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Math 2280-001
2280-1 home page
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Lecture notes will be posted at least a day before class, and it will be your responsibility to print out and bring a copy . 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. The .pdf versions of the notes are for printing out. They are created from the Maple worksheets having the .mw suffix.
Week 1: Jan 12-16
jan12.pdf jan12.mw 1.1-1.2 introduction to differential equations
jan14.pdf jan14.mw 1.1-1.2 1.4 separable differential equations, and ones of the form y'(x)=f(x).
jan16.pdf jan16.mw 1.3-1.4 slope fields, solution graphs, and existence-uniqueness for first order IVP's; examples using separable DE's.
Week 2: Jan 21-23
jan21.pdf jan21.mw 1.3-1.4 continued
jan23.pdf jan23.mw 1.5 linear differential equations
Week 3: Jan 26-30
jan26.pdf jan26.mw 2.1 improved population models
jan28.pdf jan28.mw 2.2 autonomous differential equations; phase diagrams for equilibrium stability analysis
jan30.pdf jan30.mw 2.2-2.3 phase diagram analysis for applications; begin improved velocity models section.
Week 4: Feb 2-6
feb2.pdf feb2.mw 2.3 improved velocity models
feb4.pdf feb4.mw 2.4-2.6 numerical methods. Class will meet in the computer classroom LCB 115.
feb6.pdf feb6.mw 3.1 introduction to higher order linear differential equations
Week 5: Feb 9-13
feb9.pdf feb9.mw 3.2 nth order linear differential equations
feb11.pdf feb11.mw 3.2-3.3 linear independence tests; algorithm for solutions space bases, for constant coefficient homogeneous linear differential equations.
feb13.pdf feb13.mw 3.3-3.4 complex roots in the characteristic polynomial; applications to mechanical oscillations.
Week 6: Feb 18-20
feb18.pdf feb18.mw review notes for exam; we will spend the first part of class finishing last Friday's notes, and then review.
exam 1 on February 20
Week 7: Feb 23-27
feb23.pdf feb23.mw 3.5 finding particular solutions to L(y)=f.
feb25.pdf feb25.mw 3.4, 3.5, 3.6 pendulum and mass-spring experiment day; overview of 3.6
feb27.pdf feb27.mw 3.6 forced oscillations
Week 8: Mar 2-6
mar2.pdf mar2.mw 3.7 RLC circuits
mar4.pdf mar4.mw 4.1 systems of differential equations
mar6.pdf mar6.mw 5.1-5.2 systems of linear differential equations
Week 9: Mar 9-13
mar9.pdf mar9.mw 5.1-5.2 continued - complex eigenvalues and applications
March 11: finish Monday's notes and discussion!
mar13.pdf mar13.mw 5.3 phase portraits for homogeneous linear first order systems of two differential equations.
Week 10: Mar 23-27
mar23.pdf mar23.mw 5.4 unforced mass-spring systems
mar25.pdf mar25.mw 5.4 forced oscillations in mass-spring systems
mar27.pdf mar27.mw 5.5 solving linear systems x'=Ax when the matrix A is not diagonalizable.
Week 11: Mar 30 - Apr 3
mar30.pdf mar30.mw 5.5 continued
exam2review.pdf exam2review.mw review sheet for exam 2
Week 12: Apr 6-10
apr6.pdf apr6.mw 5.6 matrix exponentials
apr8.pdf apr8.mw 5.6-5.7 matrix exponentials and variation of parameters for inhomogeneous systems
apr10.pdf apr10.mw 7.1-7.2 Laplace transforms and initial value problems
Week 13: Apr 13-17
apr13.pdf apr13.mw 7.1-7.4 Laplace transforms and applications
apr15.pdf apr15.mw 7.3-7.5 Laplace transforms and applications
apr17.pdf apr17.mw 7.5-7.6 applications of convolution to forced oscillation problems
Week 14: Apr 20-24
apr20.pdf apr20.mw 9.1-9.2 Introduction to Fourier Series
apr22.pdf apr22.mw 9.1-9.3 Fourier Series
apr24.pdf apr24.mw 9.4 Understanding general periodic forced oscillation problems - via superposition and Fourier series for the forcing function.
Week 15: Apr 27
Math_2280_review.pdf
apr29.pdf apr29.mw free bonus day! - optional survey of 6.1-6.4. The new material is not on the final exam but does tie together several of the course themes: linearization in non-linear problems; linear systems of differential equations; phase diagrams for homogeneous linear systems via eigendata analysis. I've reserved LCB 225, at the other end of the hall from our usual classroom, for this Wednesday meeting, at the usual class time.