Grant Gustafson at math.utah.edu

Engineering Math Spring 2006

Updated: Tue May 9 11:55:52 MDT 2006
  1. Errors in examAVE 2250-2 found by M.Torres were fixed May 9.
  2. Grades will be posted 10 May. Waiting for error reports by email.
  3. Semester Records link for 7:30 class 2250-1
    Electronic records for 2250-1 7:30 S2006 [5 May 2006]
  4. Semester Records link for 10:45 class 2250-2
    Electronic records for 2250-2 10:45 S2006 [5 May 2006]
    Electronic records for 2250-2 10:45 S2006 [9 May 2006]
  5. Final Exam 7:30 solution keys available (pdf)
  6. Final Exam 10:45 solution keys available (pdf)
  7. Midterm 3 solution keys available (pdf)
  8. Midterm 2 solution keys available (pdf)
  9. Extra credit problems added to due dates page. These optional problems affect the dailies score of 30 percent, but have no effect on the exam scores or class rank.
  10. Exam review 7:30 20-Apr-2006 in JTB 140, run by Tomm and 10:45 in JWB 335 run by Trung.
  11. FAQ for maple lab 4 available.
  12. Exam 3 sample available. Exam date 25 April.
  13. Final exam study guide available. Exam date 3 May and 4 May.

2250-1 and 2250-2 Due Dates Spring 2006

  1. 2250 [7:30am and 10:45am] Actual due dates for submitted work
    Due dates updated daily
    Problem list for Fall 2006 available in 2250gradesheetS2006.pdf
  2. Gustafson's 2250 (7:30am or 10:45am) gradesheet Spring 2006.
    gradesheet (72k pdf)
  3. Gustafson's 2250 (7:30am or 10:45am) syllabus Spring 2006.
    syllabus (103k pdf)
  4. 2250 format suggestions for submitted work
    How to improve your written work

FLASH Animations of applications

  • The physics animations in the link below [85 animations] were written by David M. Harrison, Dept. of Physics, Univ. of Toronto. They are Copyright 2002 - 2006 David M. Harrison.
    Harrison's physics animations
    The areas covered in the 85 animations appear below. A high percentage of them touch the subject matter of this course.
    1. Chaos
    2. Classical Mechanics
    3. Electricity and Magnetism
    4. Micrometer Caliper
    5. Miscellaneous
    6. Nuclear
    7. Optics
    8. Oscilloscope
    9. Quantum Mechanics
    10. Relativity
    11. Sound Waves
    12. Vectors
    13. Waves

    Maple labs 2250 Spring 2006

    Updated: Tue Jan 10 06:41:59 MST 2006
    1. Maple Lab 1, Solving quadratics and plotting functions
      pdf document Lab 1 Spring 2006
      maple worksheet text Lab 1 Spring 2006
    2. Maple Lab 2, Newton Cooling
      pdf document Lab 2 Spring 2006
      maple worksheet text Lab 2 Spring 2006
    3. Maple Lab 3, Matrix Algebra
      pdf document Lab 3 Spring 2006
      maple worksheet text Lab Spring 2006
    4. Maple Lab 4, Mechanical Oscillations
      Frequently asked questions Lab 4 Spring 2006
      pdf document Lab 4 Spring 2006
      maple .mws Lab 4 Spring 2006
      Press SHIFT and then mouse-click to save the file to disk. Open the saved file in xmaple.
      In Mozilla firefox, save to disk using Alt-mouseclick (invokes download manager).
    5. Optional Extra Credit Maple Lab 5: Tacoma Narrows L5.1, L5.2, L5.3
      pdf document Lab 5 [optional] Spring 2006
      maple .mws Lab 5 Spring 2006
      Press SHIFT or ALT and then mouse-click to save the file to disk. Open the saved file in xmaple.
      maple plain text .txt Lab 5 Spring 2006
      Tacoma page Fall 2004 Explanation of maple lab 5. Video clip. Photos. Don't use 2004 lab sources there!
    6. Optional Extra Credit maple Lab 6, Earthquakes L6.1, L6.2, L6.3, L6.4, L6.5, L6.6
      quake project Spring 2006 (PDF)
      quake project Spring 2006 worksheet .mws (Shift or alt-click to write file to disk)
      quake project Spring 2006 worksheet text .txt

    2250-1 and 2250-2 Midterm Exams Spring 2006 (Spring and Fall 2005 references also)

    1. Updated: Sat Apr 15 10:53:50 MDT 2006
    2. Midterm 1 for 2250-1 and 2250-2 (7:30am or 10:45am) Spring 2006
      S2006 Sample Midterm 1, review 7 Feb, Exam date Feb 14 2006 (pdf).
      Solution Key for 7:30 Midterm 1 Spring 2006
      Solution Key for 10:45 Midterm 1 Spring 2006
      Old exams follow...
      S2005 Sample Midterm 1, Exam date Feb 16 2005 [old exam] (pdf).
      S2005 Solution Key for 7:30 Midterm 1 Spring 2005 [old]
      S2005 Solution Key for 10:45 Midterm 1 Spring 2005 [old]
      Solution Key for 7:30 Midterm 1 Fall 2005 [old]
      Solution Key for 10:45 Midterm 1 Fall 2005 [old]
    3. Midterm 2 for 2250-1 and 2250-2 (7:30am or 10:45am) Spring 2006
      S2006 Sample Midterm 2, Exam date Mar 28, 2006 (pdf)
      S2006 Midterm 2 solution key 7:30 S2006 [Mar 28, 2006] (pdf)
      S2006 Midterm 2 solution key 10:45 S2006 [Mar 28, 2006 + retest problem 4] (pdf)
      Old exams follow...
      S2005 Sample Midterm 2, Exam date Mar 28 (pdf)
      S2005 Answers and answer check for Sample Midterm 2 from Fall 2004
      S2005 Solution Key for 7:30 Midterm 2 Spring 2005 (26 Apr)
      S2005 Solution Key for 10:45 Midterm 2 Spring 2005 (26 Apr)
      Sample exam 2 and answers Fall 2005 (pdf)
      Solution Key for 7:30 Midterm 2 Fall 2005
      Solution Key for 10:45 Midterm 2 Fall 2005
    4. Midterm 3 for 2250-1 and 2250-2 (7:30am or 10:45am) Spring 2006
      S2006 Sample Exam 3 and Solutions, Exam date Apr 25 (pdf), updated Sat 15 Apr 2006
      S2006 Exam 3 typeset Solutions 10:45 Spring 2006 (pdf)
      S2006 Exam 3 handwritten grading key 7:30 Spring 2006 (pdf)
      Old exams, keys and samples appear below.
      S2005 Sample Exam 3 and Solutions, Exam date Apr 20 (pdf), updated Sat 16 Apr 2005
      S2005 Exam 3 and Solution Key 7:30 (pdf)
      S2005 Exam 3 and Solution Key 10:45 (pdf)
      Fall 2005 Sample Exam 3, 10 problem study guide. Exam date 2 Dec 2005 (2 pages pdf)
      Fall 2005 Sample Exam 3, 10 problem study guide with Solution Key. Exam date 2 Dec 2005 (4 pages pdf)
      Fall 2005 Exam 3 solution key 7:30am [2 Dec 2005] (5 pages pdf)
      Fall 2005 Exam 3 solution key 10:45am [2 Dec 2005] (5 pages pdf)
    5. Final Exam for 2250-1 and 2250-2 (7:30am or 10:45am) Spring 2006

      Grading key for the 10:45 final exam, Spring 2006 [May 3, 2006]
      Grading key for the 7:30 final exam, Spring 2006 [May 4, 2006] The 7:30 section exam is 7:45am May 4 2006. The 10:45 section exam is 10:10am May 3 2006.
      Study guide for the final exam, Spring 2006
      Please use previous semester final exams and solution keys provided below plus S2006 exams 1,2,3 (see above) to study for the final exam.
    6. Previous Final Exam for 2250-1 and 2250-2 (7:30am or 10:45am) Spring 2005
      Study guide for the final exam, Fall 2005
      Study guide for the final exam, Spring 2005
      Sample 2250 7:30 final Exam. The actual 2250 final exam from Fall 2004
      No sample final answers available, please don't ask, answers don't exist. Yes, this is 12 months old.
      Grading key for the 10:45 Fall 2004 2250-2 final Exam.
      Answers only, sketch of solution. Yes, this is 12 months old.
    7. Final Exam Keys Spring 2005 7:30 and 10:45 2250 classes
      7:30 2250-1 Spring 2005 Final Exam Grading key (pdf)
      10:45 2250-2 Spring 2005 Final Exam Grading key (pdf)
    8. Final Exam Keys Fall 2005 7:30 and 10:45 2250 classes
      Fall 2005 Final Exam grading key 7:30am [14 Dec 2005] (6 pages pdf)
      Fall 2005 Final Exam grading key 10:45am [13 Dec 2005] (6 pages pdf)

    2250 Syllabus and Gradesheet Spring 2006

    1. Gustafson's 2250 (7:30am or 10:45am) course syllabus Spring 2006
      pdf postscript syllabus (124k)
      Engineering differential equations, Edwards-Penney
      Print locally or use Adobe AcroRead [acrobat reader]
    2. Gustafson's 2250 (7:30am or 10:45am) gradesheet Spring 2006.
      pdf postscript gradesheet (72k)
    3. 2250 format for submitted work
      How to improve your written work

    DE and Linear Algebra Lecture Slides Spring 2006

    Updated: Sat Jan 21 13:59:15 MST 2006
    1. Spring 2006 construction completed Jan 20.
    2. Week 1 slides
      Three Examples, Fundamental Theorem of Calculus, Method of quadrature, Decay law derivation, Background formulae (6 pages, pdf)
      Three Examples, solved 1.2-1,2,5,8,10 by Tyson Black, Jennifer Lahti, GBG (11 pages, pdf)
      Recipes for 1st, 2nd order and 2x2 Systems of DE PDF Document (2 pages, 50kb)
      Log+exponential Background+Direction fields PDF Document (4 pages, 450k). Decay law derivation. Problem 1.2-2. Direction field examples.
      For more on direction fields, print Direction fields document (typeset, 11 pages, pdf)
    3. Week 2 slides
      Picard-Lindelof and Peano Existence theory (typeset, 9 pages, pdf)
      Picard-Lindelof and Peano Existence Example, similar to 1.3-14 (1 page, pdf)
      1.4 Page 40 Exercise slides (4 pages, 500k)
      Separable Equations (typeset, 9 pages, PDF)
      Linear DE method, Section 1.5 slides: 1.5-3,5,11,33+Brine mixing (9 pages, pdf)
      Linear DE part I (Integrating Factor Method), (typeset, 8 pages, pdf)
      Linear DE part II (Variation of Parameters, Undetermined Coefficients), (typeset, 7 pages, pdf)
      How to do a maple answer check for y'=y+2x (TEXT 1k)
    4. Week 3 slides
      Verhulst logistic equation (typeset, 5 pages, pdf)
      Kinetics, falling bodies, projectiles (typeset, 16 pages, pdf)
      Science and Eng Applications, Torricelli law (typeset, 15 pages, pdf)
      Phase Line and Bifurcation Diagrams (includes "Stability, Funnel, Spout, and bifurcation") (typeset, 6 pages, 161k pdf)
      ch2 sections 1,2,3 Slides: 2.1-6,16,38, 2.2-4,10, 2.3-9,27+Escape velocity (8 pages, pdf)
      ch2 Numerical Methods Slides, Exercises 2.4-5,2.5-5,2.6-5 plus Rect, Trap, Simp rules (5 pages, pdf)
      ch2 DEplot maple example 1 for exercises 2.2, 2.3 (1 page, 1k)
      ch2 DEplot maple example 2 for exercises 2.2, 2.3 (1 page, 1k)
    5. Week 4 slides
      Report details on 2.4,2.5,2.6 prob 6
      Report details on 2.4,2.5,2.6 prob 12
      Numerical Solution of First Order DE (typeset, 19 pages, 220k pdf)
      Sample Report for 2.4-3 (pdf 3 pages, 350k)
      Numerical DE coding hints, TEXT Document (1 pages, 2k)
      Sample maple code for Euler, Heun, RK4 (maple worksheet)
      Sample maple code for exact/error reporting (maple worksheet)
    6. Weeks 5,6 slides
      Linear algebra, no matrices, (typeset, 21 pages, pdf)
      PDF Document (11 pages, 113k)
      Matrix equations (typeset, 6 pages, 92k)
      Ch3 Page 149+ slides, Exercises 3.1 to 3.6 (6 pages, 890k pdf)
    7. Week 7 slides
      Determinants and Cramer's Rule(typeset, 11 pages, 140k pdf)
      Vector space, Independence, Basis, Dimension, Rank (typeset, 17 pages, 180k pdf)
      Ch4 Page 237+ slides, Exercises 4.1 to 4.7 (4 pages, 480k pdf)
    8. Weeks 8,9 slides
      Basic Reference: First order constant coefficient recipe + theory + variation of parameters and undetermined coefficients (typeset, 11 pages pdf)
      Ch5. Constant coefficient recipe (typeset, 2 pages, pdf)
      Second order constant coefficient recipe + theory (typeset, 7 pages pdf)
      Second order variation of parameters (typeset, 7 pages pdf)
      Second order undetermined coefficients (typeset, 8 pages pdf)
      Higher order linear differential equations. Higher order recipe. Higher order undetermined coefficients. (typeset, 9 pages pdf)
      History of undetermined coefficients, Kummer's method, Table method (2k text)
      Ch5. Slides for exercises 5.1 to 5.6 (16 pages, 1.9mb pdf)
      Ignore the 5.5 examples which refer to Kummer's method or Cauchy's kernel. When edited out this message will vanish.
    9. Weeks 9,10 slides
      Ch5 undetermined coeff example PDF Document (3 pages, 0,5mb)
      This is a basic undetermined coffficient example. The textbook references are to an older edition.
      Problem notes 5.4: 34 (1 page, text)
      Problem notes 5.5: 48, 52, 60 (1 page, text)
      Unforced mechanical oscillations (typeset, 8 pages pdf)
      Forced mechanical oscillations (typeset, 8 pages pdf)
      Resonance (typeset, 7 pages pdf)
    10. Week 11 slides
      Ch6 Eigenanalysis slides, 6.1 and 6.2 (6 pages, 1.3mb pdf)
      Eigenanalysis-I manuscript S2006 (typeset 19 pages, 145k pdf)
    11. Week 12 slides
      Ch7 Systems of DE slides 7.1,7.2,7.3 (4 pages, 0.8mb pdf)
      Recipes for 1st, 2nd order and 2x2 Systems of DE PDF Document (2 pages, 50kb)
      DE systems manuscript F2005 (typeset 66 pages, 909k pdf)
    12. Week 13 slides
      Ch10 Laplace slides, 10.1 to 10.4 (9 pages, 1.95mb pdf)
      Laplace theory manuscript (typeset, 34 pages, 300k pdf)
      Heaviside's method (typeset, 4 pages, 86k pdf)

    DE and Linear Algebra manuscripts

    Updated: Sun Jan 22 07:23:37 MST 2006
    1. Exponential Modeling manuscript
      PDF Document (34 pages, 350k)
    2. Direction fields manuscript
      Direction fields (typeset, 11 pages, pdf)
    3. Computing and Existence manuscript
      Picard-Lindelof and Peano Existence theory (9 pages, pdf)
    4. Separable Equations manuscript
      Separable Equations (typeset, 9 pages, PDF)
    5. Linear First Order Differential Equations manuscripts
      Linear DE part I (Integrating Factor Method), (typeset, 8 pages, pdf)
      Linear DE part II (Variation of Parameters, Undetermined Coefficients), (typeset, 7 pages, pdf)
    6. Verhulst Logistic Equation manuscript
      Verhulst logistic equation (typeset, 5 pages, pdf)
    7. Kinetics manuscript
      Kinetics, falling bodies, projectiles (typeset, 16 pages, pdf)
    8. Phase line and bifurcation manuscript
      PDF Document (6 pages, 161k)
    9. Science and Engineering Applications manuscript
      Science and Eng Applications, Torricelli law (typeset, 15 pages, pdf)
    10. Numerical DE manuscript
      PDF Document (19 pages, 220k)
    11. Numerical DE maple coding hints
      TEXT Document (1 pages, 2k)
    12. Linear Algebraic Equations manuscript
      Linear algebra, no matrices, (typeset, 21 pages, pdf)
    13. Vector and matrix manuscript
      PDF Document (11 pages, 113k)
    14. Matrix Equations manuscript
      PDF Document (6 pages, 92k)
    15. Determinants and Cramer's Rule manuscript
      PDF Document (11 pages, 140k)
    16. Independence, Rank, Dimension manuscript
      PDF Document (17 pages, 180k)
    17. First and Second order DE manuscripts
      First order constant coefficient recipe + theory + variation of parameters and undetermined coefficients (PDF 11 pages)
      Second order constant coefficient recipe + theory (PDF 7 pages)
      Second order variation of parameters (PDF 7 pages)
      Second order undetermined coefficients (PDF 8 pages)
    18. Higher order equations manuscript
      Document on Higher order linear differential equations. Higher order recipe. Higher order undetermined coefficients. (9 pages pdf)
      History of undetermined coefficients, Kummer's method, Table method (2k text)
    19. Mechanical oscillations and Resonance manuscript
      Document on unforced mechanical oscillations (8 pages pdf)
      Document on forced mechanical oscillations (8 pages pdf)
      Document on resonance (7 pages pdf)
    20. Eigenanalysis and Fourier's Method manuscript. Updated S2006.
      Eigenanalysis-I manuscript S2005 (PDF 19 pages, 145k)
    21. Differential systems examples and theory, manuscript. Updated F2005.
      DE systems manuscript F2005 (PDF 66 pages, 909k)
    22. Laplace transform manuscript
      PDF Document (34 pages, 300k)
    23. Heaviside coverup method manuscript
      PDF Document (4 pages, 86k)

    OLD Engineering Math Local Documents 1998-2004

    1. Link to Fall 2004 Eng Math documents
      Click here
    2. Link to Spring 2004 Eng Math documents
      Click here
    3. Link to Fall 2003 Eng Math documents
      Click here
    4. Link to Spring 2003 Eng Math documents
      Click Here
    5. Link to Fall 2002 Eng Math documents
      Click Here
    6. Link to Spring 2002 Eng Math documents
      Click Here
    7. Link to 2000-2001 Eng Math documents
      Click Here
    8. Link to 1995-1999 Eng Math documents
      Click Here
    9. Link to 2001 Math 5410 documents
      Click Here
    Mail address: 
            Grant B. Gustafson
        155 South 1400 East Room 233
        Salt Lake City, UT 84112-0090
    Office phone: (801) 581-6879

    Grant Gustafson. For email address, see class notes.
    Link to Department of Mathematics, University of Utah