Halkos, George and Tsilika, Kyriaki
(2014):
*Perspectives on integrating a computer algebra system into advanced calculus curricula.*

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## Abstract

We introduce a topic in the intersection of symbolic mathematics and computation, concerning topics in multivariable Optimization and Dynamic Analysis. Our computational approach gives emphasis to mathematical methodology and aims at both symbolic and numerical results as implemented by a powerful digital mathematical tool, CAS software Xcas. This work could be used as guidance to develop course contents in advanced calculus curricula, to conduct individual or collaborative projects for programming related objectives, as Xcas is freely available to users and institutions. Furthermore, it could assist educators to reproduce calculus methodologies by generating automatically, in one entry, abstract calculus formulations.

Item Type: | MPRA Paper |
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Original Title: | Perspectives on integrating a computer algebra system into advanced calculus curricula |

Language: | English |

Keywords: | Symbolic computations; computer-based education; Xcas computer software. |

Subjects: | C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C88 - Other Computer Software |

Item ID: | 63898 |

Depositing User: | G.E. Halkos |

Date Deposited: | 25 Apr 2015 17:48 |

Last Modified: | 26 Sep 2019 15:59 |

References: | Chiang A. (1984). Fundamental Methods of Mathematical Economics, 3rd Edition, McGraw-Hill Book, Singapore. Halkos G.E. and K. D. Tsilika (2011a). Computing Optimality Conditions in Economic Problems, Journal of Computational Optimization in Economics and Finance, 3(3): 143-155. Halkos G.E. and K. D. Tsilika (2011b), Xcas as a Programming Environment for Stability Conditions of a Class of Linear Differential Equation Models in Economics, AIP Conference Proceedings 1389, 9th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2011), Halkidiki, Greece, 2011, pp. 1769-1772. DOI:10.1063/1.3636951. Halkos G.E, and K. D. Tsilika (2012a). Computational Techniques for Stability Analysis of a Class of Discrete Time Discrete State Dynamic Economic Models, American Journal of Applied Sciences, 9(12): 1944-1952, 2012. Halkos G.E. and K. D. Tsilika (2012b). Stability Analysis in Economic Dynamics: A Computational Approach, MPRA paper 41371. Available at http://mpra.ub.uni-muenchen.de/41371/ Halkos G.E. and K. D. Tsilika (2014a). Programming Identification Criteria in Simultaneous Equation Models, Computational Economics (Springer), DOI: 10.1007/s10614-014-9444-9. Halkos G.E. and K. D. Tsilika (2014b). A Dynamic Interface for Trade Pattern Formation in Multi-regional Multi-sectoral Input-Output Modeling, Computational Economics (Springer), DOI 10.1007/s10614-014-9466-3. Halkos G.E. and K. D. Tsilika (2014c). Analyzing and Visualizing the Synergistic Impact Mechanisms of Climate Change Related Costs, Applied Mathematics and Computation (Elsevier), 246: 586-596. Huang C. and P. Crooke (1997). Mathematics and Mathematica for Economists, Oxford Blackwell Publishers, Massachusetts. Jury E.I. (1974). Inners and Stability of Dynamic Systems, Wiley, New York. Kadry, S. and M. El Shalkamyb (2012). Toward New Vision in Teaching Calculus, IERI Procedia, 2: 548–553. Neumann M. (1979). Weak stability for matrices, Linear Multilinear Algebra, 7: 257-262. Parisse B. (2007). An Introduction to the Xcas Interface. Available at http://www-fourier.ujf-grenoble.fr/~parisse/giac/tutoriel_en.pdf Samuelson P.A. (1947). Foundations of Economic Analysis, Harvard University Press. Strang G. (1988). Linear Algebra and its Applications, 3rd Edition, Harcourt Brace Jovanovich College, Philadelphia, New York. Zhang W.B. (2005). Differential Equations, Bifurcations, and Chaos in Economics. Series on Advances in Mathematics for Applied Sciences Vol. 68, World Scientific, New Jersey. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/63898 |