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Math 2280-002
2280-2 home page
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It is my goal to have lecture note outlines for each week posted by Friday evening of the preceding week. It is recommended that you use these notes in conjunction with attending class. I will bring hard copies to class on Mondays and 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 7-11 Sections 1.1-1.4
week1.pdf Notes that include outline for entire week
jan7.pdf 1.1 introduction to differential equations
jan8.pdf 1.2, 1.4 antidifferentiation differential equations and separable differential equations.
jan9.pdf 1.2-1.4 continued: separable and antidifferentiation differential equations, and mathematical modeling for applications.
jan11.pdf 1.3-1.4 continued: slope fields and the existence-uniqueness theorem for IVP's.
week1_post.pdf filled-in notes from week 1.
Week 2: January 14-18 Sections 1.3-1.5, 2.1
week2.pdf Notes that include outline for entire week
jan14.pdf 1.3 careful discussion of existence-uniqueness for IVP's, with examples.
jan15.pdf 1.5 how to identify and solve a first order linear differential equation
jan16.pdf 1.5 the constant coefficient linear first order DE; 1.4 Toricelli model
jan18.pdf 2.1 Improved population models, e.g. the logistic model.
week2_post.pdf filled-in notes from week 2.
Week 3: January 22-25 Sections 1.5-2.3
week3.pdf Notes that include outline for entire week
jan22.pdf 2.1, 1.5 input-output modeling with differential equations; application of logistic DE.
jan23.pdf 2.2 autonomous differential equations, phase diagrams, stable and unstable equilbria.
jan25.pdf 2.2 applications of phase portrait analysis; 1.5 input-output example
week3_post.pdf filled-in notes from week 3.
Week 4: January 28 - February 1 Sections 2.3-2.6, 3.1
week4.pdf Notes that include outline for entire week
jan28.pdf 2.3 improved velocity models.
jan29.pdf 2.4-2.5 Euler and improved Euler for numerical solutions to DE's.
jan30.pdf 2.6 Runge Kutta
feb1.pdf 3.1-3.2 second order linear differential equations and vector space theory
week4_post.pdf filled-in notes from week 4.
Week 5: February 4-8 Sections 3.1-3.3
week5.pdf Notes that include outline for entire week
feb4.pdf 3.1-3.2 second order linear differential equations and vector space theory, continued.
feb5.pdf 3.1-3.2, intro to 3.3-3.4: vector space theory for non-homogeneous linear DE's.
feb8.pdf 3.3 characteristic polynomial and solutions to homogeneous linear DE's with constant coefficients.
week5_post.pdf filled-in notes from week 5.
Week 6: February 11-13 Sections 3.3-3.4
week6.pdf Notes that include outline for entire week
feb11.pdf 3.3-3.4 complex roots for characteristic polynomial; damped mass-spring configuration applications.
feb12.pdf 3.4 continued, together with discussion of last homework problem.
feb13.pdf 3.4 pendulum model; pendulum and mass spring experiments; review for midterm 1.
week6_post.pdf filled-in notes from week 6.
Week 7: February 19-22 Sections 3.5-3.6
week7.pdf Notes that include outline for entire week
feb19.pdf 3.5 Method of undetermined coefficients to find particular solutions for L(y)=f.
feb20.pdf 3.5 continued.
feb22.pdf 3.5-3.6 introduction to forced oscillations, more method of undetermined coefficients.
week7_post.pdf filled-in notes from week 7.
Week 8: February 25 - March 1 Sections 3.6-3.7, 4.1, 5.1-5.2
week8.pdf Notes that include outline for entire week
feb25.pdf 3.6: beating and resonance for undamped forced oscillators
feb26.pdf 3.6-3.7: practical resonance for undamped forced oscillators, illustrated for forced damped mass-spring systems and RLC circuits.
feb27.pdf 4.1: introduction to systems of differential equations
mar1.pdf 5.1-5.2 introduction to solving linear homogeneous systems of differential equations, x'=Ax, using eigendata of the matrix A.
week8_post.pdf filled-in notes from week 8.
Week 9: March 4-8 Sections 4.1, 5.1-5.3, introduction to Chapter 6
week9.pdf Notes that include outline for entire week
mar4.pdf 5.1-5.2: universal product rule, writing higher order DE's as first order systems and correspondence of solutions and "characteristic polynomial" "Wronskian" terminology.
mar5.pdf 5.1-5.2: continued
mar6.pdf 5.2: what to do with complex eigendata
mar8.pdf 5.2-5.3: complex eigendata, glucose-insulin model; spiral and elliptical phase portraits for complex eigendata.
week9_post.pdf filled-in notes from week 9.
Week 10: March 18-22 Sections 5.3, 6.1-6.4
week10.pdf Notes that include outline for entire week
mar18.pdf 5.3: phase portrait geometry for homogeneous linear systems, A2x2 and real eigendata.
mar19.pdf 6.1-6.2: autonomous systems of two first order differential equations and how to linearize at equilibrium solutions.
mar20.pdf 6.3: interacting populations models
mar22.pdf 6.3-6.4: non-linear mechanical systems; showing that equilibria with borderline linearization (stable center) actually are, by finding a conserved function.
week10_post.pdf filled-in notes from week 10.
Week 11: March 25-27 Sections 6.4, 5.4
week11.pdf Notes that include outline for entire week
mar25.pdf 6.4 and further directions in higher dimensions, 6.5.
mar26.pdf 5.4 unforced mass-spring systems.
mar27.pdf 5.4 unforced mass-spring systems and experiment; exam 2 review notes.
week11_post.pdf filled-in notes from week 11.
Week 12: April 1-4 Sections 5.4, 5.6-5.7
week12.pdf Notes that include outline for entire week
apr1.pdf 5.4 forced mass-spring systems and resonance
apr2.pdf 5.4 shake table model and demo; 5.6 introduction to matrix exponentials
apr3.pdf 5.6 matrix exponentials and solutions to homogeneous systems of linear differential equations.
apr5.pdf 5.6 matrix exponentials integrating factor for nonhomogeneous systems of linear differential equations.
week12_post.pdf filled-in notes from week 12.
Week 13: April 8-12 Sections 5.6, 9.1-9.3
week13.pdf
apr8.pdf 5.6 matrix exponential examples for diagonalizable and non-diagonalizable matrices
apr9.pdf 9.1 introduction to Fourier series
apr10.pdf 9.1-9.2 understanding truncated Fourier series as orthogonal projection; computing Fourier coefficients.
apr12.pdf 9.2-9.3 integrating and differentiating Fourier series; 2L-periodic Fourier series.
week13_post.pdf filled-in notes from week 13.
Week 14: April 15-19 Sections 9.3-9.6
apr15.pdf 9.3: even and odd extensions; 9.4 forced oscillations, revisited.
apr16.pdf 9.5 introduction to heat equation
apr17.pdf 9.5 solutions to initial boundary value problems for the heat equation, using Fourier series.
apr19.pdf 9.6 introduction to the wave equation, and some special solutions.
Week 15: April 22-23 9.6, and course review
apr22.pdf Fourier series and solutions to initial boundary value problems for the wave equation; slinky wave modeling and experiments.
2280_course_review.pdf For Tuesday April 23.