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Math 2280-001
2280-1 home page
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Lecture notes for each week should be posted by Friday at 3:00 p.m. on the preceding week. Printing for Math classes is free in the Rushing Student Center, in the basement of LCB. It is recommended that you use these notes in conjunction with attending class. After each class I will post the filled-in versions for that day. At the end of the week I'll post the entire week's filled-in notes.
Week 1: January 9-13 Sections 1.1-1.3 and part of 1.4
week1.pdf Notes that include outline for entire week
The daily post-notes from this week are below:
jan9.pdf 1.1 introduction to differential equations
jan11.pdf 1.2, and separable DE solution algorithm from 1.4
jan13.pdf 1.3
jan9-13.pdf 1.1, 1.2, parts of 1.3, 1.4
Week 2: January 17-20 Sections 1.3-1.4 and part of 1.5
week2.pdf Notes that include outline for entire week
jan18.pdf 1.3-1.4 Toricelli model and experiment
jan20.pdf 1.5 linear DE's
jan17-20.pdf 1.3-1.5
Week 3: January 23-27 Sections 2.1-2.3
week3.pdf Notes that include outline for entire week
jan23.pdf 1.5-2.1 input-output modeling; population models
jan25.pdf 2.1-2.2 logistic model; autonomous differential equations, equilibrium solutions, stability.
jan27.pdf 2.2
jan23-27.pdf 1.5-2.2
Week 4: January 30 - February 3 Sections 2.3, 2.4-2.6, 3.1
week4.pdf Notes that include outline for entire week
week4.mw Maple version
jan30.pdf 2.3 improved velocity models
feb1.pdf feb1.mw 2.4-2.6 numerical methods ... as it was filled in during class.
feb3.pdf 3.1-3.2 introduction to higher order differential equations
jan30-feb3.pdf 2.3, 3.1 (Monday, Friday) filled in notes.
Week 5: February 6-10 Sections 3.1-3.4
week5.pdf Notes that include outline for entire week
feb6.pdf 3.1-3.2 higher order DE's; linear DE's and structure of solution space for homogeneous and inhomogeneous DE's
feb8.pdf 3.2 theory and examples for homogeneous and nonhomogeneous linear DE's.
feb10.pdf 3.3 characteristic polynomial and solution algorithms for constant coefficient homogeneous linear DE's.
feb6-10.pdf 3.1-3.3 filled in notes
Week 6: February 13-17 Section 3.4, exam review
week6.pdf Notes that include outline for entire week
feb13.pdf 3.4 unforced mass-spring configuration
feb15.pdf 3.4 mass-spring and pendulum experiments; review notes for first midterm on Friday. Note: two practice exams and solutions are posted on CANVAS.
Week 7: February 22-24 3.5-3.6 non-homogeneous linear DE's; application to forced oscillations
week7.pdf Notes that include outline for entire week
feb22.pdf 3.5 method of undetermined coefficients for finding yP.
feb24.pdf variation of parameters for finding yP, and rank+nullity theorem to justify method of undetermined coefficients.
feb22-24.pdf 3.5 filled in notes
Week 8: February 27 - March 3 3.6-3.7 non-homogeneous linear DE's; application to forced oscillations in damped mass-spring and RLC circuit modeling; 4.1, 5.1-5.2 first order systems of differential equations
week8.pdf Notes that include outline for entire week
feb27.pdf 3.6 forced mass-spring systems and associated physical phenomena
mar1.pdf 3.6-3.7 and RLC circuits; brief intro to Chapters 4-5.
mar3.pdf 4.1, 5.1 intro to systems of DE's.
feb27-mar3.pdf 3.6-4.1 filled in notes
Week 9: March 6-10 5.1-5.3 first order linear systems of differential equations
week9.pdf Notes that include outline for entire week
mar6.pdf 5.1-5.2 first order systems of DE's as universal framework for all differential equations and systems of DE's; homogeneous solution space bases via eigendata
mar8.pdf 5.2 continued; example with complex eigendata
mar10.pdf 5.3 phase portraits and classification for homogeneous systems of two first order differential equations.
mar6-10.pdf 5.1-5.3 filled in notes
Week 10: March 20-24 5.4, 5.6 mass-spring systems; matrix exponentials
week10.pdf Notes that include outline for entire week
mar20.pdf 5.4 multiple mass-spring systems
mar22.pdf 5.4 continued. Plus understanding solutions to x'=Ax and x''=Ax for diagonalizable A, overview using similarity transformations.
mar24.pdf 5.4 continued...forced oscillation problems, transverse oscillations.
mar20-24.pdf 5.4, 5.6 filled in notes
Week 11: March 27-29 5.6-5.7 matrix exponentials, FSM's and symbolic solution formulas for solving linear systems x'=Ax+f
week11.pdf Notes that include outline for entire week
mar27.pdf 5.6 fundamental matrices and matrix exponentials
mar29.pdf 5.6 continued - matrix exponentials for diagonalizable and non-diagonalizable matrices
mar27-29.pdf week 11 filled in notes
Week 12: April 3-7 5.7, 7.1-7.3 symbolic solution formulas for solving linear systems x'=Ax+f; Laplace transform
week12.pdf Notes that include outline for entire week
apr3.pdf 5.7: symbolic solution formulas for solving linear systems x'=Ax+f
apr5.pdf 7.1-7.2 Laplace transforms and IVP's
apr7.pdf 7.1-7.3 continued ...
apr3-7.pdf week 12 filled in notes
Week 13: April 10-14 7.4-7.6, 9.1-9.2 Laplace transforms with engineering forcing; Fourier series
week13.pdf Notes that include outline for entire week
apr10.pdf 7.4-7.5 piecewise forcing
apr12.pdf 7.5-7.6 impulse (delta function) forcing; convolution formula for solutions to linear DE's.
apr14.pdf 9.1-9.2 Fourier series
apr10-14.pdf week 13 filled in notes
Week 14-15: April 17-21, 24. 9.1-9.4, 6.1-6.4 Fourier series with application to forced oscillations; nonlinear autonomous systems.
week14-15.pdf Notes that include outline for entire week
apr17.pdf 9.1-9.3 Fourier series, continued
apr19.pdf 9.4 Fourier series for forced oscillation problems
apr21.pdf 6.1-6.4 nonlinear systems of DE's
apr17-21.pdf week 14 filled in notes
Math_2280_review.pdf review of our course
apr24.pdf 6.1-6.4 nonlinear systems of DE's, including predator-prey model and borderline nature of equilibria that linearize to stable centers