Variable Calculus Research Articles

Extended Stroh formalism for plane problems of thermoelasticity of quasicrystal media

This study provides a mathematical method for the analysis of plane phonon-phason thermomechanical fields in quasi-crystalline bodies, which was developed based on the complex variable calculus and the Stroh formalism. Constitutive and balance equations of thermoelasticity of quasicrystal solids are written in a generalized form using extended phonon-phason vectors and tensors. Adapting the methods of the Stroh formalism, the formulated general problem is reduced to the search for 7 analytical functions (1 for temperature and 6 for phonon-phason fields). The obtained approach was used to construct the integral equations of the corresponding two-dimensional problems of the thermoelasticity of quasicrystal solids, and on its basis a specific problem for a quasi-crystalline medium with a crack was solved. Distributions of temperature and mechanical fields in the body and functions of asymptotic distributions of phonon-phason fields near the crack tip using intensity coefficients of phonon and phason stresses were obtained.

KALMUL Software Assited by GeoGebra (A New Media for Learning Multivariable Calculus)

Multivariable calculus is one of the compulsory subjects for study programmes in the fields of science and technology. The graphical approach to of two variable calculus written in a book or board usually makes it difficult for students to understand. This research aims to build a tool for learning multivariable calculus using GeoGebra. GeoGebra provides three-dimensional visualization facilities through the GeoGebra 3D Graphing Calculator software. This software has an android application so that it can be accessed via a smart phone. This research developed learning media for multivariable calculus using GeoGebra software in the form of an android application. The lecture material is limited to multivariable derivative. The research method used in this study is research and development (R & D) with development of 4-D models (Four D) for research design. The design of this study includes four main stages, namely the definition phase, the design stage, the development stage, and the dissemination stage. The results of validating media products are in good criteria and the results of small and large scale tests are very good criteria.

Encountering ideas about teaching and learning mathematics in undergraduate mathematics courses

We study the ideas about teaching and learning mathematics that undergraduate students generate when they encounter tasks designed to embed approximations of teaching practice in mathematics courses taken by a general population of students. These tasks attend to the dual goals of developing an understanding of mathematics content and an understanding of how teachers provide classroom experiences that foster mathematics learning. The study employs a qualitative, multiple-case study methodology, with four cases bounded by the content areas of abstract algebra, single variable calculus, discrete mathematics, and introductory statistics. The data for the study come from undergraduate students’ written work on mathematical tasks, interviews with a subset of students from each course, and interviews with each instructor throughout the term during which they implemented the tasks. Our findings indicate that students identified the broad applicability of teaching skills (discussed by 32 of the 61 interviewed students), recognized the value of examining hypothetical learners’ mathematical work (discussed by 59 of the 61 interviewed students), and reported empathy for hypothetical learners (discussed by 38 of the 61 interviewed students). These findings persisted across the course content and course levels we studied, leading us to conclude that our findings can transfer to additional mathematics courses in secondary mathematics teacher preparation.

Influence of Imperfect Interface of Anisotropic Thermomagnetoelectroelastic Bimaterial Solids on Interaction of Thin Deformable Inclusions

Abstract This work studies the problem of thermomagnetoelectroelastic anisotropic bimaterial with imperfect high-temperature conducting coherent interface, whose components contain thin inclusions. Using the extended Stroh formalism and complex variable calculus, the Somigliana-type integral formulae and the corresponding boundary integral equations for the anisotropic thermomagnetoelectroelastic bimaterial with high-temperature conducting coherent interface are obtained. These integral equations are introduced into the modified boundary element approach. The numerical analysis of new problems is held and results are presented for single and multiple inclusions.

Is economics STEM? Process of (re)classification, requirements, and quantitative rigor

From 2012 to 2019, the proportion of undergraduate economics degrees denoted as “Econometrics and Quantitative Economics” (STEM-eligible) conferred annually increased from 1 percent to 22 percent. The authors present results from a survey of the 73 institutions conferring at least one STEM-eligible economics degree in 2017 or 2018. They find that most institutions (59%) offer both traditional and STEM-eligible degrees and report needing departmental, college/university committee, and provost/dean approval to (re-)classify. The main motivation for this change is maintaining consistency with an increasingly quantitative discipline (73%). The significant differences in requirements between STEM-eligible and traditional economics degrees are the proportion requiring single variable calculus (91% vs. 69%), multivariable calculus (70% vs. 31%), linear algebra (48% vs. 21%), basic econometrics (96% vs. 77%), and advanced econometrics (48% vs. 8%).

An Unorthodox Approach to Skinning a Definite Integral

Summary In this article we showed how the following improper real integral I n = ∫ 0 ∞ d x x n + 1 = π / n sin π / n which is typically evaluated using complex variables and contour integration for general n can actually be evaluated using the integration by partial fractions technique of single variable Calculus.

The Effectiveness of Hybrid Learning in Improving of Teacher-Student Relationship in Terms of Learning Motivation

The Advanced Mathematical Thinking (AMT) ability is one of the prioritized mathematical abilities needed to be developed in learning mathematics during tertiary education. The present study sought to test the effectiveness of hybrid learning in improving students' advanced mathematical thinking. The research used a quasi-experimental design with a non-equivalent control group design. The subject of this study was students of a mathematics education study program at a university in Bandung who attended lecture for the multi-variable in a calculus course. The sampling technique used was purposive sampling. Of the many variable calculus classes consisting of 2 classes, one class was chosen as the experiment group and the other class as the control group. The sample consists of 40 people for each group. Data analysis used the MANOVA test with normality and homogeneity tests as a prerequisite test. The results showed a difference in AMT's significance between the hybrid learning and conventional groups, where hybrid learning had a higher AMT. Other than that, there is a difference in the significance of AMT between the high motivation group and the low motivation group, where high motivation has a higher AMT, and there is an interaction of learning models and motivational factors to increase AMT. Doi: 10.28991/esj-2021-01288 Full Text: PDF

Strategy on The Effectiveness of Learning Outcomes of Manufacturing Calculus Using Edlink in The Covid-19 Pandemic

The Covid-19 pandemic in Indonesia has resulted in a change in the learning implementation system at IKIP Muhammadiyah Maumere, carried out face-to-face. Even so, the EdLink platform's presence in the learning system at IKIP Muhammadiyah Maumere can be a solution by providing easy online learning offers for lecturers and students. Therefore, this study aims to analyze the strategies for learning achievement effectiveness during the pandemic in the variable calculus course using the EdLink platform. This research uses qualitative descriptive data, with the target of testing is mathematics education students in semester 5 and semester 7 with a total of 29 students. The research scale used is the percentage score of the effectiveness of learning outcomes. The assessment scale uses an item scale with a score of 0-100 to assess students towards lecturers. Whereas the student questionnaire used a Likert scale with a score of 1-4. The results showed that the students enthusiastically joined the variable calculus class using the EdLink application. The results showed that for student learning outcomes and the assessment questionnaire results, EdLink was effectively applied during the Covid-19 pandemic.

A Case Study of Teaching Single Variable Calculus Traditionally vs. Virtually: A Semester Bifurcated

The pedagogical discussion between the merits of traditional learning versus online learning provides much discussion from both camps. Following the Coronavirus of 2019 pandemic in the spring of 2020, undergraduate students enrolled in the freshman Single Variable Calculus course at the United States Military Academy at West Point were forced to switch from traditional, in-person classes to learning virtually at the half-way mark of the semester. This provides an interesting case study, showing the dichotomy of a semester bifurcated; half of a semester in a traditional classroom and the other half in an online one. Comparing the transition and techniques of analogous approaches to a virtual learning experience, the framework of dynamic and static teaching approaches is explored through analytic reflection.

MELITOPOL SCHOOL OF APPLIED GEOMETRY. HISTORY AND WORK EXPERIENCE

The work examines the history of formation, development and the main scientific works of the Melitopol School of Applied Geometry. The materials give a general characteristic of the main scientific directions of the school: variable discrete geometric modeling (VDGM) and point calculus Balyub-Naidish (BN calculus). The materials cover the list and peculiarities of scientific and organizational measures carried out by scientists of the school. The scientific school of applied geometry was founded by Meer Moiseevich Yuditsky in the 60s of the last century. The active personal, scientific and organizational activities of M. M. Yuditsky, the participation of scientists of the department in conferences and seminars of various levels, the defense of dissertations that took place in subsequent years gave the basis for the formation of a regional scientific center for applied geometry on the basis of the department. In 1977, Vladimir Mikhailovich Naydysh became the head of the school, which was called the Melitopol Scientific School of Applied Geometry. One of the significant results of the work of the school and its head personally is the holding in Melitopol of the annual International Scientific and Practical Conference "Modern Problems of Geometric Modeling" (held since 1994). The main scientific direction of the school is the development of the theory and applied aspects of discrete applied geometry. Since 2007, Andrei Vladimirovich Naydysh, Doctor of Technical Sciences, took over the leadership of the scientific school. Today, the basic institution of higher education for the school is the Bogdan Khmelnitsky Melitopol State Pedagogical University. Materials The modern state of the school, the level of its scientific developments, the personal achievements of the school's specialists give reason to consider the Melitopol School of Applied Geometry as having all the features of a scientific school by type - a school as a research team.

A Collaborative Approach to Coordinating Calculus 1 to Improve Student Outcomes

ABSTRACT Faced with students failing to complete Calculus 1 at rates of almost 50%, the Department of Mathematics at Western Michigan University addressed the lack of progression of STEM majors through this gateway course and, thus, through their intended majors. In this case study, we describe the four-year process of redesigning our single variable Calculus 1 course. We coordinated instruction with a changing, highly collaborative instructional team of faculty and graduate students. Conversations among team members have been driving changes in instruction and assessment, and collaborative coordination is helping institutionalize the successful elements of the redesign. At the end of the paper, we describe the major take-aways we have gained as a result of this experience.

The Secondary-Tertiary Transition in Mathematics: What High School Teachers Do to Prepare Students for Future Success in College-Level Calculus

Quantitative analysis of the Factors Influencing College Success in Mathematics (FICSMath) Survey data indicates that high school mathematics teachers’ abilities to teach for conceptual understanding is a significant and positive predictor of student performance in single- variable college calculus. To explore these findings further, we gathered and analyzed interview data gained from a representative sample of high school precalculus teachers from across the U.S., identified by their students as requiring high levels of conceptual understanding (n = 13). Seventeen themes were identified and then combined into five overarching phenomenological themes. These overarching themes suggest that teachers who teach for high conceptual understanding (a) support relational understanding during problem solving, (b) require students to learn how to study to build on prior knowledge and learn from mistakes, (c) use mathematical language and ask critical questions to support learning, (d) focus on content knowledge necessary to make connections, and (e) use technology to support learning concepts but limit calculator use. Comparison of these results to quantitative findings further illuminate that intentional development of disciplinary knowledge, cognition, and language are noteworthy points of intersection for teachers and researchers alike.

Pengembangan Bahan Ajar Kalkulus Peubah Banyak Berbantuan Software Geogebra Bagi Mahasiswa Pendidikan Matematika

Variable calculus is a subject that requires students to have high mastery and competence. This is because the material presented requires students to think critically and creatively to solve problems. In fact the results of the previous semester's assessment analysis, the percentage of students who graduated with grades A or B was very low. The research method is research and development, with ADDIE development stages, namely Analysis, Design, Development, Implementation, and Evaluation. The results of the needs analysis showed that students need teaching material for calculus variable which is assisted by a technology of mathematical applications, where students' opinions on the need for a mathematical application such as geogebra software in learning, there are 66.7% of students strongly agree, and there are 33.3% agree . The validation results show that the average of all aspects of the assessment of teaching materials obtained an average of 4.29 means that the teaching materials are valid. The results of the practicality questionnaire analysis of the 20 students who took the lecture obtained an overall average of 4.28, which means practical. The results of student responses to the teaching material questionnaire from the aspects of teaching materials and learning activities obtained an average percentage of total positive responses of students amounted to 81.67% meaning that teaching materials are effectively used by students in learning

English-medium instruction Calculus in Confucian-Heritage Culture: Flipping the class or overriding the culture?

We discuss the flipped classroom implementation for a Single Variable Calculus (SVC) course in a Confucian Heritage Culture (CHC) environment. A theoretical framework is composed of Bloom's taxonomy, English-medium instruction (EMI) and technology adaptation. Four different types of instructions were designed, three were flipped and one acts as a control. We investigate both quantitative and qualitative aspects of the pedagogy. Quantitative analysis indicates a statistically significant difference in the exam scores between fully-flipped and single-topic flipped instruction as determined by one-way ANOVA (F(3, 306) = 2.67, p = 0.0477) with a small practical significance of the effect size (η2 = 0.0255). Qualitative findings suggest that although students’ engagement and communication with instructors have been enhanced, some challenges related to language and culture, along with minimizing competition and learning about a new technological tool persist.

EFEKTIVITAS PENGGUNAAN MODEL PEMBELAJARAN DISCOVERY LEARNING TERHADAP HASIL BELAJAR MAHASISWA MATA KULIAH KALKULUS PEUBAH BANYAK

Abstract. Student activity will affect effectiveness for student learning outcomes. The effectiveness of learning consists of four indicators, namely the quality of instruction, the suitability appropriate level of instruction, incentive, and time. The purpose of this study is to: (1) Know how the effectiveness of student learning outcomes in variable calculus subjects after getting learning with discovery learning learning models. (2) Knowing whether there is an increase in student learning outcomes in many variable calculus subjects after getting learning with discovery learning learning models. The data analysis techniques are carried out from the data description test stage, then the prerequisite test is the normality and linearity test, then test the hypothesis. The steps in the study are as follows: (1) The researcher provides a stimulus for the sample class, namely the discovery learning model; (2) At the time of the learning process the partner lecturers see the activity, student learning; (3) Provide essay tests to see the level of success of students in learning; (4) Perform statistical tests to see the effectiveness of student learning outcomes using discovery learning learning models. The results of this study are that there is an effect on the effectiveness of mathematics learning using the discovery learning model of student learning outcomes in many variable calculus subjects, and there is an increase in student learning outcomes after learning with discovery learning models of many variable calculus subjects as much as 20.53.Keywords: Discovery Learning, Learning Outcomes, Calculus

Energy Efficient Design of Wireless Sensor Network: Clustering

One of the significant criteria of wireless sensor network is energy efficiency. Focused on the energy problem, researchers design a few algorithms based on clustering in the present era but lack of proper mathematically rigor justification. To fill this research gap, a system and method has been proposed with a mathematical proof induced from the concept of Hessian matrix of multi variable calculus for Energy efficient techniques of data gathering or routing in Wireless Sensor Networks. It is assumed that Wireless Sensor Nodes are distributed in a multidimensional space. Illustrations verify that the proposed system mathematical design for any clustering approach promises a low-energy communication structure.

Calculus Course Assessment Data

In this paper we describe computer-aided assessment methods used in online Calculus courses and the data they produce. The online learning environment collects a lot of timestamped data about every action a student makes. Assessment data can be harnessed into use as a feedback, predictor, and recommendation facility for students and instructors. We also describe late professor Mika Seppälä’s seminal work at the University of Helsinki to develop online materials and tools for learning mathematics since 2001. He also utilized these methods in Calculus teaching at Florida State University. The open online course “Single Variable Calculus” was held in Helsinki in 2004. This intensive work evolved into a complete online English Calculus curriculum starting from the Fall 2013 and soon recognized as an alternative route for taking traditional university Calculus courses in Helsinki. Automatic assessment systems of mathematical competencies, such as STACK and WeBWorK, can take a student’s answer as a mathematical object, e.g. a function or an equation, and check whether it satisfies the requirements set for a correct answer as well as give immediate and meaningful feedback. That is a powerful tool especially for formative assessment: log data shows that many students prefer to start with quizzes and when necessary, consult lecturing materials

Stroh formalism in evaluation of 3D Green’s function in thermomagnetoelectroelastic anisotropic medium

The paper presents studies on the Green’s function for thermomagnetoelectroelastic medium and its reduction to the contour integral. Based on the previous studies the thermomagnetoelectroelastic Green’s function is presented as a surface integral over a half-sphere. The latter is then reduced to the double integral, which inner integral is evaluated explicitly using the complex variable calculus and the Stroh formalism. Thus, the Green’s function is reduced to the contour integral. Since the latter is evaluated over the period of the integrand, the paper proposes to use trapezoid rule for its numerical evaluation with exponential convergence. Several numerical examples are presented, which shows efficiency of the proposed approach for evaluation of Green’s function in thermomagnetoelectroelastic anisotropic solids.

Boundary Integral Equations for an Anisotropic Bimaterial with Thermally Imperfect Interface and Internal Inhomogeneities

Abstract This paper studies a thermoelastic anisotropic bimaterial with thermally imperfect interface and internal inhomogeneities. Based on the complex variable calculus and the extended Stroh formalism a new approach is proposed for obtaining the Somigliana type integral formulae and corresponding boundary integral equations for a thermoelastic bimaterial consisting of two half-spaces with different thermal and mechanical properties. The half-spaces are bonded together with mechanically perfect and thermally imperfect interface, which model interfacial adhesive layers present in bimaterial solids. Obtained integral equations are introduced into the modified boundary element method that allows solving arbitrary 2D thermoelacticity problems for anisotropic bimaterial solids with imperfect thin thermo-resistant inter-facial layer, which half-spaces contain cracks and thin inclusions. Presented numerical examples show the effect of thermal resistance of the bimaterial interface on the stress intensity factors at thin inhomogeneities.

PENGEMBANGAN MODUL KALKULUS 2 PADA PROGRAM STUDI PENDIDIKAN MATEMATIKA DI STKIP PGRI SUMATERA BARAT

<p align="center">Students' abilities can be developed through lectures, one of which is variable Calculus 2. In order for the maximum tuition required of a material that can support course lectures. In West Sumatra, Padang PGRI STKIP students only rely on one textbook only when the lectures, so the motivation and low student interest in learning. Therefore it takes a lecture materials that can help facilitate students in the lecture, which is a modul. The purpose of this study is to develop a modul valid, practical and effective in subjects STKIP PGRI Calculus 2 in West Sumatra. This study is a research development. This modul was developed by using the 4D model (define, design, develop, and desseminate). Phase desseminate not done. The data was collected with the validation and testing of the modul. modul is validated by the lecturer and expert Calculus 2, as well as Indonesian lecturers. Tests carried out on mathematics education students STKIP PGRI West Sumatera to know praktikalitas and effectiveness of the modul. The results showed that: 1) modul is valid (including the content and construct validity) of the validator's point of view, 2) the use of modul in the lecture did not experience significant barriers. The book is a practical work according to students and lecturers; and 3) modul have been effective. This is evident from the activities of students and high motivation to learn after the lecture.</p>