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Math 2280-1
2280-1 home page
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Lecture notes will be posted by 4:00 p.m. the day before class, and it will be your responsibility to bring a copy to class. Most people find it useful to have the notes handy so as to minimize copying directly from the blackboard, thus leaving time in class to work on and write down example details and key explanations.
Week 1: Jan 11-15
jan11.pdf 1.1: introduction to differential equations.
jan12.pdf 1.2-1.3: first order DE's, solution graphs and slope fields.
jan13.pdf 1.2-1.4: surprisingly interesting examples of purely antidifferentiation 1st order DE's (1.2); separable DE examples illustrating solution graphs and slope fields (1.3, 1.4); existence and uniqueness for IVP's, when the slope field function is sufficiently nice (1.3).
jan15.pdf 1.3-1.4: Maple class notes to accompany Wednesday's notes. The aim is to reintroduce Maple, and to get an understanding the existence - uniqueness theorem for first order initial value problems and its consequences.
jan15.mw the Maple 13 document that made these notes (open this from Maple 13, if you wish to play with or copy various commands.)
2270mapleintro.mw an introduction to Maple, in the context of linear algebra - open from Maple.
2270mapleintro.pdf browser readable .pdf format, to see what the Maple file says.
Week 2: Jan 19-22
jan19.pdf 1.4: more separable DE's, the Toricelli model for draining tanks, and an experiment.
jan20.pdf 1.5: first order linear DE's
project1.pdf Friday notes are about your Newton's law of cooling Maple project - we'll go over these after finishing Wednesday's notes.
Week 3: Jan 25-29
jan25.pdf 2.1: improved population models,
jan26.pdf 2.1-2.2 and general autonomous first order differential equations.
jan27.pdf 2.2 stability theorem for autonomous first order DEs; also review of phase-amplitude form for sinusoidal functions.
Week 4: Feb 1-4
feb1.pdf 2.3: improved velocity-acceleration models.
feb2.pdf 2.4-2.6: numerical solutions to first order differential equations.
numerical1.mw Maple worksheet of feb2.pdf
feb3.pdf 3.1-3.2 linear differential equations.
feb5.pdf 3.1-3.3 linear algebra and the structure of solution spaces to linear differential equations.
Week 5: Feb 8-12
feb8.pdf 3.2-3.3: general linear differential equations and the special case of constant coefficient operators.
feb9: finish Monday (and last page of Friday) notes!
feb10.pdf 3.3: solutions when characteristic polynomial has complex roots.
feb12.pdf 3.4: unforced mechanical oscillations.
Week 6: Feb 16-19
feb16.pdf 3.4 continued; pendulum, mass-spring experiments.
feb17.pdf 3.5 using linear algebra rank+nullity theorem to predict the form of particular solutions to non-homogeneous constant coefficient linear DE's...last page of notes is a review page for Friday exam.
Week 7: Feb 22-26
feb22.pdf 3.5 continued: theoretical justification for "undetermined coefficients" and the will-always-work-but-it-might-be-technical "variation of parameters" method.
feb23.pdf 3.5 continued, begin 3.6.
feb24.pdf 3.6 forced oscillations; resonance, and "beating" on the way to resonance.
feb26.pdf 3.6 forced oscillations with damping.
Week 8: March 1-5
mar1.pdf 3.7 electrical circuits.
mar2.pdf 4.1 introduction to systems of first order differential equations
mar3.pdf 4.1, 5.1 theory overview for first order systems of DE's.
numerical2.pdf 4.3 Euler's and related methods for first order systems of DE's.
numerical2.mw Maple 12 code
mar5.pdf 5.1-5.2 the eigenvalue-eigenvector method for solving constant matrix first order systems of DE's.
Week 9: March 8-12
mar8 Friday's notes will suffice!
mar9.pdf 5.3 begin undamped spring systems
mar10.pdf 5.3 forced undamped spring systems; also Maple computations.
mar12.pdf 5.4 what to do with defective eigenspaces
Week 10: March 15-19
mar15 Friday's notes will suffice!
mar16.pdf 5.5 matrix exponentials.
mar17.pdf 5.5 continued, and the universal product rule for differentiation.
MatrixExponential.pdf computing matrix exponentials with Maple.
mar19.pdf 5.5 discussion and examples continued.
Week 11: March 29-April 2
mar29.pdf 5.6 undetermined coefficients and variation of parameters for nonhomogeneous linear systems of DEs
mar30.pdf review sheet for exam - we'll finish mar29.pdf and mar19.pdf too.
mar31.pdf overview of chapter 6.
Week 12: April 5 - April 9
apr5.pdf 6.1-6.2 classification of equilibria for non-linear autonomous first order systems of DE's.
apr6.pdf 6.3 ecological models
April 7 use notes from Tuesday.
apr9.pdf overview of solution complexity as a function of the number of first order autonomous DE's, and examples of periodic solutions when n=2.
Week 13: April 12 - April 16
apr12.pdf 6.4 mechanical systems
apr13.pdf 7 introduction to Laplace transform magic.
apr14.pdf 7.1-7.3 Filling in the Laplace transform table, and looking at our old linear DE's in a new light.
apr16.pdf 7.4-7.5 translations, convolutions, playing the resonance game.
Week 14: April 19 - April 23
apr19.pdf 9 introduction/recollection of Fourier series
apr20.pdf 9.1-9.2 Fourier series, continued.
apr21.pdf 9.3-9.4 even and odd extensions, and the resonance game revisited.
apr23.pdf 9.3-9.4 continued
apr23maple.pdf maple resonance game with Fourier series
Week 15: April 26 - April 28
apr26.pdf 9.5-9.6 the one space dimension heat and wave equations.
apr27.pdf 9.6 slinky math
apr27heatmaple.mws maple heat equation examples
apr27wavemaple.mws maple wave equation examples
apr28.pdf review sheet