The Turing factoring of a matrix is a variation on the familiar LU decomposition of a matrix. It ... more The Turing factoring of a matrix is a variation on the familiar LU decomposition of a matrix. It allows us to introduce a factoring approach to row reduction, and if it is taught in courses, students can transfer what they know to computers with a minimum of difficulty. From the point of view of computer algebra systems, the main advantage is that special case information is not lost.
Starting in September 1999, new students at ETS were required to own the TI-92 Plus or TI-89 symb... more Starting in September 1999, new students at ETS were required to own the TI-92 Plus or TI-89 symbolic calculator and since September 2002, the Voyage 200. Looking back at these ten years of working with a computer algebra system on every student's desk, one could ask whether the introduction of this hand-held technology has really forced teachers to reassess their goals in teaching mathematics. For some teachers--in fact, fewer than expected--the answer is "yes". But what has really changed? Although some exam questions are different because students almost always have access to their calculator during tests, the curriculum is essentially the same. The power of computer algebra generally remains underused; it is considered merely a substitute for pencil and paper techniques or a way to illustrate concepts. This paper will give our personal perspective on this ten-year experiment based in part on informal discussions with colleagues as well as positive feedback from stu...
Starting in September 1999, new students at ETS were required to own the TI-92 Plus or TI-89 symb... more Starting in September 1999, new students at ETS were required to own the TI-92 Plus or TI-89 symbolic calculator and since September 2002 the Voyage 200. Looking back at these ten years of working with a computer algebra system on every student's desk, one could ask whether the introduction of this hand-held technology has really forced teachers to reassess their goals in teaching mathematics. For some teachers – in fact, fewer than expected − the answer is "yes". But what has really changed? Although some exam questions are different because students almost always have access to their calculator during tests, the curriculum is essentially the same. Many professors still continue to ignore the power of computer algebra; they consider it merely a substitute for pencil and paper techniques or a way to illustrate concepts. This paper will give our perspective on this ten-year experiment based in part on many discussions with colleagues as well as positive feedback from st...
Piecewise functions are important in applied mathematics and engineering students need to deal wi... more Piecewise functions are important in applied mathematics and engineering students need to deal with them often. In Nspire CAS, templates are an easy way to define piecewise functions; in DERIVE, linear combination of indicator functions can be used. Nspire CAS integrates symbolically any piecewise continuous function ─ and returns, as expected, an everywhere continuous antiderivative ─ as long as this function is not multiplied by another expression. DERIVE knows how to integrate sign(a x + b) f(x) where f is an arbitrary function, a and b real numbers and "sign" stands for the signum function: this is why products of a piecewise function with any other expression can be integrated symbolically. This will be the first part of our talk.
The École de technologie supérieure is an engineering school specializing in applied engineering ... more The École de technologie supérieure is an engineering school specializing in applied engineering and technology. Since 1999 fall semester, graphic calculators TI-92 Plus or TI-89 have been a compulsory purchase for every new student. This paper will give two examples of how we use these symbolic tools and will show how the calculator has changed the type of questions we ask our students. We will focus on Calculus and Differential Equations. We have been using computer algebra systems (like Derive) for 10 years now. But our students have to go to the computer labs if they want to use it. This is one of the major reasons for choosing hand-held technology like the TI-92 Plus. It can be used by the teacher and the student in order to teach and learn mathematics in a very original manner. One of our goals is to continue to teach "classical maths" with innovative approaches. This is possible if you can make use of technology in the classroom, when you need it, when you want it, ...
In most calculus textbooks, piecewise continuous functions do not constitute an important subject... more In most calculus textbooks, piecewise continuous functions do not constitute an important subject: students are rarely asked to use the fundamental theorem of calculus with a piecewise continuous integrand! But in signal analysis courses, engineering students have to deal with integrals of piecewise continuous functions, especially in the study of a (continuous) linear time invariant system, the so-called LTI system. Here is the reason: if x(t) is the input signal, then the output signal y(t) is the convolution of x(t) with the system impulse response h(t). Usually, the signals are piecewise continuous and have compact support in order to avoid convergence problems with the improper integral. The talk will show how easy it can be to perform a convolution for any compact support signal using the CAS DERIVE and its built-in indicator function (if one signal is an impulse, we can take a limit of indicator function). Then we will try to do the same using the templates of TI-Nspire CAS f...
This paper presents the experimental accuracy performance of each of the approximation expression... more This paper presents the experimental accuracy performance of each of the approximation expressions relative to the exact period for large amplitudes of a simple pendulum in the interval 0± · µ · 180±. The plots of the linearized exact period as a function of linearized formulae were carried out and relative errors in these expressions were investigated. In addition, this paper gives a clear idea how each formula approximates the exact period. Keywords: Large amplitude; simple pendulum; approximation expressions; exact period; linearization; laboratory experiment.
ACA 2014, July 9 - 12, 2014. Fordham University, New York City.
140 people attended the twentiet... more ACA 2014, July 9 - 12, 2014. Fordham University, New York City. 140 people attended the twentieth conference in this series.
The Turing factoring of a matrix is a variation on the familiar LU decomposition of a matrix. It ... more The Turing factoring of a matrix is a variation on the familiar LU decomposition of a matrix. It allows us to introduce a factoring approach to row reduction, and if it is taught in courses, students can transfer what they know to computers with a minimum of difficulty. From the point of view of computer algebra systems, the main advantage is that special case information is not lost.
Starting in September 1999, new students at ETS were required to own the TI-92 Plus or TI-89 symb... more Starting in September 1999, new students at ETS were required to own the TI-92 Plus or TI-89 symbolic calculator and since September 2002, the Voyage 200. Looking back at these ten years of working with a computer algebra system on every student's desk, one could ask whether the introduction of this hand-held technology has really forced teachers to reassess their goals in teaching mathematics. For some teachers--in fact, fewer than expected--the answer is "yes". But what has really changed? Although some exam questions are different because students almost always have access to their calculator during tests, the curriculum is essentially the same. The power of computer algebra generally remains underused; it is considered merely a substitute for pencil and paper techniques or a way to illustrate concepts. This paper will give our personal perspective on this ten-year experiment based in part on informal discussions with colleagues as well as positive feedback from stu...
Starting in September 1999, new students at ETS were required to own the TI-92 Plus or TI-89 symb... more Starting in September 1999, new students at ETS were required to own the TI-92 Plus or TI-89 symbolic calculator and since September 2002 the Voyage 200. Looking back at these ten years of working with a computer algebra system on every student's desk, one could ask whether the introduction of this hand-held technology has really forced teachers to reassess their goals in teaching mathematics. For some teachers – in fact, fewer than expected − the answer is "yes". But what has really changed? Although some exam questions are different because students almost always have access to their calculator during tests, the curriculum is essentially the same. Many professors still continue to ignore the power of computer algebra; they consider it merely a substitute for pencil and paper techniques or a way to illustrate concepts. This paper will give our perspective on this ten-year experiment based in part on many discussions with colleagues as well as positive feedback from st...
Piecewise functions are important in applied mathematics and engineering students need to deal wi... more Piecewise functions are important in applied mathematics and engineering students need to deal with them often. In Nspire CAS, templates are an easy way to define piecewise functions; in DERIVE, linear combination of indicator functions can be used. Nspire CAS integrates symbolically any piecewise continuous function ─ and returns, as expected, an everywhere continuous antiderivative ─ as long as this function is not multiplied by another expression. DERIVE knows how to integrate sign(a x + b) f(x) where f is an arbitrary function, a and b real numbers and "sign" stands for the signum function: this is why products of a piecewise function with any other expression can be integrated symbolically. This will be the first part of our talk.
The École de technologie supérieure is an engineering school specializing in applied engineering ... more The École de technologie supérieure is an engineering school specializing in applied engineering and technology. Since 1999 fall semester, graphic calculators TI-92 Plus or TI-89 have been a compulsory purchase for every new student. This paper will give two examples of how we use these symbolic tools and will show how the calculator has changed the type of questions we ask our students. We will focus on Calculus and Differential Equations. We have been using computer algebra systems (like Derive) for 10 years now. But our students have to go to the computer labs if they want to use it. This is one of the major reasons for choosing hand-held technology like the TI-92 Plus. It can be used by the teacher and the student in order to teach and learn mathematics in a very original manner. One of our goals is to continue to teach "classical maths" with innovative approaches. This is possible if you can make use of technology in the classroom, when you need it, when you want it, ...
In most calculus textbooks, piecewise continuous functions do not constitute an important subject... more In most calculus textbooks, piecewise continuous functions do not constitute an important subject: students are rarely asked to use the fundamental theorem of calculus with a piecewise continuous integrand! But in signal analysis courses, engineering students have to deal with integrals of piecewise continuous functions, especially in the study of a (continuous) linear time invariant system, the so-called LTI system. Here is the reason: if x(t) is the input signal, then the output signal y(t) is the convolution of x(t) with the system impulse response h(t). Usually, the signals are piecewise continuous and have compact support in order to avoid convergence problems with the improper integral. The talk will show how easy it can be to perform a convolution for any compact support signal using the CAS DERIVE and its built-in indicator function (if one signal is an impulse, we can take a limit of indicator function). Then we will try to do the same using the templates of TI-Nspire CAS f...
This paper presents the experimental accuracy performance of each of the approximation expression... more This paper presents the experimental accuracy performance of each of the approximation expressions relative to the exact period for large amplitudes of a simple pendulum in the interval 0± · µ · 180±. The plots of the linearized exact period as a function of linearized formulae were carried out and relative errors in these expressions were investigated. In addition, this paper gives a clear idea how each formula approximates the exact period. Keywords: Large amplitude; simple pendulum; approximation expressions; exact period; linearization; laboratory experiment.
ACA 2014, July 9 - 12, 2014. Fordham University, New York City.
140 people attended the twentiet... more ACA 2014, July 9 - 12, 2014. Fordham University, New York City. 140 people attended the twentieth conference in this series.
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Papers by Michel Beaudin
140 people attended the twentieth conference in this series.
140 people attended the twentieth conference in this series.