- 4 The Model to Document the Proposal -- 4.1 Travel Time for Proposed Routes -- 5 Maple Algorithm for the Model -- 6 Results and Discussion -- 7 Conclusive Notes -- References -- Understanding Math Concepts in Music and Vice-Versa -- 1 Introduction -- 2 Basic Terms/Math -- 3 Basic Terms/Music -- 4 Pitch Frequencies and Tuning -- 5 Creating Notes in Maple -- 6 Counterpoint -- References -- Numerical Solution for Radial Distortion Rectification in Optical Systems -- 1 Introduction -- 2 Direct and Inverse Warp Process Transformation. 3 Numerical Solution Algorithm for Radial Distortion Parameters with Gauss-Newton Approach -- 4 Results -- 5 Discussion -- 6 Conclusion -- A Homogeneous coordinates -- A.1 Correspondence Between Planes -- A.2 Homogeneous Coordinates and DLT Maple Listings -- B Support Functions Maple Listings -- C Numerical Solution for Radial Distortion Maple Listings -- References -- A Simplified Introduction to Virus Propagation Using Maple's Turtle Graphics Package Suitable for Children -- 1 Introduction -- 1.1 Turtle Geometry and Logo Programming Language -- 1.2 Other Implementations of Turtle Geometry -- 2 Revisiting the 1994 Maple Implementation of Turtle Geometry -- 2.1 Main Procedures of the Implementation -- 2.2 List of Commands Implemented in Maple -- 2.3 Available Information About the Status of the Turtle -- 2.4 Examples of the Use of the Turtle Geometry Maple Package -- 3 The Origin of this Work -- 4 The Original Tale (Scratch 3 Version) -- 5 The Maple Version of the Tale -- 6 Conclusions -- References -- A Maple Toolchain for Rigid Body Dynamics of Serial, Hybrid and Parallel Robots -- 1 Introduction and State of the Art -- 2 Comparison of Existing Toolboxes for Robot Dynamics -- 3 Robot Dynamics and Unit Testing Framework -- 3.1 Serial-Link Robots -- 3.2 Serial-Hybrid Robots -- 3.3 Parallel Robots -- 4 Description of the Proposed Toolchain -- 5 Application to a Model Database Framework -- 6 Conclusion -- References -- Rational Trigonometry Using Maple -- 1 Norman J. Wildberger's Dream -- 2 Re-definitions (Vector Version) -- 2.1 Quadrance -- 2.2 Spread -- 3 Five Laws for Rational Trigonometry -- 3.1 Pythagoras' Theorem (PT) -- 3.2 Triple Quad Formula (TQF) -- 3.3 Cross Law (CL) -- 3.4 Spread Law (SL) -- 3.5 Triple Spread Formula (TSF) -- 4 An Application -- 4.1 The Rational Way -- 4.2 The Transcendent Way -- 5 Conclusion -- References. Power Series Representations of Hypergeometric Type Functions. |
| Record Nr. | UNISA-996464498803316 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Maple in Mathematics Education and Research : 4th Maple Conference, MC 2020, Waterloo, Ontario, Canada, November 2–6, 2020, Revised Selected Papers / / edited by Robert M. Corless, Jürgen Gerhard, Ilias S. Kotsireas
| Maple in Mathematics Education and Research : 4th Maple Conference, MC 2020, Waterloo, Ontario, Canada, November 2–6, 2020, Revised Selected Papers / / edited by Robert M. Corless, Jürgen Gerhard, Ilias S. Kotsireas |
| Edizione | [1st ed. 2021.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2021 |
| Descrizione fisica | 1 online resource (474 pages) |
| Disciplina | 510.285 |
| Collana | Communications in Computer and Information Science |
| Soggetto topico |
Application software
Computer science—Mathematics Mathematics—Data processing Image processing—Digital techniques Computer vision Artificial intelligence Computer and Information Systems Applications Mathematical Applications in Computer Science Computational Mathematics and Numerical Analysis Computer Imaging, Vision, Pattern Recognition and Graphics Artificial Intelligence |
| ISBN | 3-030-81698-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Bohemian Matrices: Past, Present and Future -- The TruncatedSeries Package for Solving Linear Ordinary Differential Equations Having Truncated Series Coefficients -- Computation of the Observed Spectral Sequence Spectrum for Nucleotide Sequence Alignments -- Multivariate Power Series in Maple -- Bernoulli's problem x^y=y^x and Maple -- Student satisfaction determinants in hybrid learning environments based on MAPLE -- Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs -- A MAPLE Package -- Algebraic Aspects of a Rank Factorization Problem Arising in Vibration Analysis -- Computation of the L∞-norm of finite-dimensional linear systems -- A Maple package to deal with the birationality of curves and surfaces parametrizations -- A Maple implementation of the finite element method for solving boundary-value problems for systems of second-order ordinary differential equations -- Blends in Maple -- Certified evaluations of Hölder continuous functions at roots of polynomials -- Maple for Distance Education in Secondary Schools during the Covid-19 Emergency -- Development of Problem Solving Skills with Maple in Higher Education -- Modelling and sensitivity analysis of nonlinear firefighting systems using Maple -- Merging Maple and GeoGebra Automated Reasoning Tools -- AGADE---A Maple Package for Computing Rational General Solutions of Parametrizable First-Order Algebraic ODEs -- Estimation of Travel Time for Additional Metrobus Route -- Understanding math concepts in music and vice-versa -- Numerical solution for radial distortion rectification in optical systems -- A simplified introduction to virus propagation using Maple's Turtle Graphics package suitable for children -- A Maple Toolchain for Rigid Body Dynamics of Serial, Hybrid and Parallel Robots -- Rational Trigonometry Using Maple -- Power Series Representations of Hypergeometric Type Functions -- Rational cone of norm-invariant vectors under a matrix action -- Branching out into Structural Identifiability Analysis with Maple: Interactive Exploration of Uncontrolled Linear Time-Invariant Structures -- A Maple exploration of Problem 6 of the IMO 88 -- An Isometric Embedding of the Impossible Triangle into the Euclidean Space of Lowest Dimension -- "A Poly-algorithmic Quantifier Elimination Package in Maple" Erratum. |
| Record Nr. | UNINA-9910495173103321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||