Newton and Laplace

Engineering Math 2250-1 Spring 2014

2250 meets 7:30am daily in JTB 140
Updated: Wednesday April 30: 15:28PM, 2014  
Today: Thursday November 23: 19:03PM, 2017

Announcements

Week 11: Changes made to HW, Quiz and Lab package numbering. Each package is due the next week after it is assigned. For instance, HW11 is assigned in Week 11 and due in Week 12. Week 10 was Spring Break. There is no HW10, no Quiz10, no Lab10. Syllabus, Bookmark and Due Date documents were updated to relect the numbering, which affects Weeks 11,12,13,14,15.

If you discover a mistake or bad link, then please write to the email address on the doorcard posted Here.

Tutoring in WEB 1622 is staffed every weekday: Times and Staff WEB1622

Daily Calendar

Previous Announcements

Canvas will be used during the semester to communicate grades and publish messages; see the syllabus below for more info.
Please update your email address at the Registrar's web site Here

Abbreviations:
  EP = Edwards-Penney, Differential Equations and Linear Algebra 3/E
  EPbvp = Edwards-Penney, Differential Equations and Boundary Value Problems, any edition
  EPH = Edwards-Penney-Haberman hybrid textbook for Utah, 2013 (the required textbook)

The book supplements are sections 3.7 and 7.6 from any edition of the 2280 book, Edwards-Penney Boundary Value Problems, available for checkout from the math center. Available as PDF files from Professor Korevaar [Google search "EP3.7.pdf" and "EP7.6.pdf"]:
Section 3.7 EP3.7.pdf HERE
Section 7.6 EP7.6.pdf HERE

1.2-2: This is the first homework problem. A copy is submitted for review on Jan 8 and returned ungraded, with style comments, on Jan 10; details Here

1.3-8: Print and use the graphic Here.

Daily Calendar Weeks 1-6 (Jan 6 to Feb 14)
WEEK 1, Jan 6-10
======
1.1; differential equation, mathematical model.
1.2; integral as a general or particular solution.
1.3; slope field.
1.4; separable differential equation.
Quiz1 Sample. 
Quiz1 Sample Solutions.
Take-home Quiz1 and 
Homework HW1 due next Tuesday.
Thursday Lab 1 Here.

WEEK 2, Jan 13-17
======
1.5; linear differential equation.
EPbvp 3.7; LR and RC circuits.
2.1, 2.2, 2.3; mixture model, population model, cascades, equilibrium solution,
stability, acceleration-velocity models.
Quiz2 Sample and Solutions with graphs
Take-home Quiz2 and Homework HW2 due next Tuesday.
Thursday Lab 2 Revised Here.

WEEK 3, Jan 20-24
======
Monday Holiday, Martin Luther King. No classes.
2.3; escape velocity, Jules Verne problem.
2.4, 2.5, 2.6; numerical solutions.
Quiz3 Sample and Solutions
Take-home Quiz3 and Homework HW3 due next Tuesday.
Thursday Lab 3 Here.


WEEK 4, Jan 27-31
======
3.1, 3.2, 3.3; linear systems, matrices, Gaussian elimination;
Quiz4 Sample and Solutions
Take-home Quiz4 and Homework HW4 due next Tuesday.
Thursday Lab 4 Here.
Study Sample Exam 1 and Sample Exam 1 Solutions for Feb 14 Midterm 1.


WEEK 5, Feb 3-7
======
3.4; reduced row echelon form.
3.5; matrix operations, matrix inverses.
3.6; determinants.
Quiz5 Sample and Solutions
Take-home Quiz5 and Homework HW5 due next Tuesday.
Thursday Lab 5 Here.
Study Sample Exam 1 and Sample Exam 1 Solutions for next Friday, Feb 14.

WEEK 6, Feb 10-14
======
4.1; vector spaces, linear combinations in R^n.
4.2; span and independence.
4.3; subspaces.
Study Sample Exam 1 and Sample Exam 1 Solutions for Friday, Feb 14.
Wednesday 4pm Exam review,  blackboard photo directory
Friday Midterm Exam 1 over Weeks 1, 2, 3, 4.
Midterm Exam 1 Solutions
Quiz6 Sample and Solutions
Take-home Quiz6 and Homework HW6 due next Tuesday.
Thursday Lab 6 Here.
Daily Calendar Weeks 7-11 (Feb 17 to Mar 21)
WEEK 7, Feb 17-21
======
Monday Holiday, President's Day. No classes.
4.4; bases and dimension.
4.7; abstract vector spaces and solution space of a DE.
5.1; second-order linear DE.
Quiz7 Sample and Solutions
Take-home Quiz7 due next Friday.  Homework HW7 due next Tuesday. 
Thursday Lab 7 Here.

WEEK 8, Feb 24-28
======
5.1, 5.2, 5.3; constant coefficients, general solutions, superposition
5.4; mechanical vibrations, phase-amplitude
EPbvp 3.7; circuits.
Quiz8 Sample with interleaved solutions.
Take-home Quiz8 and Homework HW8 due next Tuesday.
Thursday Lab 8 Here.

WEEK 9, Mar 3-7
======
5.4; mechanical vibrations, pendulum model.
5.5; particular solutions to non-homogeneous problems.
5.6; forced oscillations, resonance and mechanical vibrations.
Quiz9 Sample with interleaved solutions.
Take-home Quiz9 and Homework HW9 due next the Tuesday after Spring Break.
Study Sample Exam 2 and Sample Exam 2 Solution key for the next Friday after Spring Break, Mar 21.
Thursday Lab 9 Here. Problem 3 was moved to extra credit.
Thursday Lab 9 Extra Credit Problem  due April 10.

WEEK 10, Mar 8-16 is Spring Break. No classes.
=======
No Lab10. No Quiz10. No HW10.

WEEK 11, Mar 17-21
=======
10.1, 10.2, 10.3; Laplace transforms, solving a DE with transforms.
7.1; Intro to systems for Laplace theory.
Thursday, 20 March 4pm Exam review,  blackboard photo directory
Study Sample Exam 2 and Sample Exam 2 Solution key for Friday, Mar 21.
Friday Exam 2 over Weeks  5, 6, 7, 8. Starts 7am.
Exam 2 Solution key
Quiz11 Sample with interleaved solutions.
Take-home Quiz11 and Homework HW11 due next Tuesday.
Thursday Lab 11 Here. [No Lab10]

Daily Calendar Weeks 12-17 (Mar 24 to Apr 23)
WEEK 12, Mar 24-28
=======
10.4; partial fractions, s-differentiation, shift theorem.
EPbvp 7.6; impulse response. Dirac impulse approximations.
10.5; Unit step, ramp, convolution. Second shifting theorem.
6.1; eigenanalysis, eigenpairs.
7.1; intro to first-order systems of ODE.
Quiz12 Sample with interleaved solutions.
Take-home Quiz12 due Friday 4 April,and Homework HW12 due Tuesday 1 April.
Thursday Lab 12 Here.

WEEK 13, Mar 31 to Apr 4
=======
7.1; Conversion to a first-order system of ODE.
6.2; diagonalization, Fourier's model.
6.3; power method, Cayley-Hamilton.
7.2; Matrix systems of DE
7.3; eigenanalysis method, spring systems, forced undamped systems.
Quiz13 Sample questions only and  Sample solutions 
Take-home Quiz13 due Monday after Exam 3
Homework HW13 due next Tuesday.
Thursday Lab 13 Here.
Study Sample Exam 3 questions for Friday 18 April.
Reference Sample Exam 3 Answers

WEEK 14, Apr 7-11
=======
Extra Credit Ch1-Ch5 only due Wednesday, April 9.
Extra Credit Labs due Thursday, April 10.
No QUIZ due this week because of the exam.
7.4; systems and practical resonance.
7.5; Laplace impact on these topics
9.1; equilibria, stability.
Thursday April 10, 4pm in WEB L102, Exam 3 Review session, 
blackboard photo directory
No Take-home Quiz this week.
Homework HW14 due next Tuesday.
Thursday Lab 14 Here.
Study Sample Exam 3 questions for next Friday.
Reference Sample Exam 3 Answers

WEEK 15, Apr 14-18
=======
9.2; phase portraits for non-linear systems.
9.3; populations and ecological models;
 Friday Exam 3 over Weeks 9, [Week 10=break], 11, 12, 13 (last midterm). Starts 7am.
Exam 3 Questions and Solution key
   Study Sample Exam 3 questions and Sample Exam 3 Answers
Thursday Lab 15 Here.
Homework HW15 due by 6pm Wednesday 30 April under the door JWB 113.
Study the Sample Final Exam Questions and  Answers
Study the Final Exam Study Guide

WEEK 16, Apr 21-23
=======
9.4; nonlinear mechanical systems
Sample Final Exam. Covers Chapters 1-2, 3, 4, 5, 6, 7, 9, 10.
Comprehensive Final Exam review.
Study the Sample Final Exam Questions and  Answers
Study the Final Exam Study Guide

WEEK 17
=======
Finals week: Comprehensive final exam, Tuesday 29 April, 7:30-10:00 a.m. in JTB 140.
Homework HW15 due by 6pm, under the door 113 JWB, Wednesday 30 April.
Final Exam S2014 Questions only
Final Exam S2014 Questions and answers

Due Dates, Extra Credit, Problem Notes

  1. Updated due dates (20 Mar 2014, 5.4K html)
  2. Extra credit Extra Math and Technology Problems to Cancel Zeros and Fifties.
  3. Problem notes FAQ, Solution Notes for Exercises and Extra Credit Maple Projects.

Reading, Lecture Notes, Slides, Manuscripts

  1. Reading Textbook Reading Schedule and WEB Site lecture links
  2. Lectures What happened in class? Lecture material, slides and references.
  3. Click here for Notebook Computer files: lecture slides, manuscripts and documents.

Midterm and Final Exam

The exam dates are Fridays Feb 14, Mar 21, Apr 18. Final Exam on Tuesday 29 Apr 2014 at 7:30am. [Corrected 19 Feb and 1 Apr] Click here for all S2014 exam materials, including samples, old exam keys with solutions, keys to this semester's exams, and related study guides for exams.

Syllabus, Book Mark, Roster, Reports

  1. Gustafson's 2250-1 7:30am syllabus S2014. syllabus
  2. Gustafson's 2250-1 7:30am book mark with problem list (136 problems to be graded) S2014. Book Mark
  3. Gustafson's 2250-1 7:30am Roster and Majors S2014. Roster (pdf)
  4. 2250 format suggestions: How to improve written reports.
  5. Khan Academy
    Video Tutorials on Differential Equations and Linear Algebra
  6. Learning Math
    Peter Alfeld's Guide to Understanding Mathematics
Maple, Matlab and Mathematica Tutorials

Maple Tutorials

  1. Maplesoft Quick Reference Cards Click Here
  2. Douglas Meade's Quick Reference Card for Maple 12 to 17 Click Here
  3. A rookie maple tutorial for the impatient from Indiana University Click Here
  4. Maple programming examples by topic from Kettering University Click Here
  5. Utah Maple tutorial 2014 in html format
    Used in LCB115 maple intro lectures.
    Click Here
  6. How to use maple 17 under unix, windows, OS/X (text)
    Here
  7. Maple graphics and low speed internet
    Maple at home
  8. Peter Stone's Maple Resource page for undergraduate math topics Click Here

Matlab Tutorials

  1. A one-page pdf Matlab cheat sheet from Strang's linear algebra course at MIT Click Here
  2. A matlab tutorial at MIT, contains basic information. No video camera, only code examples and text information. Link is HERE
  3. Mathworks matlab tutorials and documents are HERE. Register for the short tutorials, then try a few using your univ of Utah computer account. Matlab has a site license valid for all campus computers.

Mathematica Tutorials

  1. Printed or free PDF tutorials on special topics are available at Wolfram Research: HERE
  2. New users can start with John McLoone's YouTube video (2010) HERE
  3. A complete set of short tutorial videos are available at Wolfram Research, addressing special topics HERE
  4. Wolfram videos and screencasts cover a wide range of applications and interests. See Wolfram Broadcast Videos
Old Engineering Math Local Documents 1998-2013
  1. Link to Spring 2013 Eng Math documents Click here
  2. Link to Spring 2012 Eng Math documents Click here
  3. Link to Fall 2010 Eng Math documents Click here
  4. Link to Spring 2010 Eng Math documents Click here
  5. Link to Fall 2009 Eng Math documents Click here
  6. Link to Spring 2009 Eng Math documents Click here
  7. Link to Fall 2008 Eng Math documents Click here
  8. Link to Spring 2008 Eng Math documents Click here
  9. Link to Fall 2007 Eng Math documents Click here
  10. Link to Spring 2007 Eng Math documents Click here
  11. Link to Fall 2006 Eng Math documents Click here
  12. Link to Spring 2006 Eng Math documents Click here
  13. Link to Fall 2005 Eng Math documents Click here
  14. Link to Spring 2005 Eng Math documents Click here
  15. Link to Fall 2004 Eng Math documents Click here
  16. Link to Spring 2004 Eng Math documents Click here
  17. Link to Fall 2003 Eng Math documents Click here
  18. Link to 1995 to Spring 2003 Eng Math documents Click Here
FLASH Animations of applications
  1. The 85 physics animations in the link below are Copyright 2002 David M. Harrison, Dept. of Physics, Univ. of Toronto.
    Harrison's physics animations
    A high percentage of the areas covered in the 85 animations touch the subject matter of this course: Chaos, Classical Mechanics, Electricity and Magnetism, Micrometer Caliper, Miscellaneous, Nuclear, Optics, Oscilloscope, Quantum Mechanics, Relativity, Sound Waves, Vectors, Waves.
  2. The physics animations in the link below are Copyright 2002 Dan Russell, Dept. of Physics, Kettering Univ. See in particular the movies and animations for harmonic motion, forced oscillations and resonance.
    Dan Russell's physics animations
  3. Dan Russell has returned to Penn State as Professor of Acoustics. See Russell's Demo Collection 2014
    * Simple Harmonic Oscillator - with and without damping, transfer of energy between kinetic and potential forms
    * Damped Harmonic Oscillator - underdamped, overdamped, and critically damped
    * Forced Harmonic Oscillator - transient and steady state response to a force applied to the mass
    * The Simple Pendulum - comparing the linear approximation (small angle) with a real pendulum
    * Coupled Oscillators - energy transfer between two mass-spring systems coupled together
    * Dynamic Absorbers - J.P. Den Hartog's classical undamped tuned dynamic absorber
    * Tacoma Narrows Bridge  - (0.668 MB mpeg movie) - resonance and aerodynamic flutter, historical film 1940
Mail, Phone, Email Address
Mail address:
        Grant B. Gustafson
        155 South 1400 East Room 233
        Salt Lake City, UT 84112-0090
Office phone: (801) 581-6879

For email address, see class notes or click here for the doorcard.

Link to Department of Mathematics, University of Utah