CHARLES V. SCHAEFER JR. SCHOOL OF ENGINEERING
RESEARCH AND INNOVATION IN ENGINEERING EDUCATION (RIEE)
Enhanced Integration of Mathematics and Physics
into the Engineering Curriculum
Hamid Hadim
Department of Mechanical Engineering
Ed Whittaker
Department of Physics and Engineering Physics
George DeLancey
Department of Chemical, Biomedical & Materials Engineering
Patrick Miller
Department of Mathematics
Enhanced Integration of Math, Physics & Engineering
RIEE-NJCC Meeting, September 27, 2005
1
BACKGROUND
• An average of approximately 40% of students nationally leave
engineering before graduation
• Unsuccessful experiences in freshmen courses was found to be
one of the major factors contributing to this retention problem
• Mathematics and physics are at the core of engineering problem
solving and engineering design
• Freshmen and sophomore engineering students fail to
recognize the applicability of mathematics and physics to
engineering
• Students may lack the motivation necessary to obtain a
thorough understanding of key mathematical and physics
concepts or do not retain key elements of knowledge needed for
the engineering courses
• traditional approach of teaching students the required
mathematics and physics simply as prerequisites to subsequent
engineering courses is unsatisfactory
• A more integrated approach is needed
Enhanced Integration of Math, Physics & Engineering
RIEE-NJCC Meeting, September 27, 2005
2
PROJECT OBJECTIVES
GOAL: Develop modules with engineering applications and “proof-ofconcept” methodologies needed to enhance integration of mathematics
and physics into the engineering core courses.
Achieving this goal is expected to result in:
•
Improved retention of key knowledge in mathematics and physics
needed in future engineering courses
•
Greater understanding of key concepts in math and physics and their
application to engineering
•
Enhanced interest in mathematics and physics
•
Increased student motivation/engagement
•
Increased student satisfaction
•
Increased student retention
Enhanced Integration of Math, Physics & Engineering
RIEE-NJCC Meeting, September 27, 2005
3
PROJECT TASKS
• Conducted a comprehensive literature search
• Conducted a survey of engineering faculty to identify key skills
and competencies in mathematics and physics that are
necessary to core engineering courses
• Developed sample modules in mathematics with engineering
applications
• Developed a common methodology for systematic problem
solving
• Coordinated the course outcomes for mathematics, physics and
mechanics of solids
• Developed physics lecture demonstrations for active learning;
some of them will be integrated into related engineering courses
• Prepared surveys for assessment of the project modules and
methodologies
Enhanced Integration of Math, Physics & Engineering
RIEE-NJCC Meeting, September 27, 2005
4
MODULES IN MATHEMATICS WITH ENGINEERING
APPLICATIONS
Engineering Topic/Application
Laminar Blood Flow through blood
vessels
Work and energy conversion
Manufacturing Process Monitoring
Related Math Skills
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Beam deflection (Euler beam theory)
Application of differentiation
Application of surface/volume integrals
Fundamental theorem of calculus
Evaluation of definite integrals
Partial fractions
L’Hopital’s rule and differentiation
Preparation of two dimensional plots
Relation of function properties to plot
behavior
Roots of cubic equation
Trial and error for roots of nonlinear
algebraic equation
Differentiation
Integration of physical requirements with
mathematics
 Differentiation and its applications
 Graphical solutions and parametric
trends
Enhanced Integration of Math, Physics & Engineering
RIEE-NJCC Meeting, September 27, 2005
5
WEB SITE FOR MODULES WITH
ENGINEERING APPLICATIONS
• Collection of modules that connect math and physics
to engineering applications
• Each module includes the following components:
 Engineering application background information
 Concepts or skills in math and physics that are covered
 Exercises (interactive) that are assigned for credit.
 Links to other websites to allow further exploration of the
engineering application or related engineering discipline
 Contact information to a faculty member with professional
interest in the topic or related application
Enhanced Integration of Math, Physics & Engineering
RIEE-NJCC Meeting, September 27, 2005
6
SURVEY OF SKILLS IN MATHEMATICS AND PHYSICS
NECESSARY TO ENGINEERING
Skill/Concept
Taught in
my course
Reviewed in
my course
Just utilized
in my
course
Math Skills:
Systems of Algebraic Equations
Matrix manipulations
Differentiation
Application of differentiation
Integration
Application of integration
Evaluation of limits
Vector Algebra
Vector cross product and dot product and their
applications
Linear Ordinary Differential Equations
Enhanced Integration of Math, Physics & Engineering
RIEE-NJCC Meeting, September 27, 2005
7
SURVEY OF SKILLS IN MATHEMATICS AND PHYSICS
NECESSARY TO ENGINEERING (Continued)
Skill/Concept
Taught in
my course
Reviewed in
my course
Just utilized
in my
course
Physics Skills:
Distinguishing between velocity and acceleration
Concept of Force and Newton’s 2nd Law
Equilibrium
Free-body diagrams
Conservation laws
Applications of vector cross product and dot product
Torque
Moment of inertia
Angular motion
Oscillations
Enhanced Integration of Math, Physics & Engineering
RIEE-NJCC Meeting, September 27, 2005
8
SURVEY OF SKILLS IN MATHEMATICS AND PHYSICS
NECESSARY TO ENGINEERING (Continued)
Skill/Concept
Taught in
my course
Reviewed in
my course
Just utilized
in my
course
General Problem Solving Skills:
Ability to define/represent a problem using sketches
and diagrams
Ability to use symbols to represent physical quantities
and clearly defining these symbols
Ability to identify knowns and unknowns; variables
versus parameters
Ability to use physical laws to establish relationships
Ability to recognize and sketch graphs of commonlyused functions
Ability to use graphical tools (e.g. Excel)
Enhanced Integration of Math, Physics & Engineering
RIEE-NJCC Meeting, September 27, 2005
9