Math 2250-1
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Send e-mail to :
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.
Week 1: Aug 25-29
aug25.pdf 1.1: differential equations and mathematical models
aug26.pdf 1.2: differential equations solvable by antidifferention
aug27.pdf 1.3: slope fields; existence and uniqueness of solutions to IVP's.
aug29.pdf 1.3-1.4: slope fields; existence and uniqueness of solutions to IVP's, illustrated by solving separable DEs.
aug29.mws This is the Maple worksheet (mws) corresponding to the .pdf lecture notes above. Try opening this worksheet in Maple!
Week 2: Sept 2-5
sept2.pdf 1.4: separable DEs and 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 in two weeks, September 19.
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: logistic model and general autonomous first order DEs.
sept10.pdf 2.2: autonomous DEs, stable and unstable equilbria; harvesting a logistic population.
sept12.pdf 2.3: improved velocity-acceleration models.
sept12b.pdf converting sinusoidal functions into phase-amplitude form.
sept12b.mws maple worksheet
Week 4: Sept 15-19
sept15.pdf 2.4-2.6: numerical approximation for solutions to differential equations.
numerical1.mws Maple worksheet version
sept16 is clean-up day (no fresh notes): linear and quadratic drag in sept12.pdf; sinusoidal conversion in sept12b.pdf; maple commands in commands.pdf. (Maple version on Maple page). Bring copies of all, and questions on chapters 1-2 and project!
sept17.pdf 3.1-3.2: review/introduction to linear systems, matrics, gaussian elimination.
sept19.pdf 3.1-3.3: Gaussian elimination, reduced and row-reduced echelon forms.
Week 5: Sept 22-26
sept22.pdf 3.3 reduced row echelon form, and what it means about solutions sets to linear systems of equations.
sept22.mws Maple worksheet for rref.
sept23.pdf 3.3-3.4 rref, consequences, general form of solution to Ax=b in terms of particular solution and homogeneous solution.
sept24.pdf 3.4 matrix algebra.
sept26.pdf 3.5 matrix inverses.
Week 6: Sept 29-Oct 3
sept29.pdf 3.6 determinant definition and computation using minors and cofactors.
sept30.pdf 3.6 determinant properties related to row (or column) operations, the adjoint formula for matrix inverses, and Cramer's rule.
oct1.pdf 3.6-4.1; finish determinants, begin chapter 4
oct3.pdf 4.1-4.3 linear combinations and span; exam review sheet appended
Week 7: Oct 6-Oct 10
oct7.pdf 4.1-4.3 linear independence and vector spaces
oct8.pdf 4.3 vector spaces and subspaces
oct10.pdf 4.4 basis and dimension
Week 8: Oct 20-Oct 24
oct20.pdf 4.4,4.7 bases for the solution space; general vector space facts and examples.
oct21.pdf 5.1 second order linear differential equations
oct22.pdf 5.2-5.3 nth order linear DEs, and finding the general solution to homogeneous DEs by trying exponentials.
oct24.pdf 5.3 distinct, repeated, and/or complex roots in the characteristic polynomial: finding a basis of solutions to any constant coefficient, homogeneous linear, nth order DE.
Week 9: Oct 27-Oct 31
oct27.pdf 5.3-5.4 Case III complex roots; mechanical vibrations.
oct28.pdf 5.4 undamped, over, under, and critical damping
oct29.pdf 5.5 finding particular solutions for the inhomogeneous linear constant coefficient DE L(y)=f.
oct31.pdf 5.6 forcing the undamped mass-spring system.
Week 10: Nov 3-7
nov3.pdf 5.6 forced damped springs; practical resonance
nov4.pdf pendulum and mass-spring experiment day; how accurate is our modeling? Also EP 3.7, RLC circuits.
nov5.pdf 10.1-10.2 introduction to Laplace transform magic.
nov7.pdf 10.2-10.3 filling in the Laplace transform table and IVP examples with partial fractions and completing the square.
Week 11: Nov 10-14
nov10.pdf 10.4-10.5 filling in more of the Laplace table: resonance formulas and the translation theorem.
nov11.pdf 10.4-10.5 convolution and playing the resonance game.
nov11maple.pdf nov11maple.mws Maple files for resonance game.
nov12.pdf 6.1 matrix eigenvalues and eigenvectors, for solving systems of differential equations
nov14.pdf 6.1-6.2 eigenvector bases and diagonalizable matrices....last pages are review sheets for exam 2. These are posted individually on our exam page.
Week 12: Nov 17-21
nov18.pdf 6.2-6.3 matrix diagonalization and powers of matrices
nov19.pdf 6.3 applications of eigenvectors and diagonalization....one of the neatest is the google page-rank algorithm, which we discuss. For a more complete discussion (found using google), see
http://www.ams.org/featurecolumn/archive/pagerank.html
nov21.pdf 7.1 (and intro to 7.2,7.3) systems of differential equations.
Week 13: Nov 24-26
nov24.pdf 7.2-7.3 existence, uniqueness for systems of first order DEs, and the eigenvalue-eigenvector method for the general solution to homogeneous linear systems of first order DEs.
nov25.pdf 7.3 applications of first order systems of DEs
nov25maple.mws the maple file with eigenvector computations and graphs.
nov26.pdf 7.4 second order systems: undamped spring systems
nov26maple.mws Maple notes for our experiment (.pdf included in nov26.pdf class notes)
Week 14: Dec 1-4
dec1.pdf 7.4b: forced undamped spring systems, and deducing practical resonance for slightly damped systems.
dec1maple.mws Maple file, also linked on project page, because it contains useful commands for the earthquake project.
dec2.pdf 7.5 chains for defective eigenspaces - we've made this section (and its homework) optional.
dec3.pdf 9.1-9.2 equilibria, stability, linearization, for autonomous systems of DEs.
dec5.pdf 9.2 linearization near equilibrium solutions to autonomous first order systems of DEs.
Week 15: Dec 8-12
dec8.pdf 9.2-9.3 classification of equilbria, and a predator prey example.
dec9.pdf 9.3 competition models
dec10.pdf 9.4 phase portraits for mechanical systems
dec12.pdf review sheet, and one problem to review a lot of the course concepts.