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PDF version (1.1 MB)
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Teaching Statement
Student Comments by Course
Teaching and Advising:
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| 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. |
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| Applied Algebra |
Course description, syllabus and final.
Final exam from a similar course taught at Stonehill
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| Precalculus |
| Student Feedback |
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| Applied Calculus for Business |
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A syllabus, an exam, and the final.
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| Calculus for Biology I & II |
| Course description |
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| 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.
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Larmor Precession
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New integral curves
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Integral Curves
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Differential Equations
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A handout illustrating the variation of parameters formula is at right.
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Handout
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| Here is an animation of three coupled harmonic oscillators. This was also done in Mathematica. |
Animation
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| 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. |
Animation
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| At right the heat equation on a line segment with zero boundary conditions is solved for a delta function initial condition. |
Animation
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A differential equations
quiz,
exam1,
exam2,
Taylor series review handout,
final.
Student Feedback
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Linear Algebra
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Syllabus,
quiz,
final.
Student Feedback
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Finite Mathematics
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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. |
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Real and Complex Analysis
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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 |
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Mathematical Probability and Statistics
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We used Larsen and Marx. Here is a quiz, quiz, quiz, quiz and final, quiz.
Student Feedback |
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Numerical Analysis
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Syllabus
Maple Handout
Exam
Student Feedback
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Quantum Mechanics
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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).
Syllabus. |
Particle evolution.
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Seminar in Applied Math, Partial Differential Equations
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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
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