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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 10-14
jan10.pdf 1.1: introduction to differential equations
jan11.pdf 1.2-1.3: integral solutions and slope fields.
jan12.pdf 1.2-1.3: integral solutions applications (1.2), and the initial value existence-uniqueness theorem (1.3).
jan14.pdf 1.3-1.4 illustrating the local existence uniqueness theorem for IVP's with separable DE's.
Week 2: Jan 18-21
jan18.pdf 1.4-1.5 Toricelli model/experiment, then intro to linear DE's.
jan18.mw Don't print this out - it's gibberish unless you open it with Maple.
jan19.pdf 1.5 linear differential equations
jan21.pdf 2.1 improved population models
Week 3: Jan 24-28
jan24.pdf 2.1-2.2 equibria and stability for autonomous first order differential equations
jan21.mw Maple document for U.S. population data and logistic equation
jan25.pdf 2.1-2.2 continued
jan26.pdf 2.3 improved velocity models
jan28.pdf 1.5 project: Newtons law of cooling with time-periodic ambient temperature and a stable steady periodic solution.
Week 4: Jan 31 - Feb 4
jan31.pdf 2.4-2.6 numerical solutions to initial value problems for first order differential equations.
numerical1.mw file to open from Maple (output removed).
feb1.pdf Euler, improved Euler, Runge-Kutta templates. (We'll mainly use Monday's notes.)
feb2.pdf 3.1-3.2 Introduction to higher order linear differential equations.
feb4.pdf 3.1-3.3 and the structure of the solution space in terms particular and n-dimensional homogeneous solution space.
Week 5: Feb 7 - Feb 11
feb7.pdf 3.3 homogeneous linear DE's with constant coefficients
feb8.pdf 3.3 cont'd - complex roots to the characteristic polynomial.
feb9.pdf 3.4 applications to springs
feb11.pdf 3.4 linearizing the pendulum, and experiments!
Week 6: Feb 14 - Feb 18
feb14.pdf 3.5 particular solutions for non-homogeneous linear DE's - undetermined coefficients.
feb15.pdf 3.5 continued; variation of parameters.
feb16.pdf 3.6 forced oscillation problems
Week 7: Feb 22 - Feb 25
February 22: we'll use the notes from February 16, on section 3.6. Notice the new homework assignment, sections 3.6-3.7 on our homework page
feb23.pdf 3.6: total energy to find natural undamped modes susceptible to resonance; forced oscillations with damping.
feb25.pdf 3.6-3.7: practical resonance and electrical circuits.
Week 8: Feb 28 - Mar 4
feb28.pdf 3.7-4.1: circuits and then introduction to systems of differential equations.
mar1.pdf 4.1 systems of differential equations.
mar2.pdf 4.3: numerical methods for systems of first order differential equations
numerical2.mw the Maple worksheet which generated March 2 notes - should be useful for one of your homework problems.
mar4.pdf 5.1-5.2: solving homogeneous first order systems of differential equations with constant coefficients.
Week 9: Mar 7 - Mar 11
mar 7: Friday's notes will suffice.
mar8.pdf 5.2-5.3 finish complex roots in first order systems and begin second order mass-spring systems.
mar9.pdf 5.3 forced undamped mass spring systems, with implications for practical resonance in slightly damped systems.
mar11.pdf experiment with two masses and three springs; begin section 5.4 for systems of first order DE's for which the matrix is not diagonalizable.
Week 10: Mar 14 - Mar 18
mar 14: Friday's notes will suffice!
mar15.pdf 5.5: fundamental matrix solutions and matrix exponentials.
mar16.pdf 5.5: more matrix exponential computations.
mar18.pdf 5.5: more matrix exponential computations, and connecting the two algorithms via linear algebra.
Week 11: Mar 28 - Apr 1
mar28.pdf 5.6: non-homogeneous linear systems with undetermined coefficients and with variation of parameters.
mar29.pdf 5.6 continued; review sheet for exam 2.
March 30: homework problem session for sections 5.5 and 5.6, and review exam topics.
Week 12: Apr 4 - 8
apr4.pdf 6.1-6.2 introduction to non-linear systems of DEs.
apr5.pdf 6.2 classification of equilibria for systems of two first order autonomous differential equations
apr6.pdf 6.3 population models.
apr8.pdf 6.1-6.3 solution complexity depending on number of first order autonomous differential equations.
Week 13: Apr 11 - 15
apr11.pdf 6.4 nonlinear oscillations.
april 12: we'll finish Monday's notes, and then illustrate several facets of chaos in dynamical systems using Maple codes - bring text section 6.5 to compare. Here are the Maple files:
discretechaos.mw
DEchaos.mw
apr13.pdf 7.1-7.2 Laplace transform for linear differential equations.
apr15.pdf 7.2-7.3 Laplace transform table entries and examples.
Week 14: Apr 18 - 22
apr18.pdf 9.1-9.2 introduction to Fourier series.
Notes from Math 2270 which include the details we went over on Monday about nearest point projection formulas via orthonormal bases, and the generalization from Euclidean space to inner product spaces:
oct19.pdf orthonormal bases and Euclidean projection
nov3.pdf generalization to inner product spaces
apr19.pdf 9.1-9.2 continued
apr20.pdf 9.3 Fourier series for 2L-periodic functions; sine series and cosine series.
apr22.pdf 9.3-9.4 finish 9.3, begin forced oscillations via Fourier series, section 9.4
apr22maple.pdf predicting resonance
apr22maple.mw to open from Maple
Week 15: Apr 25 - 27
apr25.pdf 9.5 heat equation (although a lot of the lecture will be a discussion of pages 4-6 Friday's notes: 9.4 forced oscillations revisited)
apr26.pdf 9.6 wave equation: we'll discuss how to solve the natural initial boundary value problems for the one space dimension heat and wave PDE's, using Fourier series ideas.
apr26heatmaple.mw heat equation examples
apr26wavemaple.mw wave equation examples
apr27.pdf review sheet!