Math 2280-1
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Professor Korevaar
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Lecture notes will (usually) be posted by 4:00 p.m. the day before class, and it will be your responsibility to bring a copy to class.
aug25.pdf 1.1: differential equations and mathematical models
aug26.pdf 1.2-1.3: antidifferentiation for some first order DE's; slope field interpretation.
aug27.pdf 1.3-1.4: slope fields, separable DEs, and the existence-uniqueness theorem for IVPs.
aug29.pdf 1.3-1.4: Maple notes.
aug29.mws the Maple worksheet (.mws) for the class notes - you can open this from Maple and work with it.
sept2.pdf 1.4: separable DEs and the Toricelli experiment
sept3.pdf 1.5: linear DEs
project1.pdf These are our notes for Sept 5! They discuss the section 1.5: linear DEs application - and contain your first Maple project assignment! We'll talk about the underlying math ideas in class, after we do the Lake Erie input-output model in Wednesday's notes. Make sure to bring a copy of these notes to class!!! This project is due September 15.
project1.mws maple worksheet version opens in Maple.
Week 3: Sept 8-12
sept8a.pdf 2.1: improved population models
sept8b.pdf 2.1: maple example
sept9.pdf 2.1-2.2: population models and general autonomous first order DEs.
sept10.pdf 2.2: autonomous DEs, stable and unstable equilibria, and an example of harvesting a logistic population.
sept12.pdf Notes about the phase-amplitude form for sinusoidal curves. (We meet in LCB 115, to work on Maple projects.)
sept12.mws Maple worksheet version.
Week 4: Sept 15-19
sept15.pdf 2.3 improved velocity/acceleration models
sept16.pdf 2.4-2.6 numerical approximation for solutions to differential equations.
see also the maple commands sheet, commands.pdf, which is posted on our maple page as a Maple worksheet.
sept17.pdf 3.1-3.2 introduction to higher order linear differential equations; (with appendix proof for chapter 2, that phase portraits of first order autonomous DEs don't lie!)
sept19.pdf 3.1-3.2 linear differential equations; particular and homogeneous solutions; structure of the solution space.
Week 5: Sept 22-26
sept22.pdf 3.2-3.3 A basis for the solution space, for constant coefficient linear homogeneous DEs: the case of real roots.
sept23.pdf key theorem summary sheet, so far.....if you're confused, find a specific question to ask!
sept24.pdf 3.3 continued - homogeneous solutions to constant coefficient homogeneous linear DEs: complex roots
sept26.pdf 3.3 - complex roots
Week 6: Sept 29-Oct 3
sept29.pdf 3.4 undamped and damped oscillators.
sept30.pdf 3.4 experiment day with mass-spring and pendulum
oct1.pdf 3.5 guessing a particular solution by the "method of undetermined coefficients", and review sheet.
Week 7: Oct 6-10
oct6.pdf 3.5 variation of parameters for particular solutions. Warning: starting today I will only be bringing one or two extra copies of the notes to class - so print your own copy before class!
oct7.pdf 3.6 forced oscillations - no damping.
oct8.pdf 3.6 forced oscillations with damping.
oct10.pdf 4.1 introduction to systems of differential equations
Week 8: Oct 20-24
oct 20: we'll use the notes from October 10. I've posted homework for the 27th on our homework page.
oct21.pdf 4.1, 5.1 existence and uniqueness theorem for first order linear system IVP, and consequences.
oct22.pdf 4.3 existence and uniqueness theorem, as understood from approximate numerical solutions (Euler and improved Euler). The Maple file for these notes is posted on our Maple page with link "numerical2.mws".
oct24.pdf 5.2 the eigenvalue-eigenvector method of solving homogeneous constant coefficient first order systems of DEs... page 6 is the class problem assigned on Wednesday.
oct24maple.pdf, oct24maple.mws Maple examples of first-order systems
Week 9: Oct 27-31
oct27.pdf 5.3 undamped spring systems
oct28.pdf 5.3 continued
oct28maple.pdf, oct28maple.mws Maple work for mass-spring systems - might help for section 5.3 earthquake exploration!
oct29.pdf 5.4 ...what to do when A has defective eigenspaces? but first do a 5.3 experiment with 2 masses and 3 springs !!
oct29experiment.pdf oct29experiment.mws, notes for our two mass, three spring experiment, along with a "challenge problem."
oct31: use the notes from October 29 - the "defective" train example will be fun!
Week 10: Nov 3-7
nov3.pdf 5.5 fundamental solution matrices and matrix exponentials
nov4.pdf 5.5 continued
nov5.pdf 5.6 nonhomogenous linear systems of DEs - guessing particular solutions. (Variation of parameters next lecture!)
nov7.pdf 5.6 nonhomogenous linear systems of DEs - variation of parameters (also 5.5 example.)
Week 11: Nov 10-14
nov10.pdf 5.6 variation of parameters
nov10maple.pdf nov10maple.mws Maple worksheet with automated variation of parameters
nov11.pdf 5.4-5.5 bonus day: chain bases, Jordan canonical form and matrix exponentials. (I'm late posting these notes and will have enough copies for everyone in class.)
nov12.pdf exam review sheet and section 6.1 - introduction to nonlinear systems of DEs.
Week 12: Nov 17-21
nov 17: 6.1 - we'll use the notes from November 12....also, I probably won't have the exams graded yet.
nov18.pdf 6.1-6.2 phase plane for non-linear systems of DEs, and linearization.
nov19.pdf 6.2 phase plane for non-linear systems of DEs, classification of equilibrium solutions to autonomous systems.
nov21.pdf 6.3 ecological models
Week 13: Nov 24-26
nov24.pdf 6.3-6.4 - ecological models and nonlinear springs
nov25.pdf 7.1-7.2 introduction to Laplace transform magic
nov26: we'll use yesterday's notes, and as a special inducement for you to come to class, we'll talk about homework problems with all our extra time.
Week 14: Dec 1-4
dec1.pdf 7.1-7.3 filling the Laplace transform table, and IVP examples.
dec2.pdf 7.4-7.5 the unit step function and convolution, with bonus applications
dec3.pdf 9.1 Fourier series
dec5.pdf 9.1-9.2 Fourier series
Week 15: Dec 8-12
dec8.pdf 9.3-9.4 Sine and cosine series, integration and differentiation of Fourier series, and how Fourier series explain the resonance game mysteries from December 2.
dec9.pdf 9.4 resonance game revisited - Fourier series always explains whether or not you get resonance with periodic forcing.
dec9maple.mws the maple file.
dec10.pdf 9.5-9.6 bonus day: survey of the one space dimension heat and wave equations.
heatmaple.mws heat equation demos in maple...download and play with these!
wavemaple.mws
dec12.pdf review sheet, and one problem to review many course concepts