Course 18.085: Mathematical Methods for Engineers I
(Spring 2004)

• Lecturer:
  
  David Ingerman (2-372)    Ph: 3-4344 ingerman@math.mit.edu
  
  
• Syllabus (Fall 2003) (pdf)
  
  
• Textbook: Introduction to Applied Mathematics by Gilbert Strang
  Published by Wellesley-Cambridge Press
  
  
• Supplementary Material:
  
  Section 1.1: Four Special Matrices (ps)(pdf)
  Section 1.2: Elimination Leads to K=LDL^T (ps)(pdf)
  Section 1.3: Differences, Derivatives, Boundary Conditions (ps)(pdf)
  Section 1.4: Inverses and Delta Functions (ps)(pdf)
  Section 1.5: Eigenvalues and Eigenvectors (ps)(pdf)
  Section 1.6: Positive Definite Matrices (ps)(pdf)
  Section 2.1: The Stiffness Matrix (pdf)
  
  
• Getting started with Matlab: http://ocw.mit.edu/OcwWeb/Mathematics/18-385Nonlinear-Dynamics-and-ChaosFall2002/RelatedResources/index.htm
  
  

  ---

  Some related links

• Least Squares: The Importance of Error Bars
  
  14. Distributed Climate Model Aims For Errors, NewScientist
  Excerpts: A new distributed computing project is aiming to put error bars on the global warming predictions made by computer models of the Earth's climate. Until now, a lack of computing power has meant the complex models could only be run a small number of times. But many repetitions are needed to assess the uncertainty in, for example, a predicted rise in temperature.
  The project, called climateprediction.net, was launched on Friday and hopes to provide the computing power required by using the spare computer time of thousands of volunteers.
  * Distributed Climate Model Aims For Errors, Jenny Hogan, 03/09/12, NewScientist
  
  
• Exams and Solutions (Fall 2003)
  Exam 1 (pdf) and solutions (pdf)
  Exam 2 (pdf) and solutions (pdf)
  Exam 3 (pdf) and solutions (pdf)
  
  
• Exams and Solutions (Fall 2002)
  Exam 1 (.ps) (.pdf) and solutions (.ps) (.pdf)
  Exam 2 (.ps) (.pdf) and solutions (.ps) (.pdf)
  Exam 3 (.ps) (.pdf) and solutions (.ps) (.pdf)
  
  
• Exams and Solutions (Fall 2001):
  Exam 1 (.ps) (.pdf) and solutions (.ps) (.pdf)
  Exam 2 (.pdf) and solutions (.pdf)
  Exam 3 (.ps) (.pdf) and solutions (.pdf)
  
  

  ---

  Problem Sets (Fall 2003)

• Homework 1:   Text 1.2 #1,4,6,10   1.3 #1    Web 1.1 #5   1.2 #2,3   1.3 #1    Solutions   It is OK to use MATLAB on 5 by 5 matrices! Also for 3 by 3 inverses if necessary.
  
• Homework 2:   Text 1.4 #1,2,4,8,10,11,12    Web 2.1 #3,4,5
• Homework 3 + MATLAB:   MATLAB #1,2   Text 2.1 #2-10
  
• Homework 4:   These exercises from the text on trusses will not be collected and graded. They are preparation for Quiz 1 on October 6 at 11 in Walker:   Text 2.4 #1-4, 7-9, 15, 19
  
• Homework 5:   due WEDNESDAY October 15   From the text Section 3.1: 1, 2, 4, 6, 12, 13   Also turn in this MATLAB problem / stapled with the text problems MATLAB #4
  
• Homework 6:   due FRIDAY October 24   Section 3.3: 1,2,6,8,13,14,17,18   and MATLAB problem MATLAB #5
  
• Homework 7:   consists of problems from Quiz 2 in earlier years. These will be discussed in review and NOT COLLECTED. Some solutions will be provided before the exam on Friday November 7.   Homework #7   Solutions to problems 4 and 9 only:   Solutions #4,9   Reminder: HELP Thursday 4-6 with Pavel.
  
• Homework 8:   due WEDNESDAY November 19   Section 4.1: 2-6, 16, 23, 24, 26   Section 4.2: 1-3    Reminder: HELP Tuesday 5-7 with Pavel
  
• Homework 9 + Class problem + MATLAB:   due WEDNESDAY November 26 (or MON Dec 1 is OK but then not graded and returned before Quiz 3 on WED DEC 3). The quiz will cover the same material as the lectures and homeworks 8 and 9. The homework has problems from the book, 1 from class, and MATLAB:   Section 4.2: 4, 5, 10, 21 (some syllabus problems removed!)   Section 4.3: 1, 2, 3, 8, 10, 11, 12, 28   Class problem + MATLAB
  

  ---

  
  
  
• More Exams and Matlab Homeworks from previous years
  
  
• Videos of Professor Strang's Lectures (Lincoln Lab, Spring 2001)
  
  
• Linear algebra demos
  
• Fourier and signal processing resources (thanks to Julie)
  
  http://web.mit.edu/6.555/www (The spectral analysis demo is accessible to all. Students who would like access to the spectral analysis tutorial should send Julie an email).
  http://www.jhu.edu/~signals
  http://links.math.rpi.edu
  http://jdsp.asu.edu
  http://homepages.udayton.edu/~westerka/applets.htm
  http://www.isip.msstate.edu/projects/speech/software/demonstrations/applets/
  

  ---

  You are visitor number since September 2, 1997.

  © 1997 Massachusetts Institute of Technology