DOCSLIB.ORG

Use of Robotics in First-Year Engineering Math Laboratory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Use of Robotics in First-Year Engineering Math Laboratory Session F1C Use of Robotics in First-Year Engineering Math Laboratory Rod Foist and Grace Ni Dept. of Electrical & Computer Engineering, California Baptist University 8432 Magnolia Avenue, Riverside, CA, 92504 [email protected], gni@ calbaptist.edu Abstract - According to National Science Foundation was to increase student retention, motivation, and success in (NSF) research, engineering mathematics courses with a engineering. The WSU model focuses on a novel first-year laboratory (“hands-on”) component are more effective engineering math course, taught by engineering faculty, in helping students grasp concepts, than lecture-only which includes lecture, lab, and recitation. The course uses approaches. Beginning in 2008, California Baptist an application-oriented, hands-on approach—and only University (CBU) received NSF funding through Wright covers the math topics that students actually use in their State University to develop a first-year Engineering core engineering courses. Klingbeil et al reported in 2013, Math course (EGR 182) with laboratory projects. Our based on careful assessments, that the results have been new College of Engineering currently offers nine degrees encouraging [2]. They also point out that a student’s and all freshmen must take this course. The lab projects success in engineering is strongly linked to his/her success aim to illustrate key mathematic concepts via hands-on in math “and perhaps more importantly, on the ability to experiments representing each discipline. Two new connect the math to the engineering”. That is, to see the projects were introduced during the 2013-2014 school relevance of math to engineering. year. This paper reports on a trigonometry-with- Beginning in 2008, California Baptist University robotics lab. A companion paper describes a calculus- (CBU) received NSF funding through WSU to develop this themed project using electronic filters. The new type of first-year engineering math course (EGR 182) trigonometry lab runs for two lab sessions. In the first and create laboratory projects. Our new College of session, students focus on taking angle-versus-lengths Engineering offers ABET-accredited degrees in Civil, measurements with a sun-dial-like instrument and Mechanical, and Electrical and Computer Engineering, plus calipers. The simple Plexiglas “sun-dial” simulates a six other degrees. All freshmen must take EGR 182. The two-link planar robotic arm. Given an angle, students lab projects aim to illustrate key mathematic concepts via dial it onto the instrument, then measure the x and y hands-on experiments representing each discipline. lengths; or vice versa. They also create MATLAB function and script files to cross-check and validate the HANDS-ON APPROACHES TO ENGINEERING EDUCATION measurements. In session two, a computer-controlled The use of hands-on or learn-by-doing approaches is humanoid robot replaces the “sun-dial”. Students type becoming widespread in engineering education. Another in shoulder and elbow joint angles, watch the robot name for this is “problem-based” learning. The STEM Lab move its arm, then hear the robot report verbally the Report states [3]: final location coordinates of its hand. Conversely, robot “Throughout higher education in engineering, colleges are hand coordinates can be typed in to determine the requiring students to pull their gaze from a text-book to resulting joint angles. Also, MATLAB files are edited to perform real-world, hands-on, team-based project learning. create equivalent files tailored to the robot. After In short, they are teaching students to become engineers by running the new lab for two semesters, no statistical data having them work as engineers.” has yet been acquired regarding final grade Furthermore, they claim that research shows that such improvements. However, student feedback indicated a “project-based” learning works at all ages, even as early as high level of popularity with the lab. They felt that it pre-school. As an example of this, Ghalia [4] showed how showed a good real-world application of math concepts even high school geometry students’ outcomes improved by and was a “cool way” to introduce robotics. using electrical engineering hands-on projects to illustrate geometry and its importance to solving real-world problems Index Terms – lab project, mathematics with engineering in radar. Observations in the classroom also indicated applications, robotics, trigonometry greater student interest (i.e., enjoyment). Aloul et al [5] INTRODUCTION stated that first-year engineering courses often use problem- based curriculum to “…ensure that students find relevance The National Science Foundation (NSF) funded an initiative in the Physics and Math courses being taken in the first two at Wright State University (WSU), circa 2004, to “redefine years of engineering.” the way engineering mathematics is taught”[1]. The goal 6th First Year Engineering Experience (FYEE) Conference August 7 – 8, 2014, College Station, TX F1C-1 Session F1C Drawing from the above references, the key benefits of LAB PROJECT ON APPLICATION OF TRIGONOMETRY IN hands-on approaches for students are better outcomes, ENGINEERING AND ROBOTICS seeing the relevance of math (and engineering) with real- world examples, deeper understanding, more enjoyment, Historically, the trigonometry lab runs for two weeks. and persistence in engineering. Originally (without robots), in the first week, students focused on taking angle-versus-lengths measurements with USING ROBOTICS TO TEACH MATH a sun-dial-like instrument (shown in Figure 1) and calipers. Using robots to teach programming and math concepts is not new [6]. Over 40 years ago, MIT educator Seymour Papert used his “turtle robots” to teach programming. More recently, educational researchers at Carnegie Mellon’s Robotics Academy have used robots to teach science, technology, engineering, and mathematics (STEM) education, with a focus on math [7]. The academy’s mission is to help teachers excite their students about math and science [8]. Educational resource companies are also turning to robotics to teach math. The “RobotsLAB BOX” is an award-winning teaching aid that uses a set of robots to teach math and includes 50 specific math lessons [9]. FIGURE 1 The current paper’s contribution is to provide a complete lab THE SUN-DIAL LIKE INSTRUMENT. project that includes the use of a humanoid robot’s arm motions as a simple, fun, and enlightening real-world The simple, Plexiglas “sun-dial” simulates a two-link application of trigonometry. A computer interface program planar robotic arm (Figure 2). Given an angle, students dial for controlling the robot (described below) was developed to it onto the instrument, then measure the x and y lengths; or enable this activity. vice versa. In addition, they began to create MATLAB function and script files to cross-check and validate the EGR182 – INTRODUCTORY MATHEMATICS FOR measurements. The second week focused on finishing the ENGINEERING APPLICATIONS MATLAB work, and repeating any measurements, if necessary. Finally, students must write a carefully- CBU’s EGR 182 is a 4-credit course. Based on the WSU formatted lab report. model [1], it has a lecture and lab, but no recitation component. However, tutorial sessions are provided twice weekly throughout the semester. As in the WSU course, the lecture addresses only the “salient math topics” which are needed in the core engineering courses—such as trigonometry, vectors and complex numbers, systems of equations and matrices, and calculus. We use the textbook developed by the WSU authors [10]. The weekly lab session meets for 90 minutes and provides hands-on lab projects that illustrate selected math topics from the lecture material. Students work in teams of FIGURE 2 two to perform the lab experiments and write a carefully POLAR-RECTANGULAR COORDINATES FOR SIMPLIFIED TWO-LINK PLANAR formatted report. A substantial part of the lab grade is based ROBOTIC “ARM”. on the written report, since we believe that good writing is In the new lab, week one is much the same, but with important in an engineering career. A nearly-complete fewer measurements (and fewer MATLAB files required). sample lab report is provided for the first lab report, to serve However, in the second week, a humanoid robot, called as a guide to proper writing. In lab one, the MATLAB “NAO”, replaces the “sun-dial”. The robots were purchased software tool is introduced, and this tool is woven into with a grant provided by the W. M. Keck Foundation. A nearly all of the other labs during the semester. user-friendly computer interface was developed (see below) Two new projects were introduced during the 2013- so that during the lab, students type in shoulder and elbow 2014 school year. This paper reports on a trigonometry- joint angles, watch the robot move its arm accordingly, then with-robotics lab (an upgrade to an existing lab). A hear the robot report verbally the final location coordinates companion paper describes a calculus-themed project using of its hand. Students can also specify the coordinates of the electronic filters. robot hand, watch the robot move its arm, and hear the corresponding joint angles reported by the robot. In addition, students edit their MATLAB files to create 6th First Year Engineering Experience (FYEE) Conference August 7 – 8, 2014, College Station, TX F1C-2 Session F1C equivalent files tailored to the robot (which includes real- world elbow offsets not found in the “sun-dial”). Very little programming or knowledge of the robot is required, but a pre-lab assignment requires students to watch a short introductory video, read the lab assignment, and take a short on-line quiz. The key trigonometric equations from week 1 (for sun- dial), which are used or modified in week 2 (for robot), are given below (defined in Figure 2): FIGURE 3 x = x1 + x2 (1) HUMANOID ROBOT NAO - T14 MODEL. y = y1 + y2 (2) x1 = l1 cos θ1 . (3) This lab project was focused on the forward and inverse y1 = l1 sin θ1 . (4) kinematics of NAO’s left arm, with 2 DOF for the shoulder, x2 = l2 cos (θ1 + θ2) (5) 2DOF for the elbow and 1 DOF for the wrist, namely y2 = l2 sin (θ1 + θ2) .
Load more

Recommended publications
  • Bachelor of Engineering Program in Robotics Engineering and Automation System
    Bachelor of Engineering Program in Robotics Engineering and Automation System Production Engineering Department, Faculty of Engineering King Mongkut's University of Technology North Bangkok 1518 Pracharad 1 Rd., Wongsawang, Bangsue, Bangkok 10800 Thailand Tel. 02-555-2000 ext 8208 Fax 02-587-0029 Brief History Since founded in 1984, Production Engineering Department has offered only one undergraduate curriculum. With ample available resources, the department identifies the next step as a new curriculum responding to industrial needs. PE Students become so skillful that they have won many prizes in various robot competitions. Curriculum Objectives Produce graduates in Robotics Engineering and Automation System for industry and ASEAN. Produce students with skills and knowledge to proudly represent KMUTNB uniqueness. Support innovative creation according to KMUTNB philosophy Program of Study for Robotics Engineering & Automation System ( . 2556) Total = 143 Credits Semester 1 Semester 2 Semester 3 Semester 4 Semester 5 Semester 6 Summer Semester 7 Semester 8 = 18 Credits = 20 Credits = 22 Credits = 21 Credits = 18 Credits = 19 Credits = 240 hours = 11 Credits = 14 Credits 040203111 3(3-0-6) 040203112 3(3-0-6) 040203211 3(3-0-6) 010243102 3(3-0-6) 010243xxx 3(x-x-x) 010243xxx 3(x-x-x) 010243210 1(0-2-1) 010243211 3(0-6-3) Engineering Engineering Engineering Mechanics of Technical Elective Technical Elective p RE Project I RE Project II Course I Course II ) Mathematics I Mathematics II Mathematics III i Materials 0 - h 0 s 4 n 2 r - 0 e
    [Show full text]
  • Nanosicence & Nanoengineering
    Why Study at Sakarya University? Nanosicence & Sakarya is one of the most central states in Turkey. The city hosts a number of industrial companies such as Toyata Motor Manufac- Nanoengineering turing Turkey, Hyundai EURotem Train Factory and Otokar. It is Graduate Studies surrounded by beautiful landscapes and historical places, and an economical city for students. Istanbul is about one and half hour from the campus by car or bus. The capital city, Ankara, is nearly 300 km’s away. The campus is fully equipped with modern buildings and overlooks the very famous Sapanca Lake. Sakarya University has more than 60,000 students enrolled in higher-education, undergraduate and graduate studies in such areas as Engineering, Natural Sciences, Medicine, Law and Management. Each year hundreds of international students also pursue their studies individually or through some programs such as ERASMUS Student Exchange. Sakarya University is constantly seeking for improvements in CONTACT US educational processes and is the first university in Turkey to start quality development and evaluation and to receive the National Tel : +90 264 295 50 42 Quality Reward. Fax: +90 264 295 50 31 E-mail: [email protected] Address: Sakarya University Esentepe Campus TR - 54187 Sakarya / TURKIYE www.sakarya.edu.tr/en www.sakarya.edu.tr/en Nanoscience and Nanoengineering Graduation Requirements & Courses** Why Master’s or Ph.D. Degree in Graduate Program* Nanoscience and Nanoengineering? The graduate program in Nanosci- Eight courses with a total of 60 ECTS Current research in nanoscience ence and Nanoengineering is an course credits, both Master’s and and nanotechnology requires an inter-disciplinary study and aims to Ph.D.
    [Show full text]
  • Mathematics and Engineering in Computer Science
    NBSIR 75-780 Mathematics and Engineering in Computer Science Christopher J. Van Wyk Institute for Computer Sciences and Technology National Bureau of Standards Washington, D. C. 20234 August, 1975 Final Report U S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS NBSIR 75-780 MATHEMATICS AND ENGINEERING IN COMPUTER SCIENCE Christopher J. Van Wyk Institute for Computer Sciences and Technology National Bureau of Standards Washington, D. C. 20234 August, 1975 Final Report U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary James A. Baker, III, Under Secretary Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director I I. Introduction The objective of the research which culminated in this document 'was to identify and characterize areas of mathematics and engineering v/hich are relevant to computer science. The descriptions of technical fields were to be comprehensible to laymen, yet accurate enough to satisfy technically knowledgeable personnel, and informative for all readers. The division of the fields, shown in the table of contents, is somewhat arbitrary, but it is also quite convenient. A short expla- nation might be helpful. The mathematical fields can be grouped by noting the importance of a field to computer science, and, to a lesser extent, the existence of the field independent of computer science. For example. Boolean algebra and information theory could (and did) exist without computers being available. On the other hand, most problems in artificial intelligence or optimization, once they reach even moderate complexity, must be solved with a computer, since hand solution would take too much time.
    [Show full text]
  • Robotics and Early-Years STEM Education: the Botstem Framework and Activities
    European Journal of STEM Education, 2020, 5(1), 01 ISSN: 2468-4368 Robotics and Early-years STEM Education: The botSTEM Framework and Activities Ileana M. Greca Dufranc 1, Eva M. García Terceño 1, Marie Fridberg 2, Björn Cronquist 2, Andreas Redfors 2* 1 Universidad de Burgos, SPAIN 2 Kristianstad University, SWEDEN *Corresponding Author: [email protected] Citation: Greca Dufranc, I. M., García Terceño, E. M., Fridberg, M., Cronquist, B. and Redfors, A. (2020). Robotics and Early-years STEM Education: The botSTEM Framework and Activities. European Journal of STEM Education, 5(1), 01. https://doi.org/10.20897/ejsteme/7948 Published: April 17, 2020 ABSTRACT botSTEM is an ERASMUS+ project aiming to raise the utilisation of inquiry-based collaborative learning and robots-enhanced education. The project outputs are specifically aimed to provide in- and pre-service teachers in Childhood and Primary Education and children four-eight years old, with research-based materials and practices that use integrated Science Technology Engineering Mathematics (STEM) and robot-based approaches, including code-learning, for enhancing scientific literacy in young children. This article presents the outputs from the botSTEM project; the didactical framework underpinning the teaching material, addressing pedagogy and content. It is a gender inclusive pedagogy that makes use of inquiry, engineering design methodology, collaborative work and robotics. The article starts with a presentation of the botSTEM toolkit with assorted teaching practices and finishes with examples of preliminary results from a qualitative analysis of implemented activities during science teaching in preschools. It turns out that despite perceived obstacles that teachers initially expressed, the analysis of the implementations indicates that the proposed STEM integrated framework, including inquiry teaching and engineering design methodologies, can be used with children as young as four years old.
    [Show full text]
  • Engineering Ontologies
    Int . J . Human – Computer Studies (1997) 46 , 365 – 406 Engineering ontologies P IM B ORST † AND H ANS A KKERMANS ‡ Uniy ersity of Twente , Information Systems Department INF / IS , P .O . Box 2 1 7 , NL - 7 5 0 0 AE Enschede , The Netherlands . email : borst / akkerman ê cs .utwente .nl J AN T OP Agro - Technological Research Organization ATO - DLO , P .O . Box 1 7 , NL - 6 7 0 0 AA Wageningen , The Netherlands . email : j .l .top ê ato .dlo .nl We analyse the construction as well as the role of ontologies in knowledge sharing and reuse for complex industrial applications . In this article , the practical use of ontologies in large-scale applications not restricted to knowledge-based systems is demonstrated , for the domain of engineering systems modelling , simulation and design . A general and formal ontology , called P HYS S YS , for dynamic physical systems is presented and its structuring principles are discussed . We show how the P HYS S YS ontology provides the foundation for the conceptual database schema of a library of reusable engineering model components , covering a variety of disciplines such as mechatronics and thermodynamics , and we describe a full-scale numerical simulation experiment on this basis pertaining to an existing large hospital heating installation . From the application scenario , several general guidelines and ex- periences emerge . It is possible to identify various y iewpoints that are seen as natural within a large domain : broad and stable conceptual distinctions that give rise to a categorization of concepts and properties . This provides a first mechanism to break up ontologies into smaller pieces with strong internal coherence but relatively loose coupling , thus reducing ontological commitments .
    [Show full text]
  • An Interdisciplinary Research Group's Collaboration to Understand First
    Paper ID #25422 An Interdisciplinary Research Group’s Collaboration to Understand First- Year Engineering Retention Mrs. Teresa Lee Tinnell, University of Louisville Terri Tinnell is a Curriculum and Instruction PhD student and Graduate Research Assistant at the Univer- sity of Louisville. Her research interests include interdisciplinary faculty development, STEM identity, retention of engineering students, the use of makerspaces in engineering education. Ms. Campbell R. Bego, University of Louisville Campbell Rightmyer Bego is currently pursuing a doctoral degree in Cognitive Science at the University of Louisville. She researches STEM learning with a focus on math learning and spatial representations. Ms. Bego is also assisting the Engineering Fundamentals Department in the Speed School in performing student retention research. She is particularly interested in interventions and teaching methods that allevi- ate working memory constraints and increase both learning retention and student retention in engineering. Ms. Bego is also a registered professional mechanical engineer in New York State. Dr. Patricia A. Ralston, University of Louisville Dr. Patricia A. S. Ralston is Professor and Chair of the Department of Engineering Fundamentals at the University of Louisville. She received her B.S., MEng, and PhD degrees in chemical engineering from the University of Louisville. Dr. Ralston teaches undergraduate engineering mathematics and is currently involved in educational research on the effective use of technology in engineering education, the incorpo- ration of critical thinking in undergraduate engineering education, and retention of engineering students. She leads a research group whose goal is to foster active interdisciplinary research which investigates learning and motivation and whose findings will inform the development of evidence-based interventions to promote retention and student success in engineering.
    [Show full text]
  • Ontologies for Supporting Engineering Design Optimization Paul Witherell National Institute of Standards and Technology, [email protected]
    Center for e-Design Publications Center for e-Design 6-2007 Ontologies for Supporting Engineering Design Optimization Paul Witherell National Institute of Standards and Technology, [email protected] Sundar Krishnamurty University of Massachusetts Amherst, [email protected] Ian R. Grosse University of Massachusetts Amherst, [email protected] Follow this and additional works at: http://lib.dr.iastate.edu/edesign_pubs Part of the Computer-Aided Engineering and Design Commons, and the Industrial Engineering Commons Recommended Citation Witherell, Paul; Krishnamurty, Sundar; and Grosse, Ian R., "Ontologies for Supporting Engineering Design Optimization" (2007). Center for e-Design Publications. 18. http://lib.dr.iastate.edu/edesign_pubs/18 This Article is brought to you for free and open access by the Center for e-Design at Iowa State University Digital Repository. It has been accepted for inclusion in Center for e-Design Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Ontologies for Supporting Engineering Design Optimization Abstract This paper presents an optimization ontology and its implementation into a prototype computational knowledge-based tool dubbed ONTOP (ontology for optimization). Salient feature of ONTOP include a knowledge base that incorporates both standardized optimization terminology, formal method definitions, and often unrecorded optimization details, such as any idealizations and assumptions that may be made when creating an optimization model, as well as the model developer’s rationale and justification behind these idealizations and assumptions. ONTOP was developed using Protégé, a Java-based, free open-source ontology development environment created by Stanford University. Two engineering design optimization case studies are presented.
    [Show full text]
  • Roles of Ontologies of Engineering Artifacts for Design Knowledge Modeling
    In Proc. of the 5th International Seminar and Workshop Engineering Design in Integrated Product Development (EDIProD 2006), 21-23 September 2006, Gronów, Poland, pp. 59-69, 2006. ROLES OF ONTOLOGIES OF ENGINEERING ARTIFACTS FOR DESIGN KNOWLEDGE MODELING YOSHINOBU KITAMURA The Institute of Scientific and Industrial Research, Osaka University e-mail: [email protected] Keywords: Product Knowledge Modeling, Ontology Abstract: Capturing design knowledge and its modeling are crucial issues for design support systems and design knowledge management. It is important that knowledge models are systematic, consistent, reusable and interoperable. This survey article discusses the roles of ontologies of engineering artifacts for contributing to such design knowledge modeling from a viewpoint of computer science. An ontology of artifacts, in general, consists of systematic and computational definitions of fundamental concepts and relationship which exist in the physical world related to target artifacts, and shows how to capture the artifacts. This article, firstly, discusses needs, types, levels and some examples of ontologies of engineering artifacts. Then, we discuss roles of the ontologies for design knowledge modeling such as modeling specification for consistent modeling, capturing implicit knowledge and basis of knowledge systematization. 1. INTRODUCTION exchange and integration. In fact, one of the pioneering ontology research efforts in early 90’s Designing is a creative activity using several kinds aims at product data exchange among engineering of knowledge. The quality of design relies heavily tools [11]. Practical product data exchange has been on knowledge applied in the design processes. This explored mainly for CAD data models in the is why capturing necessary knowledge and its projects such as STEP and CIM-OSA.
    [Show full text]
  • Ontomathp RO Ontology: a Linked Data Hub for Mathematics
    OntoMathPRO Ontology: A Linked Data Hub for Mathematics Olga Nevzorova1,2, Nikita Zhiltsov1, Alexander Kirillovich1, and Evgeny Lipachev1 1 Kazan Federal University, Russia {onevzoro,nikita.zhiltsov,alik.kirillovich,elipachev}@gmail.com 2 Research Institute of Applied Semiotics of Tatarstan Academy of Sciences, Kazan, Russia Abstract. In this paper, we present an ontology of mathematical knowl- edge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensi- ble models. We demonstrate the applications of this representation in information extraction, semantic search, and education. We argue that the ontology can be a core of future integration of math-aware data sets in the Web of Data and, therefore, provide mappings onto relevant datasets, such as DBpedia and ScienceWISE. Keywords: Ontology engineering, mathematical knowledge, Linked Open Data. 1 Introduction Recent advances in computer mathematics [4] have made it possible to formalize particular mathematical areas including the proofs of some remarkable results (e.g. Four Color Theorem or Kepler’s Conjecture). Nevertheless, the creation of computer mathematics models is a slow process, requiring the excellent skills both in mathematics and programming. In this paper, we follow a different paradigm to mathematical knowledge representation that is based on ontology engineering and the Linked Data principles [6]. OntoMathPRO ontology1 intro- duces a reasonable trade-off between plain vocabularies and highly formalized models, aiming at computable proof-checking. OntoMathPRO was first briefly presented as a part of our previous work [22]. Since then, we have elaborated the ontology structure, improved interlinking with external resources and developed new applications to support the utility of the ontology in various use cases.
    [Show full text]
  • Enhancing Interdisciplinarity for the Engineer of 2020
    AC 2011-994: WORKING AS A TEAM: ENHANCING INTERDISCIPLINAR- ITY FOR THE ENGINEER OF 2020 Lisa R. Lattuca, Pennsylvania State University, University Park Lois Calian Trautvetter, Northwestern University Lois Calian Trautvetter Assistant Professor of Education and Director, Higher Education Administration and Policy Program, Northwestern University, [email protected] Dr. Trautvetter studies faculty development and productivity issues, including those that enhance teaching and research, motivation, and new and junior faculty development. She also studies gender issues in the STEM disciplines. David B Knight, Pennsylvania State University, University Park David Knight is a PhD candidate in the Higher Education Program at Pennsylvania State University and is a graduate research assistant on two NSF-funded engineering education projects. His research interests include STEM education, interdisciplinary teaching and research, organizational issues in higher education, and leadership and administration in higher education. Email: [email protected] Carla M. Cortes, Northwestern University Carla Cortes serves as an instructor and research associate in the Higher Education Administration & Policy program at Northwestern University. She also conducts analysis and manages projects for DePaul University’s Division of Enrollment Management and Marketing. c American Society for Engineering Education, 2011 Promoting Interdisciplinary Competence in the Engineers of 2020 Introduction A review of recent policy documents from the federal government reveals a consistent call for greater investments in interdisciplinary education at both the undergraduate and graduate levels (National Academy of Sciences, 20041; National Institutes of Health, 20062; Ramaley, 20013). These calls for greater interdisciplinarity in postsecondary and graduate education are based on the belief that interdisciplinary educational approaches are needed to foster innovation and may be more effective in doing so than discipline-based educational programs (National Academy of Engineering, 20044; U.S.
    [Show full text]
  • Advanced Engineering Mathematics AR-101 Rota Duration Semester SWS Credit Points Workload Annually WS 1 Semester 1St (Semester) 5 SWS 7 210 H 1 Modul Structure
    Advanced Engineering Mathematics AR-101 Rota Duration Semester SWS Credit Points Workload annually WS 1 Semester 1st (Semester) 5 SWS 7 210 h 1 Modul structure Course (Abbreviation) Type/ SWS Presence Self study Credits a) Advanced Engineering Lecture/ 3 SWS 45 h 90 h 4 Mathematics (AEM) b) Advanced Engineering Tutorial/ 2 SWS 30 h 45 h 3 Mathematics (AEM) 2 Language English 3 Content 1. Linear Algebra: Vector spaces, matrices and equation systems, linear maps, Jordan-, LU-, QR-, and singular value decomposition, numerical aspects. 2. Differential Equation: Linear systems, differential equations with constant coefficients. 3. Laplace-Transform: Definition, convolution and application to differential equations. 4. Differential Calculus with several variables: Derivatives, inverse and implicit functions, Taylor expansion and extreme values. 5. Stability of Differential Equations: Theorems of Ljapunov and Poincaré-Ljapunov. 6. Variational Calculus Literature: ñ Bajpai, Avinash C. , Mathematics for engineers and scientists ñ Meyer, R.M., Essential mathematics for applied fields ñ Lancaster, P., Tismenetsky, M., The theory of matrices ñ Lang, S., Linear algebra ñ Slides 4 Goals The course gives an introduction to fundamental mathematical techniques used in almost every course. Attention is given to the underlying mathematical structure. 5 Examination Requirements The final exam will be a written (2 hours) exam. 6 Formality of Examination T Module Finals § Accumulated Grade 7 Module Requirements (Prerequisites) 8 Allocation to Curriculum: Mandatory
    [Show full text]
  • Subchapter O. Science, Technology, Engineering, and Mathematics
    New Chapter 130. Texas Essential Knowledge and Skills for Career and Technical Education Subchapter O. Science, Technology, Engineering, and Mathematics Table of Contents §130.401. Implementation of Texas Essential Knowledge and Skills for Science, Technology, Engineering, and Mathematics ..................................................................................................................... 2 §130.402. Principles of Applied Engineering ............................................................................................... 2 §130.403. Principles of Biosciences ............................................................................................................... 5 §130.404. Principles of Technology .............................................................................................................. 7 §130.405. AC/DC Electronics ...................................................................................................................... 12 §130.406. Solid State Electronics ................................................................................................................ 15 §130.407. Digital Electronics ....................................................................................................................... 18 §130.408. Robotics I ..................................................................................................................................... 23 §130.409. Robotics II ...................................................................................................................................
    [Show full text]