Engineering Commons^™

How To Make Calculus Assignments Not Boring? Designing Calculus Assessment With The Constructive, Contextual, Collaborative, And Self-Directed Principles Of Problem-Based Learning., Martijn Boussé, Gavin Phillips, Stefan Jongen, Lonneke Bevers

Workshops

No abstract provided.

A Possible Solution To Avoid The Consequences Of The Covid-19 Pandemic And Reduce Dropout In Calculus Education, Brigitta Szilágyi, Csaba Szabó, Anna Koós, Bence Sipos

Research Papers

The effects of the COVID-19 are likely to stay in education for a long time to come. First year students of 2022 have completed the last two years of their high school education, which are the most important for further studies, during the worst period of the pandemic. Compared to previous years, far fewer students were able to meet the requirements of Calculus 1. Although there was a wide range of support material (interactive online interface, films, notes, elaborate calculation exercises) available to the students, they were not able to catch up and progress independently, regardless.

The calculus course consists …

Analog Circuits For Computing, Nicole Christine Pickett, Lauren Cathy Sueko Chun, Dillon Ryan Nguyen

Electrical Engineering

This project entails designing, simulating, and verifying analog circuits that can perform essential computing functions for power systems applications. The project aims to remedy critical challenges associated with handling calculations digitally, namely, time and power. This project's scope includes creating a library of circuits in SPICE that can be used to model and simulate complex mathematical equations. From these SPICE models, the circuit can be constructed physically, where the solution can be generated in less time using less power than doing the computation digitally. The performance and efficiency of analog computing will be measured and compared to conventional digital methods.

Assessing What We Value: Interactions Between Student Perceptions Of Assessments In The Calculus Classroom And Their Future-Oriented Motivation, Catherine Kenyon

All Dissertations

This work investigates interactions between first-year engineering (FYE) student perceptions of Calculus exams, their perceptions of the future, and their levels of math test anxiety. All phases of this study were conducted at a very high research (R1) institution with a common FYE program and coordinated Calculus courses. An initial pilot study explored how FYE students perceive the purpose of taking Calculus exams and how math test anxiety may play a role in these students’ perceptions of exams and their future in engineering. A second pilot study expanded on these results concerning student perceptions of Calculus exams and math test …

Mechanical Engineering News, Georgia Southern University

Mechanical Engineering News (2013-2023)

• Math Review Sessions

Application Of Fractional Calculus In Modelling Ballast Deformation Under Cyclic Loading, Yifei Sun, Buddhima Indraratna, John Philip Carter, Timothy R. Marchant, Sanjay Nimbalkar

Faculty of Engineering and Information Sciences - Papers: Part A

Most constitutive models can only simulate cumulative deformation after a limited number of cycles. However, railroad ballast usually experiences a large number of train passages that cause history-dependent long-term deformation. Fractional calculus is an efficient tool for modelling this phenomenon and therefore is incorporated into a constitutive model for predicting the cumulative deformation. The proposed model is further validated by comparing the model predictions with a series of corresponding experimental results. It is observed that the proposed model can realistically simulate the cumulative deformation of ballast from the onset of loading up to a large number of load cycles.

Neutrosophic Precalculus And Neutrosophic Calculus, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis.

Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change.

The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy.

In this book, the author presents a few examples of indeterminacies and several methods to deal with these specific indeterminacies, but many other indeterminacies there exist in our everyday life, and they have to be studied …

Characterization Of Samples For Optimization Of Infrared Stray Light Coatings, Carey L. Baxter, Rebecca Salvemini, Zaheer A. Ali, Patrick Waddell, Greg Perryman, Bob Thompson

STAR Program Research Presentations

NASA’s Stratospheric Observatory for Infrared Astronomy (SOFIA) is a converted 747SP that houses a 2.5 m telescope that observes the sky through an opening in the side of the aircraft. Because it flies at altitudes up to 45,000 feet, SOFIA gets 99.99% transmission in the infrared. Multiple science instruments mount one at a time on the telescope to interpret infrared and visible light from target sources. Ball Infrared Black (BIRB) currently coats everything that the optics sees inside the telescope assembly (TA) cavity in order to eliminate noise from the glow of background sky, aircraft exhaust, and other sources. A …

Error Reduction And Effect Of Step Size In Adjustment Calculus For Cam Applications, Sai Siddhartha Nudurupati

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

Any measurement, however carefully done, will never be free from errors. Similarly, machining of cams for automobiles is prone to contain errors. These errors are naturally a part and parcel of cam manufacturing. The nature of deviations of the manufactured cam profile from the theoretical cam determines its usability. Sometimes, allowable deviations in high speed cams may be in the order of 2540 µm. Larger deviations will disqualify the cams for applications.

Velocity and acceleration of the cam are estimated from the measured displacement of the cam follower during quality control implementation. This data helps in eliminating the unfit cams. …

Hamilton-Jacobi-Bellman Equations And Approximate Dynamic Programming On Time Scales, John E. Seiffertt Iv, Suman Sanyal, Donald C. Wunsch

Electrical and Computer Engineering Faculty Research & Creative Works

The time scales calculus is a key emerging area of mathematics due to its potential use in a wide variety of multidisciplinary applications. We extend this calculus to approximate dynamic programming (ADP). The core backward induction algorithm of dynamic programming is extended from its traditional discrete case to all isolated time scales. Hamilton-Jacobi-Bellman equations, the solution of which is the fundamental problem in the field of dynamic programming, are motivated and proven on time scales. By drawing together the calculus of time scales and the applied area of stochastic control via ADP, we have connected two major fields of research.

Project-Based Freshmen Engineering Courses In Civil Engineering Technology, Vernon W. Lewis Jr., Carol L. Considine

Engineering Technology Faculty Publications

Old Dominion University (ODU) has developed two fundamental courses for freshmen engineering students. The first course introduces the fundamentals of the practice of engineering including innovation, creativity, design and manufacturing, commercialization, teaming skills, environmental impact, and ethics. The second course is an exploration of engineering and engineering technology disciplines with an emphasis on projects. The purpose of these courses is to engage the students in the application of engineering early in their course of study with the hope that their interest will be reinforced and the likelihood of their being retained as students will increase. The courses are divided into …

Completeness Of Two Systems Of Illative Combinatory Logic For First-Order Propositional And Predicate Calculus, Wil Dekkers, Martin Bunder, Henk Barendregt

Faculty of Engineering and Information Sciences - Papers: Part A

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers 4 systems of illative combinatory logic that are sound for first-order propositional and predicate calculus.

Teaching Electromagnetic Field Theory Using Differential Forms, Karl F. Warnick, Richard H. Selfridge, David V. Arnold

Faculty Publications

The calculus of differential forms has significant advantages over traditional methods as a tool for teaching electromagnetic (EM) field theory. First, films clarify the relationship between field intensity and flux density, by providing distinct mathematical and graphical representations for the two types of fields. Second, Ampere's and Faraday's laws obtain graphical representations that are as intuitive as the representation of Gauss's law. Third, the vector Stokes theorem and the divergence theorem become special cases of a single relationship that is easier for the student to remember, apply, and visualize than their vector formulations. Fourth, computational simplifications result from the use …

Electromagnetic Boundary Conditions And Differential Forms, Karl F. Warnick, Richard H. Selfridge, David V. Arnold

Faculty Publications

A new representation for electromagnetic boundary conditions involving a boundary projection operator defined using the interior and exterior products of the calculus of differential forms is developed. This operator expresses boundary conditions for fields represented by differential forms of arbitrary degree. With vector analysis, the field intensity boundary conditions require the cross product, whereas the flux boundary conditions use the inner product. With differential forms, the field intensity and flux density boundary conditions are expressed using a single operator. This boundary projection operator is readily applied in practice, so that this work extends the utility of the calculus of differential …

Systems Of Illative Combinatory Logic Complete For First Order Propositional And Predicate Calculus, Henk Barendregt, Martin Bunder, Wil Dekkers

Faculty of Engineering and Information Sciences - Papers: Part A

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers systems of illative combinatory logic that are sound for first-order propositional and predicate calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators or, in a more direct way, in which derivations are not translated. Both translations are closely related in a canonical way. The two direct translations turn out to be complete. The paper fulfills the …