ECUE PROJECT: CONNECTING ENGINEERING AND MATH

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E-CUE PROJECTCONNECTING ENGINEERING AND MATH

• JUNE, 2007

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PROJECT GOALS

• Develop subject/modules to supplement math
  topics/abilities covered in GIR or 18.03 math
  subjects to ensure coverage of important math
  needed for engineering study
• Improve knowledge retention and understanding by
  connecting GIR math knowledge with engineering
  applications
• Improve knowledge retention of GIR and 18.03
  subjects in upper level engineering study

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Data collection

• Issues to clarify
• What are common content and skill needs across 2
  or more departments for D.E., related
  computation tools, engineering applications
  bridge
• In what prerequisite common content and skill
  areas do undergraduate instructors identify need
  for improvement in student knowledge/ ability
• Could changes in pedagogy improve student
  learning of concepts and ability to apply math in
  engineering problem solving
• Could improved integration of math and
  engineering problem solving in new/ revised
  subjects
• Data collection
• SoE Engineering Alumni Survey- Fall 2006 (classes
  1998-2004)
• Math content areas (D.E., linear algebra, stats,
  probability)- importance since graduation and
  MITs contribution to knowledge development
• Engineering Senior Survey Spring 07- develop
  supplement section to examine math topics/
  abilities of importance for undergraduate
  engineering study and preparation for study
• Undergraduate engineering faculty instructor
  survey/ interview protocol to examine math
  topics/ abilities of importance for engineering
  study and review of student preparation for study

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Spring 07 surveys of students, faculty, alumni

• Develop school wide list of needs/ key topics and
  learning objective taxonomy related to
  application of math, computation tools into
  engineering work.
• Work with key engineering undergraduate faculty
  and math department in developing and refining
  list.
• Focus on identifying key math application in
  engineering and use of computation tools that
  students are missing rather on what is already
  covered for development of pure math topic and
  ability listing.
• Draw from Mech Eng survey, Spring 2005, DMSE
  3.016 curriculum, AA faculty interview protocol.
• Develop list into surveys of students, faculty,
  alumni.

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Skill list build off 18.03 list of learning
outcomes (from Miller, 18.03 syllabus)

• Ask students and faculty about learning outcome
  achievement
• Model a simple system to obtain a ?rst order ODE.
  Visualize solutions using direction ?elds and
  isoclines, and approximate them using Eulers
  method.
• Solve a ?rst order linear ODE by the method of
  integrating factors or variation of parameter.
• Calculate with complex numbers and exponentials.
• Solve a constant coe?cient second order linear
  initial value problem with driving term
  exponential times polynomial. If the input signal
  is sinusoidal, compute amplitude gain and phase
  shift.
• Compute Fourier coe?cients, and ?nd periodic
  solutions of linear ODEs by means of Fourier
  series.
• Utilize Delta functions to model abrupt
  phenomena, compute the unit impulse response, and
  express the system response to a general signal
  by means of the convolution integral.
• Find the weight function or unit impulse response
  and solve constant coe?cient linear initial value
  problems using the Laplace transform together
  with tables of standard values. Relate the pole
  diagram of the transfer function to damping
  characteristics and the frequency response curve.
  
• Calculate eigenvalues, eigenvectors, and matrix
  exponentials, and use them to solve ?rst order
  linear systems. Relate ?rst order systems with
  higher-order ODEs.
• Recreate the phase portrait of a two-dimensional
  linear autonomous system from trace and
  determinant.
• Determine the qualitative behavior of an
  autonomous nonlinear two-dimensional system by
  means of an analysis of behavior near critical
  points.

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SoE Engineering Alumni Survey 2006 Structure

• In Fall 2006, surveyed engineering B.S. graduates
  from classes 1999-2004 (sans 2003)
• 3000 surveyed to date response rate 30
• Survey scale
• importance since graduation (5extremely
  important)
• MIT education contribution to ability development
  (5MIT greatly contributed)
• ABET learning outcomes
• apply statistics/ probability
• apply DE/linear algebra
• use computer-based tools
• Analyze data and interpret results (of an
  experiment or other research results)
• Survey results by engineering degree received and
  by career paths/ position types
• Engineering/ product development
• Engineering management
• Research/ academics
• Business/ finance

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SoE engineering alumni survey results

• Results by department show overall satisfaction
  with preparation
• Statistics, differential equations, computer
  tools topics
• Ability to analyze experimental or other research
  results
• Results by career path/position show differences
  in satisfaction with preparation
• General industrial/consulting research, and
  product development career paths alumni desire
  more preparation in computer tools topics, and in
  ability to apply these topics
• General industrial/consulting research and
  academic career path alumni desire more
  preparation in engineering /math data analysis
  abilities
• Business/finance, general engineering,
  engineering management career path alumni
  satisfied with math and computer tool preparation

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Engineering Senior Survey 2007 structure

• In Spring 2007, surveyed engineering B.S.
  graduates from class of 2007
• 532 surveyed response rate 59
• Survey scale
• importance for undergraduate engineering study
  (7extremely important)
• MIT preparation to apply math topic in
  undergraduate engineering study (7extremely
  important for undergraduate engineering study)
• ABET learning outcomes
• apply statistics/ probability
• apply differential equations
• apply linear algebra
• apply computational math computer-based tools
• analyze data and interpret results (of an
  experiment or other research results)
• List of completed math classes
• 18.03 (differential equations), 3.016
  (differential equations with computer
  applications), 18.06 (linear algebra)
• List undergraduate engineering subjects that were
  most difficult for you and why

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Engineering Senior Survey 2007 results

• Seniors satisfied with statistics/probability
  preparation for engineering study in all
  departments.
• Math preparation for engineering study varied, of
  course, by number of math subjects completed. One
  additional math subject above 18.03 (either 18.06
  or 3.016) made significant difference in
  students ability to comfortably use math
  (differential equations, computer tools) in
  engineering study.

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