Redesigned Application-oriented Integral Calculus Curriculum

Leszek Gawarecki; Yaomin Dong; Gina Rablau

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Conference: 2018 ASEE Annual Conference & Exposition
Location: Salt Lake City, Utah
Publication Date: June 23, 2018
Start Date: June 23, 2018
End Date: July 27, 2018
Conference Session: Mathematics Division Technical Session 2
Tagged Division: Mathematics
Page Count: 19
DOI: 10.18260/1-2--30921
Permanent URL: https://strategy.asee.org/30921
Download Count: 2120

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Paper Authors

biography

Leszek Gawarecki Kettering University

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Research Interests
Statistics
Probability
Stochastic Analysis
Stochastic Differential Equation

Education
M.S. Mathematics, Warsaw University, Warsaw, Poland 1984
Ph.D. Statistics, Michigan State University, Lansing, MI 1994

Experience
Department Head, Kettering University, Flint, MI, 2008-present
Professor, Kettering University, Flint, MI, 2002-present
Associate Professor, GMI Engineering & Management Institute, Flint, MI, 1998-2002
Assistant Professor, GMI Engineering & Management Institute, Flint, MI, 1994-1998

Research Activities
Consulting in statistical analysis of product design.
Consulting in biostatistical analysis of factors improving active aging.
Consulting on quality control.

Selected Recent Publications

Theresa Atkinson, Leszek Gawarecki, Massoud Tavakoli (2016) "Paired Vehicle Occupant Analysis Indicates Age and Crash Severity Moderate Likelihood of Higher Severity Injury in Second Row Seated Adults in Frontal Crashes" Accident Analysis and Prevention, 89, 88–94,

Gawarecki, L., Mandrekar, V. (2015) “Stochastic Analysis for Gaussian Random Processes and Fields: With Applications” CRC Press https://www.crcpress.com/Stochastic-Analysis-for-Gaussian-Random-Processes-and-Fields-With-Applications/Mandrekar-Gawarecki/9781498707817

Gawarecki L., Mandrekar V. (2011) “Stochastic Differential Equations in Infinite Dimensions with Applications to Stochastic Partial Differential Equations” Springer. http://www.springerlink.com/content/u040lr/#section=823672&page=1

Gawarecki, L.; Mandrekar, V. (2010) “On the existence of weak variational solutions to stochastic differential equations”, Commun. Stoch. Anal. 4, no. 1, 1–20.
Gawarecki, L.; Mandrekar, V., Rajeev, B. (2009) “The monotonicity inequality for linear tial differential equations”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 3 Vol. 12, No. 4 , 1–17.

Gawarecki, L.; Mandrekar, V. Rajeev, B. (2008) “Linear stochastic differential equations in the dual of a multi-Hilbertian space”. Theory Stoch. Process. 14 , no. 2, 28—34.

Contact Information
Email: lgawarec@kettering.edu
Phone: (810) 762-9557

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biography

Yaomin Dong Kettering University

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Dr. Yaomin Dong is Professor of Mechanical Engineering at Kettering University. He received his Ph.D. in Mechanical Engineering at the University of Kentucky in 1998. Dr. Dong has extensive R&D experience in automotive industry and holds multiple patents. Dr. Dong's
areas of expertise include metalforming processes, design with composite materials, computer graphics, computer-aided engineering and finite element analysis.

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Gina Rablau Kettering

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Abstract

This paper presents the development of application based curriculum for Integral Calculus course, a project funded by KEEN Foundation. Textbook examples are frequently disconnected from students’ immediate environment or use past data of little interest. In addition, information given on the subject is at most sketchy and the practical purpose of solving these examples is not clear. This lack of vivid applications in calculus courses motivated us to develop content that can be used by instructors to enhance students’ learning experience by engaging them directly in solving problems and applying attained skills to real life situations relevant to students’ environment. The main focus of this work is to make the integral calculus course current, engaging, and relevant for students. The objective is to create a learning environment where calculus comes to life through real world examples, real and relevant data, and through the use of physical objects. We do not adopt the Project Based Learning approach however, but rather supplement the traditional lecture with motivating examples and multiple projects. Our pedagogical approach includes curriculum enhancement, deep learning, student engagement and entrepreneurship. We provide examples and projects which have the potential to capture students’ attention and will be useful in other courses in mathematics, science, and engineering. This approach is intended to spark curiosity in students, demonstrate usefulness of the theory they study, and to answer the question “Where am I going to use this?” We divided the curriculum into three fundamental modules: (1) Integration of basic functions resulting from mathematical models and from observed data; (2) Advanced applications of integration; (3) Applications of infinite sequences and series. The proposed course learning outcomes (CLOs) are linked to KEEN Student Outcomes, particularly those that are measurable. Assessment will include student surveys, retention, grades, achievement of CLO’s, and quality of students’ projects. In order to keep the balance between mathematical rigor and engineering and science relevance, the team was designed to consist of engineering and mathematics faculty. Similar developments are conducted in single variable differential calculus and multivariate calculus to create a consistent approach in the entire calculus sequence. All motivating examples and mini projects for the entire calculus sequence will be made available on line.

Citation
Format

Gawarecki, L., & Dong, Y., & Rablau, G. (2018, June), Redesigned Application-oriented Integral Calculus Curriculum Paper presented at 2018 ASEE Annual Conference & Exposition , Salt Lake City, Utah. 10.18260/1-2--30921

TY - CPAPER
AB - This paper presents the development of application based curriculum for Integral Calculus course, a project funded by KEEN Foundation. Textbook examples are frequently disconnected from students’ immediate environment or use past data of little interest. In addition, information given on the subject is at most sketchy and the practical purpose of solving these examples is not clear. This lack of vivid applications in calculus courses motivated us to develop content that can be used by instructors to enhance students’ learning experience by engaging them directly in solving problems and applying attained skills to real life situations relevant to students’ environment. The main focus of this work is to make the integral calculus course current, engaging, and relevant for students. The objective is to create a learning environment where calculus comes to life through real world examples, real and relevant data, and through the use of physical objects. We do not adopt the Project Based Learning approach however, but rather supplement the traditional lecture with motivating examples and multiple projects. Our pedagogical approach includes curriculum enhancement, deep learning, student engagement and entrepreneurship. We provide examples and projects which have the potential to capture students’ attention and will be useful in other courses in mathematics, science, and engineering. This approach is intended to spark curiosity in students, demonstrate usefulness of the theory they study, and to answer the question “Where am I going to use this?” We divided the curriculum into three fundamental modules: (1) Integration of basic functions resulting from mathematical models and from observed data; (2) Advanced applications of integration; (3) Applications of infinite sequences and series. The proposed course learning outcomes (CLOs) are linked to KEEN Student Outcomes, particularly those that are measurable. Assessment will include student surveys, retention, grades, achievement of CLO’s, and quality of students’ projects. In order to keep the balance between mathematical rigor and engineering and science relevance, the team was designed to consist of engineering and mathematics faculty. Similar developments are conducted in single variable differential calculus and multivariate calculus to create a consistent approach in the entire calculus sequence. All motivating examples and mini projects for the entire calculus sequence will be made available on line.
AU - Leszek Gawarecki
AU - Yaomin Dong
AU - Gina Rablau
CY - Salt Lake City, Utah
DA - 2018/06/23
PB - ASEE Conferences
TI - Redesigned Application-oriented Integral Calculus Curriculum
UR - https://strategy.asee.org/30921
DO - 10.18260/1-2--30921
ER -