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Math 2280-002
2280-2 home page
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I will bring hard copies of lecture note outlines to class and post the filled-in versions after class. Notes should always be posted by 5:00 p.m. the day before class so that you may preview them if desired.
Week 1: January 6-10 Sections 1.1-1.4
jan6.pdf 1.1 introduction to differential equations and Chapter 1. jan6post.pdf after-class version.
jan7.pdf 1.2, 1.4 separable differential equations jan7post.pdf after-class version.
jan8.pdf 1.3-1.4 slope fields; existence and uniqueness theorem for first order DE IVPs. jan8post.pdf after-class version.
jan10.pdf 1.3-1.4 continued; IVP examples and the existence-uniqueness theorem. jan10post.pdf after-class version.
Week 2: January 13-17 Sections 1.4-1.5, 2.1-2.2
jan13.pdf 1.5 introduction to first order linear differential equations jan13post.pdf after-class version.
jan14.pdf 1.3-1.4 further examples; mathematical modeling and experiment for Toricelli's Law. jan14post.pdf after-class version.
jan15.pdf 1.5 input-output applications for linear differential equations. jan15post.pdf after-class version.
jan17.pdf 2.1 improved population models jan17post.pdf after-class version.
Week 3: January 21-24 Sections 2.1-2.3
jan21.pdf 2.1-2.2 population modeling and phase diagram analysis jan21post.pdf after-class version.
jan22.pdf 2.2 phase diagram analysis continued, fisheries example. jan22post.pdf after-class version.
jan24.pdf 2.3 improved velocity models. jan24post.pdf after-class version.
Week 4: January 27-31 Sections 2.3-2.6, 3.1
jan27.pdf 2.3-2.4 improved velocity models, introduction to Euler's method for first order IVPs. jan27post.pdf after-class version.
jan28.pdf 2.5-2.6 improved Euler and Runge-Kutta numerical methods. jan28post.pdf after-class version.
jan29.pdf matlab scripts for numerical computations related to IVPs. jan29post.pdf after-class version.
jan31.pdf 3.1 introduction to higher order differential equations jan31post.pdf after-class version.
Week 5: February 3-7 Sections 3.1-3.3
Monday February 3 was a snow day.
feb4.pdf 3.1-3.2 higher order linear differential equations feb4post.pdf after-class version.
feb5.pdf 3.2-3.3 higher order linear differential equations feb5post.pdf after-class version.
feb7.pdf 3.3 solution space algorithm for constant coefficient linear DE's. feb7post.pdf after-class version.
Week 6: February 10-14 Sections 3.3-3.4; exam 1
feb10.pdf 3.3-3.4 feb10post.pdf after-class version.
feb11.pdf 3.3-3.4 continued feb11post.pdf after-class version.
feb12.pdf 3.4 and exam review. feb12post.pdf after-class version.
Week 7: February 18-21 Sections 3.5-3.6
feb18.pdf 3.5 finding particular solutions to nonhomogeneous constant-coefficient linear DE's. feb18post.pdf after-class version.
feb19.pdf 3.5 completed feb19post.pdf after-class version.
feb21.pdf 3.5-3.6 case 2 in 3.5, and begin 3.6 applications to forced oscillations in mass-spring (and equivalent) configurations. feb21post.pdf after-class version.
Week 8: February 24-28 Sections 3.6-3.7, 4.1, 5.1-5.2
feb24.pdf 3.6 forced oscillations completed. feb24post.pdf after-class version.
feb25.pdf 3.6-3.7 and forced oscillations for RLC circuits feb25post.pdf after-class version.
feb26.pdf 4.1 systems of first order differential equations feb26post.pdf after-class version.
feb28.pdf 5.1 and intro to 5.2: differentiation rules for sums, products, multiples of matrix-valued functions; solving homogeneous first order linear systems of DE's using eigendata. feb28post.pdf after-class version.
Week 9: March 2-6 5.1-5.3
mar2.pdf 5.1-5.2 linear systems of DE's and exponential solutions. mar2post.pdf after-class version.
mar3.pdf 5.1-5.2 continued. mar3post.pdf after-class version.
mar4.pdf 5.2-5.3 complex eigendata; shape of phase portraits for n=2 first order linear homogeneous DE systems. mar4post.pdf after-class version.
mar6.pdf 5.3 phase portraits for real eigendata mar6post.pdf after-class version.
Week 10: March 18-20 5.3, 6.1, 6.3
mar18.pdf 5.3 phase portraits, complex and real eigendata; intro to 6.1 nonlinear systems
mar18post.pdf after-class version. YouTube: complex eigendata real eigendata nonlinear systems
mar20.pdf 6.2-6.3 linearization near equilibrium points
mar20post.pdf after-class version. YouTube: linearization
Week 11: March 23-27 6.3-6.4, midterm review.
mar23.pdf 6.3 ecological models
mar23post.pdf after-class version. YouTube: interacting species
mar24.pdf 6.4 mechanical models
mar24post.pdf after-class version. YouTube: mechanical models
exam2review.pdf midterm review notes
Week 12: March 30 - April 3 6.5 (optional); 5.4, 5.6.
mar30a.pdf 6.5: survey of higher dimensional phenomena (optional)
mar30b.pdf 5.4 unforced undamped mass-spring systems
YouTube: fundamental modes and oscillations demo, for 2-mass 3-spring configuration.
mar30bpost.pdf after-class version YouTube: unforced mass spring systems
mar31.pdf 5.4 forced undamped mass-spring systems
YouTube: shake table earthquake excitation of normal modes demo.
mar31post.pdf after-class version YouTube: forced mass spring systems
apr1.pdf 5.6 matrix exponentials and homogeneous systems of differential equations
apr1post.pdf after-class version YouTube: matrix exponentials and DE's
apr3a.pdf 5.7 matrix exponentials for inhomogeneous systems.
apr3apost.pdf after-class version YouTube: matrix exponentials as integrating factors
apr3b.pdf 5.7 exp(tA) when A is not diagonalizable
apr3bpost.pdf after-class version YouTube: exp(tA) for non-diagonalizable A
Week 13: April 6-10 9.1-9.4
apr6.pdf 9.1 intro to Fourier series
apr6post.pdf post notes. YouTube: Intro to Fourier series, as orthogonal projection.
apr7.pdf 9.3 differentiating and integrating Fourier series
apr7post.pdf post notes. YouTube: differentiating and integrating Fourier series.
apr8.pdf 9.2-9.3 Fourier series for 2L-periodic functions; even and odd extensions.
apr8post.pdf post notes. YouTube: 2L-periodic Fourier series; cosine and sine series
apr10.pdf 9.4 mass-spring systems with periodic forcing functions: resonance and practical resonance.
apr10post.pdf post notes. YouTube: Periodic forced oscillations via Fourier series
Week 14: April 13-17 9.5-9.6
April 13 is a sag day - no new material.
apr14.pdf 9.5 Introduction to the heat equation
apr14post.pdf post notes. YouTube: heat equation and product solutions, modeling and visualization
apr15.pdf 9.5 Heat equation, worked examples.
apr15post.pdf post notes. YouTube: Fourier series to solve the heat equation
apr17.pdf 9.6 Introduction to the wave equation.
apr17post.pdf post notes. YouTube: IBVPs for the wave equation, and product function solutions
Week 15: April 20-21 9.6, review notes.
apr20.pdf 9.6 examples connecting Fourier series to traveling waves solutions.
apr20post.pdf post notes. YouTube: connecting traveling wave and Fourier series solutions