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Differential Equations
2250-1 home page
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Lecture notes will be posted by 4:00 p.m. the day before class. I strongly recommend bringing a copy of these notes to class, so we can go through the concepts and fill in the details together.
Week 1: Aug 22-27
aug22.pdf 1.1-1.2: introduction to differential equations
aug23.pdf 1.2: solving dy/dx = f(x) is just antidifferentiation; applications and examples.
aug23.2.pdf example 2 solution details.
aug24.pdf 1.3 slope fields and solution curves
aug26.pdf 1.3-1.4 separable differential equations and the existence-uniqueness theorem for first order IVPs.
Week 2: Aug 29 - Sept 2
aug29.pdf 1.4-1.5 Toricelli application of separable DE's; intro to linear DE's.
aug29maple.pdf the two pages of Maple notes (not necessary to print out if you've printed the notes above).
aug29maple.mw Maple worksheet version, which one can open with Maple software.
aug30.pdf 1.5 linear differential equations.
aug31.pdf 1.5 cont'd; EP3.7 electrical circuits; start 2.1 improved population models.
sept2.pdf 2.1-2.2 improved population models and introduction to automous first order differential equations.
logisticmaple.pdf pages 2-3 above
logisticmaple.mw Maple worksheet. (No need to print these maple documents)
Week 3: Sept 6 - Sept 9
sept6.pdf 2.1-2.2 continued (mostly we'll use Friday's notes).
sept7.pdf 2.2 continued.
sept9.pdf 2.3 improved velocity-acceleration models.
sept9maple.pdf maple output for notes above.
sept9maple.mw
Week 4: Sept 12 - Sept 16
numerical1.pdf The are the notes for Monday September 12 - we'll be discussing numerical techniques for finding approximate solutions to differential equations.
numerical1.mw the Maple file, with output removed.
numericaltemplate.pdf pseudocode and pictures for Euler, improved Euler, and Runge-Kutta.
setp13.pdf finish section 2.3; introduce chapters 3-4.
sept14.pdf 3.1-3.2: using elementary equation operations to solve linear systems of equations; doing the same procedure synthetically with elementary row operations.
sept16.pdf 3.1-3.2: continued....row echelon and reduced row echelon form.
Week 5: Sept 19 - Sept 23
sept19.pdf 3.1-3.3, page 1
sept19maple.pdf pages 2-8
sept19maple.mw the Maple file, with output removed.
sept20.pdf 3.3 implications of rref computations, and some applications.
sept21.pdf 3.4-3.5 matrix algebra, and introduction to matrix inverses.
sept23.pdf 3.5 matrix inverses.
Week 6: Sept 26 - Sept 30
sept26.pdf 3.6 determinants
sept27.pdf 3.6 determinants
exam1review.pdf review questions for exam 1 on Thursday.
sept30.pdf introduction to key concepts from chapter 4.
Week 7: Oct 3 - Oct 7
oct3.pdf 4.1-4.3: concepts related to linear combinations: span; linear independence and dependence; vector spaces and subspaces.
oct4.pdf 4.1-4.3: subspaces as spans of vector collections and/or as solution sets to homogeneous matrix equations.
oct5.pdf 4.3-4.4: how to construct a basis by deleting dependent vectors from a spanning set; or by augmenting vectors to an independent but non-spanning set.
oct7.pdf 4.4 and summary: augmenting independent but non-spanning collections of vectors to work up to a vector space basis; key facts about basis and dimension; summary notes for 4.1-4.4.
Week 8: Oct 17 - Oct 21
oct17.pdf 5.1: second order linear differential equations.
oct18.pdf 5.1-5.2: and nth order linear differential equations.
oct19.pdf 5.2: nth order linear differential equations. Superposition for non-homogeneous linear DEs.
oct21.pdf 5.2-5.3: other examples of superposition principle; algorithms for finding the general solution to nth order linear homogeneous DEs.
Week 9: Oct 24 - Oct 28
oct24.pdf 5.3: Euler's formula and complex roots to the characteristic polynomial
oct25.pdf 5.4: unforced mechanical vibrations
oct25maple.pdf oct25maple.mw DE solutions and plots.
oct26.pdf 5.4: pendulum model; mass-spring and pendulum experiments: how good are our models?
pendulumspring.pdf pendulumspring.mw Maple notes for pendulum-spring experiments.
oct28.pdf 5.5: Finding particular solutions to non-homogeneous constant coefficient linear differential equations.
Week 10: Oct 31 - Nov 4
oct31.pdf 5.5, 5.6: variation of parameters for finding particular solutions; forced oscillators.
nov1.pdf 5.6 and EP 3.7: damped forced mechanical oscillators, and RLC circuits.
nov2.pdf Chapter 10 - Laplace transforms, and what they have to do with linear differential equation initial value problems.
nov4.pdf 10.1-10.2 elementary Laplace transforms and applications to differential equation IVPs.
Week 11: Nov 7 - Nov 11
nov7.pdf 10.1-10.3 filling in the Laplace transform table; working examples; application to resonance problems.
nov8.pdf 10.2-10.3 Laplace transform partial fraction and initial value problem practice... we also need to finish the last two pages of Monday's notes.
exam2review.pdf Review questions for Thursday exam...we'll fill these in during class.
exam2reviewfilledin.pdf the filled in version, from class.
nov11.pdf 10.4-10.5 Using the unit step function to turn forcing functions on and off. The convolution theorem for inverting F(s)G(s).
Week 12: Nov 14 - Nov 18
nov14.pdf 10.5, EP7.6 Laplace transform for periodic functions and instantaneous impulse forcing "functions".
EP7.6.pdf EP7.6
nov15.pdf 6.1-6.2: eigenvalues and eigenvectors for square matrices.
nov16.pdf 6.1-6.2: eigenvalues, eigenspaces, and diagonalizability for square matrices.
nov18.pdf 7.1: systems of differential equations
Week 13: Nov 21 - Nov 23
nov21.pdf 7.2-7.3: homogeneous and inhomogeneous linear systems of first order DE's; the eigenvalue-eigenvector method for x'=Ax, when A is a constant matrix.
nov22.pdf 7.3: applications of first order systems of differential equations, including x'=Ax when A has complex eigenvalues and eigenvectors.
nov22maple.pdf nov22maple.mw pages 2-6 of the notes above, in .pdf and .mw formats.
nov23.pdf 7.4: undamped unforced spring systems
Week 14: Nov 28 - Dec 2
nov28.pdf 7.4: undamped forced and unforced spring systems
nov28experiment.pdf nov28experiment.mw (pages 3-4 above)
nov28forcing.pdf nov28forcing.mw (pages 7-8 above)
nov29.pdf 7.4 continued...unmoored mass-spring trains; transverse oscillations and the earthquake project.
nov30.pdf Chapter 9: nonlinear systems of differential equations.
dec2.pdf 9.2: linearization at equilibria of autonomous systems of DE's.
Week 15: Dec 5 - Dec 9
dec5.pdf 9.2-9.3: classification of equilibria via linearization....examples from interacting populations.
dec6.pdf 9.3-9.4: equilbria and stability for the free mass-pendulum configuration.
dec7.pdf 9.4: non-linear spring models.
dec9.pdf review sheet