scholarly journals The Role of Fourier Series in Mathematics and in Signal Theory

2021 ◽  
Author(s):  
Frode Rønning
Keyword(s):  
Fourier Series ◽  
Electrical Engineering ◽  
Signal Theory ◽  
Advanced Mathematics ◽  
Mathematics Courses ◽  
Anthropological Theory ◽  
Video Lectures ◽  
Historical Origin

AbstractThis paper presents a praxeological analysis, based on ATD (Anthropological Theory of the Didactic), of the topic of Fourier series, as this topic is introduced and used in mathematics and in electrical engineering, more precisely in signal theory. The analysis is based mainly on one widely used textbook in mathematics for engineers, and a textbook and video lectures in signal theory. The aim of the analysis is to investigate possible differences in the motivation for introducing Fourier series in mathematics and in signal theory, as well as differences in the techniques used, and the justifications behind the techniques. This research is inspired by previous research showing lack of connection between mathematics courses and engineering courses applying mathematics. To get a wider perspective, the exposition in the textbook in mathematics for engineers is also compared to the exposition in more advanced books in mathematics. To add to the perspective, the historical origin of Fourier series is also discussed. The findings show that there are differences in the motivation for the topic both between mathematics and signal theory, but also between basic and more advanced mathematics. Within mathematics there are also differences in the underlying theories.

scholarly journals Using Instructor-Generated Video Lectures in Online Mathematics Courses Improves Student Learning

2015 ◽  
Vol 19 (3) ◽  
Author(s):  
Jennifer Hegeman
Keyword(s):  
Student Performance ◽  
College Algebra ◽  
Educational Resources ◽  
Retention Rates ◽  
Online Homework ◽  
Mathematics Courses ◽  
Content Provider ◽  
Learning Aids ◽  
Video Lectures

Low retention rates in online freshman-level mathematics courses are a concern, especially at postsecondary institutions that serve academically unprepared students. The purpose of this study was to determine if student performance in an online College Algebra course that relies heavily on text-based multimedia tools can be improved by replacing publisher-generated educational resources with instructor-generated video lectures. The original online College Algebra course placed the publisher-generated educational resources in the role of content provider by enabling all publisher-generated learning aids within the online homework system and treating instructor-generated educational materials as supplemental resources. In contrast, the redesigned online College Algebra course enhanced the course instructor’s teaching presence by requiring students to complete instructor-generated guided note-taking sheets while watching instructor-generated video lectures, treating publisher-generated learning aids as supplemental resources by removing them from within the online homework system. Results indicate students who enrolled in a redesigned online College Algebra course that strategically placed the instructor in the role of content provider performed significantly better on both online and handwritten assessments than did students who enrolled in an online College Algebra course that placed the publisher-generated educational resources in that role.

scholarly journals Using Instructor-Generated Video Lectures in Online Mathematics Courses Improves Student Learning

2015 ◽  
Vol 19 (3) ◽  
Author(s):  
Jennifer Hegeman
Keyword(s):  
Student Performance ◽  
College Algebra ◽  
Educational Resources ◽  
Retention Rates ◽  
Online Homework ◽  
Mathematics Courses ◽  
Content Provider ◽  
Learning Aids ◽  
Video Lectures

Low retention rates in online freshman-level mathematics courses are a concern, especially at postsecondary institutions that serve academically unprepared students. The purpose of this study was to determine if student performance in an online College Algebra course that relies heavily on text-based multimedia tools can be improved by replacing publisher-generated educational resources with instructor-generated video lectures. The original online College Algebra course placed the publisher-generated educational resources in the role of content provider by enabling all publisher-generated learning aids within the online homework system and treating instructor-generated educational materials as supplemental resources. In contrast, the redesigned online College Algebra course enhanced the course instructor’s teaching presence by requiring students to complete instructor-generated guided note-taking sheets while watching instructor-generated video lectures, treating publisher-generated learning aids as supplemental resources by removing them from within the online homework system. Results indicate students who enrolled in a redesigned online College Algebra course that strategically placed the instructor in the role of content provider performed significantly better on both online and handwritten assessments than did students who enrolled in an online College Algebra course that placed the publisher-generated educational resources in that role.

scholarly journals About the “Mixture” of Discourses in the Use of Mathematics in Signal TheoryÀ propos du «mélange» de discours dans l'utilisation des mathématiques en théorie du signal

2020 ◽  
Vol 22 (4) ◽  
pp. 454-471
Author(s):  
Reinhard Hochmuth ◽  
Jana Peters
Keyword(s):  
Mathematics Education ◽  
Electrical Engineering ◽  
Signal Theory ◽  
Mathematics Courses ◽  
University Mathematics ◽  
Engineering Studies ◽  
The Third ◽  
Engineering Sciences ◽  
Introductory Mathematics ◽  
University Mathematics Education

AbstractAn important issue for research in university mathematics education is the use of mathematics in engineering. Here we focus on praxeologies in a course on system and signal theory (SST), which represents a typical module in electrical engineering studies in the third or fourth semester. In such courses, mathematics already studied in introductory mathematics courses will be applied, but also enriched by the introduction and development of new practices, in particular the so-called Dirac-impulse. We claim that the introduction and justification of the Dirac-impulse in SST is a convenient case where basic facets of epistemological relations between mathematics and engineering sciences might be illustrated and shown to be important for a detailed description and analysis of logos blocks of praxeologies. The background for our considerations regarding logos blocks of praxeologies that concern the introduction of the Dirac-impulse is given by philosophical studies by Wahsner and Borzeszkowski (1992, 2012) and a few illuminating remarks by Dirac.Keywords: Signal Theory, Dirac impulse, Epistemology, ATD.RésuméUne question importante pour la recherche en éducation mathématique universitaire est l'utilisation des mathématiques en ingénierie. Ici, nous nous concentrons sur les praxéologies dans un cours sur la théorie du système et du signal (SST), qui représente un module typique dans les études d'ingénierie électrique au troisième ou quatrième semestre. Dans ces cours, non seulement applique-t-on les mathématiques déjà enseignées et apprises dans les cours d'introduction à la mathématique, mais on introduit et utilise aussi de nouveaux concepts mathématiques, en particulier ce que l'on appelle l'impulsion de Dirac. Nous affirmons que l'introduction et la justification de l'impulsion de Dirac dans SST est un cas pratique par lequel les facettes fondamentales des relations épistémologiques entre mathématiques et ingénierie pourraient être illustrées et démontrées importantes pour la description détaillée et l’analyse des logos blocs de praxéologies. Le contexte de nos considérations au sujet des logos blocs de praxéologies concernant l'introduction de l'impulsion de Dirac est donné par des études philosophiques de Wahsner et Borzeszkowski (1992, 2012) et quelques remarques éclairantes de Dirac.Mots-clés: Théorie du signal, impulsion de Dirac, épistémologie, TAD.

scholarly journals Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ming-Sheng Hu ◽  
Ravi P. Agarwal ◽  
Xiao-Jun Yang
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Series Solution ◽  
Differential Operators ◽  
Fractional Wave Equation ◽  
Local Fractional Calculus ◽  
Vibrating String ◽  
Fractional Differential ◽  
Fractional Differential Operators

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag-Leffler function.

scholarly journals Inverted Classroom by Topic - A Study in Mathematics for Electrical Engineering Students

2014 ◽  
Vol 4 (3) ◽  
pp. 11 ◽  
Author(s):  
Isabel Braun ◽  
Stefan Ritter ◽  
Mikko Vasko
Keyword(s):  
Prior Knowledge ◽  
Positive Feedback ◽  
Engineering Students ◽  
Electrical Engineering ◽  
Exam Performance ◽  
Teaching Model ◽  
Inverted Classroom ◽  
Video Lectures ◽  
Classroom Time ◽  
Mathematics Course

The inverted classroom is a teaching model, where the students prepare for classroom by watching video lectures. The classroom time is then dedicated to individual practice. We evaluated a mathematics course for electrical engineering students throughout three semesters, where 20% of the topics were taught using the inverted classroom model. The aim was to find out whether the model can help to better address groups with large differences in prior knowledge in mathematics. We report mainly positive feedback from the students, although the opinions vary greatly between the groups. The students appreciate the increased amount of practice in the classroom as well as the possibility to learn at their own pace. Exam performance remained constant in the topics taught using the inverted classroom compared to previous semesters. The exam performance of weaker students also remained constant.

The Role of the “New” Industries in Britain during the 1930s: A Reinterpretation

1975 ◽  
Vol 49 (2) ◽  
pp. 205-222 ◽  
Author(s):  
Neil K. Buxton
Keyword(s):  
Electrical Engineering ◽  
Ferrous Metals ◽  
Non Ferrous Metals

Professor Buxton examines the importance during the 1930s of the “new” industries in Britain (vehicle manufacturing, electrical engineering, rayon, non-ferrous metals, and paper, printing, and publishing) and finds that their role has been exaggerated by earlier interpretations.

The Influence on Mathematics Test Scores, by Ethnicity and Sex, of Prior Achievement and High School Mathematics Courses

1987 ◽  
Vol 18 (3) ◽  
pp. 180-186
Author(s):  
Lyle V. Jones
Keyword(s):  
High School ◽  
Test Scores ◽  
National Sample ◽  
Expected Improvement ◽  
White Female ◽  
Advanced Mathematics ◽  
Senior Year ◽  
Mathematics Courses ◽  
Mathematics Test ◽  
Student Socioeconomic Status

Data from a national sample of high school sophomores in 1980 from the High School and Beyond project show that senior-year mathematics test scores are highly dependent on the number of courses taken in mathematics, Algebra I or above. Within each level of course taking, senior test scores are predicted reasonably well from student socioeconomic status, sophomore-year verbal test scores, and sophomore-year mathematics test scores. The results support the theses that (a) whether black or white, female or male, sophomore students with similar levels of mathematics achievement may be expected to experience similar levels of improvement by taking additional mathematics courses and (b) the expected improvement is elevated for students with four or more credits of advanced mathematics or with three credits that include calculus.

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