Joe J Perez
 joe_j_perez @

Teaching Portfolio

All materials were developed by the author. Some were developed in collaboration with students.
PDF version (1.1 MB)
Teaching Statement

Student Comments by Course

Teaching and Advising:
Master of Science in Mathematics thesis committee member for R G Hanus. Title: Sturm-Liouville Theory and Quantum Mechanics. Thesis committee chairman, L H Thurston. March 2008
NSF STEP program advisor. May 2008
Title: Partial Differential Equations and Flow Streamlines in Mathematica.
Applied Algebra
Course description, syllabus and final.
Final exam from a similar course taught at Stonehill
Student Feedback
Applied Calculus for Business
A syllabus, an exam, and the final.
Calculus for Biology I & II
Course description
Calculus I, II, and III
Materials: Calc I exam, Calc I final, Calc I final, Calc II exam, Calc III exam, Calc III Green's Theorem Handout, Calc III final
Student feedback

In order to illustrate the product integral interpretation of the exponential function, I gave an undergraduate seminar extending the ideas to the case in which the factors do not commute. Some animations are at right.
Seminar handout.

Larmor Precession
New integral curves
Integral Curves
Differential Equations
A handout illustrating the variation of parameters formula is at right.
Here is an animation of three coupled harmonic oscillators. This was also done in Mathematica.
At right the wave equation on a line segment with zero boundary conditions is solved for a delta function initial condition for the position and zero for the initial velocity.
At right the heat equation on a line segment with zero boundary conditions is solved for a delta function initial condition.

A differential equations quiz, exam1, exam2, Taylor series review handout, final.
Student Feedback
Linear Algebra
Syllabus, quiz, final.
Student Feedback
Finite Mathematics
Course description
For a while I have tried to help students learn proofs by using examples from this discipline. We used Rosen's book. I have also tried with this.
Real and Complex Analysis
Some homework, quiz1, another quiz1, quiz3, quiz5, quiz6, a final and another final.

As an application of a theorem in Rudin's book concerning differentiating under the integral sign (a favorite trick of Feynman), I gave a little seminar on the elliptic functions in which I computed the Taylor series of these functions by differentiating the arc-length integral. I wrote very brief notes that I include here.

For complex analysis, a written up lecture, and an exam. I have taught reals from Rudin's Principles of Mathematical Analysis and Folland's Advanced Calculus. For Complex, I taught from Ahlfors.
Student Feedback
Mathematical Probability and Statistics
We used Larsen and Marx. Here is a quiz, quiz, quiz, quiz and final, quiz.
Student Feedback
Numerical Analysis
Syllabus Maple Handout Exam
Student Feedback
Quantum Mechanics
We once used Mathematica to illustrate the time-dependent Schrödinger equation for a particle in a box, animating the modulus-squared of the wave function. A related seminar handout and accompanying Mathematica notebook

Proposal (accepted).


Particle evolution.

Seminar in Applied Math, Partial Differential Equations
Course Announcement
In these courses, we used this PDE book. Variously we went through the PDE from geometry or applied math as interest indicated. At right we have a Bessel function exercise done in Mathematica.

Drum hit half radius