Engineering Differential Equations MATH.2360-201

Spring 2019

Course Materials


Exam Review Sheets, Including Sample Problems

  1. Review Sheet for Exam 1

  2. Review Sheet for Exam 2

  3. Review Sheet for Exam 3

  4. Review Sheet for Final Exam



Solutions to Sample Problems from Review SheetsPractice Exams

  1. Solutions to Exam 1 Sample Problems

  2. Solutions to Exam 2 Sample Problems

  3. Solutions to Exam 3 Sample Problems

  4. Solutions to Final Exam Sample Problems



Take-Home Parts of Exams

  1. Take-home part of Exam 1 due February 15.

  2. Take-home part of Exam 2 due March 20.

  3. Take-home part of Exam 3 due April 19.



Solution Sheets for Exams

  1. Exam 1 solution sheet

  2. Exam 2, version 1 solution sheet

  3. Exam 2, version 2 solution sheet

  4. Exam 3 solution sheet



Project

Project reports are due March 22. Here is the project description


Homework for Sections 2.4, 2.6, 4.3

  1. Section 2.4 homework handout

  2. Section 2.6 homework handout

  3. Section 4.3 homework handout



MATLAB Handouts

  1. Handout on Graphing (January 25).

  2. Handout on Symbolic Utilities (February 1).

  3. Handout on Numerical Methods (February 15). You will also need Dr. White's scripts euler.m and rk4.m and the homework assignments for section 2.4 and section 2.6.

  4. Handout on Slope Fields (February 22). You will also need the script dirfield.m. In case you don't have your textbook with you, the homework assignment on slope fields includes problems 1, 2, and 7 from section 1.3.

  5. Handout on additional MATLAB graphics commands (March 1).

  6. Handout on Phase Planes (March 26). You will also need the script phaseplane.m

  7. Handout on Numerical Methods for Systems (March 29) to be used for the section 4.3 homework. You will also need Dr. White's script rk4.m.

  8. Handout on Symbolic Laplace Transform Utilities Using Mupad (April 12).
    Handout on Symbolic Laplace Transform Utilities Using a Live Script File (April 12).

  9. Handout on Matrix Algebra Commands.



Class Handouts

  1. Solution method for first order linear equations

  2. Solving first order equations

  3. Solving second order constant coefficient equations

  4. The Method of Undetermined Coefficients

  5. Example of the Method of Variation of Parameters

  6. Examples of forced motion

  7. Example of forced motion with discontinuous forcing term

  8. Example of forced motion with an impulse force



Challenge Problems

  1. A friend of mine in college claimed that hot water freezes faster than cold water. His reasoning was that hot water loses heat at a faster rate than cold water, so if you put a container of hot water and a container of cold water in a freezer at the same time, the hot water will cool down faster and will freeze first. What does our heating/cooling model have to say about my friend's theory?

  2. The Snowplow Problem: One night it started snowing at a steady rate. A snowplow started out at midnight. At 1 a.m., it had gone 2 miles. At 2 a.m., it had gone another mile. What time did it start snowing?

  3. An interesting application of radioactive dating.

  4. The standard form of a second-order linear d.e. is y″ + p(x) y′ + q(x) y = f(x). Recalling the solution procedure for a first-order linear d.e., you might think that there is an integrating factor ρ(x) with the property that, if you multiply both sides of the d.e. by ρ(x), the left side becomes the second derivative of ρ(x)y.

  5. For people who have studied linear algebra:

  6. The total energy E of a mass-spring system is given by E = ½mv2 + ½kx2. Show that E is constant for an undamped, unforced system, and show that E is a decreasing function of time for a damped, unforced system.



[Course home page]     [Steve Pennell's home page]     [UMass Lowell Math Department]     [UMass Lowell Honors College]     [UMass Lowell]

Steve Pennell | (978) 934-2710 | stephen_pennell@uml.edu



Last Updated: April 16, 2019