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Introduction and Review
Published in Russell L. Herman, A Course in Mathematical Methods for Physicists, 2013
There are many programming languages and software packages that can be used to determine numerical solutions to algebraic equations or differential equations. For example, CAS (Computer Algebra Systems) such as Maple and Mathematica are available. Open source packages such as Maxima, which has been around for a while, Mathomatic, and the SAGE Project, do exist as alternatives. One can use built-in routines and do some programming. The main features are that they can produce symbolic solutions. Generally, they are slow in generating numerical solutions.
Fourier and Laplace Transforms
Published in Russell L. Herman, An Introduction to Fourier Analysis, 2016
In Section 2.8 we had seen how one can use computer software to compute and plot Fourier series. In this section we show how one can use MATLAB to carry out symbolic computations for Fourier and Laplace transforms. As before, one can carry out similar computations in GNU Octave and Python. Of course, there are built-in commands in CAS systems such as Maple, Mathematica, Maxima, and SageMath.
Precalculus teachers’ perspectives on using graphing calculators: an example from one curriculum
Published in International Journal of Mathematical Education in Science and Technology, 2018
Ilyas Karadeniz, Denisse R. Thompson
Technology can play a fundamental role in education in general, and in mathematics education specifically. The graphing calculator has been an important technological tool in mathematics classrooms since its invention and introduction in 1985. A graphing calculator is a hand-held device capable of computation, graphing functions, and providing graphical and numerical solutions for equations. Today, graphing calculators can be found with or without a Computer Algebra System (CAS), which is ‘software that enhances numerical and graphic operations with tools for formal manipulation of symbolic expressions… [and that] perform[s] a wide variety of the numeric, graphic, symbolic, and logical operations that form the core components of algebra’ [1, pp. 1–2]. The most important feature of a CAS is its ability to manipulate mathematical expressions in symbolic form and return a solution in symbolic form.
Students' attitude towards computer algebra systems (CAS) and their choice of using CAS in problem-solving
Published in International Journal of Mathematical Education in Science and Technology, 2019
Research on students' use of CAS reports that students main use of CAS is pragmatic, such as efficiency and validation of answers [11–13]. On the other hand, several researchers such as Heid and Edwards have called for more epistemic use of CAS [2, p.129]. These ideal epistemic uses of CAS build upon the idea that symbolic computation can be outsourced to CAS in order to focus on concepts, mathematical modelling and interpretation of answers.