Spring 2018 - Partial Differential Equations

“Among all of the mathematical disciplines the theory of differential equations is the most important...
It furnishes the explanation of all those elementary manifestations of nature which involve time.”  --Sophus Lie

“In order to solve this differential equation you look at it until a solution occurs to you.”  --George Polya

Announcements:

• Here is a short handout on the solutions to Euler equations.
• The second project has been posted on the homework page.
• One more handout.  The hyperbolic functions:  their definition, basic properties and connection to the solutions of second order constant coefficient linear ODEs with positive discriminants.  We'll need them later on, but for now you might find these results useful in Exercise 3.3.12.
• Here's a handout on the tabular integration by parts technique.  In it I prove the validity of the method, provide several examples, and apply it to integrands of the form P(x)T(ax) where P is a polynomial and T is sine or cosine.
• After class on Tuesday (2/20) a student asked me what would happen if we included a constant gravitational pull on the string represented by the wave equation.  A complete answer to this question can be found in this handout.
• Solutions to the first midterm can be found on the exam information page.
• I've moved my Wednesday office hours from the afternoon to the morning, 9:30-11:30am.
• Here are solutions to the midterm review problems.
• Details on this Thurday's (2/8) midterm, as well as review problems and odl exams, can be found on the exam information page.
• Due to the closure of the university on 1/16, the first homework assignment will be collected on 1/18 instead.

Course Links