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Differential Equations
2250-004 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 syllabus, 1.1. differential equations, solutions to DE's and to IVP's for DE's.
jan10.pdf 1.1, with extended exercises from Monday's notes about exponential growth and Newton's law of cooling modeling.
jan11.pdf 1.2 differential equations of the form y'=f(x); position, velocity, acceleration problems
jan13.pdf 1.3 slope fields and solution graphs
jan9-13.pdf 1.1-1.3
Week 2: January 17-20 Sections 1.3-1.4 and part of 1.5
week2.pdf Notes that include outline for entire week
jan17.pdf 1.3-1.4 existence-uniqueness theorem; separable DE's.
jan18.pdf continued
jan20.pdf 1.5 linear DE's
jan17-20.pdf 1.3-1.5
Week 3: January 23-27 Sections 1.5-2.3
week3.pdf Notes that include outline for entire week
jan23.pdf 1.5 input-output modeling with linear DE's.
jan24.pdf 1.5-2.1 input-output example; improved population modeling
jan25.pdf 2.1-2.2 logistic model; autonomous differential equations, equilibrium solutions, stability.
jan27.pdf 2.1-2.2
jan23-27.pdf 1.5-2.2
week3.note 1.5-2.2 Notability note - includes audio from class.
Week 4: January 30 - February 3 Sections 2.3, 2.4-2.6, 3.1
week4.pdf Notes that include outline for entire week
jan30.pdf 2.3 improved velocity models
jan31.pdf 2.3-2.4 Euler's method
feb1.pdf 2.4-2.6 Improved Euler and Runge Kutta
feb3.pdf 3.1-3.2 linear systems of equations, Gaussian elimination
jan30-feb3.pdf 2.3-2.6
week4.note 2.3-2.6 Notability note - includes audio from class.
Week 5: February 6-10 Sections 3.2-3.5
week5.pdf Notes that include outline for entire week
feb6.pdf 3.1-3.3 Gaussian elimination, row echelon and reduced row echelon form
feb7.pdf 3.2-3.3 Gaussian elimination and rref to solve Ax=b. Properties of solution set from shape of reduced matrix form of A.
feb8.pdf 3.3 The possible numbers of solutions "x" to Ax=b can often be deduced from the reduced row echelon form of A alone.
feb10.pdf 3.4 Matrix algebra
feb6-10.pdf 3.1-3.4
week5.note 3.1-3.4 Notability note - includes audio from class.
Week 6: February 13-17 Sections 3.5-3.6
week6.pdf Notes that include outline for entire week
feb13.pdf 3.5 Matrix inverses
feb14.pdf 3.6 Determinants
feb15.pdf Exam 1 review
week6.note 3.5-3.6 Notability note - includes audio from class.
Week 7: February 21-24 Sections 4.1-4.3
week7.pdf Notes that include outline for entire week
feb21.pdf 3.6 determinants: how to compute with row operations; adjoint formula for inverse; Cramer's rule
feb22.pdf 4.1: vector algebra and geometry in R2 and R3.
feb24.pdf 4.1-4.3: linear independence and span
feb21-24.pdf filled in notes from week 7
week7.note 3.6-4.3 Notability note - includes audio from class.
Week 8: February 27 - March 3 Sections 4.4, 5.1-5.2
week8.pdf Notes that include outline for entire week
feb27.pdf 4.2-4.4: subspaces of Rn, basis, dimension.
feb28.pdf 4.2-4.4: continued...focus on what sets are and are not subspaces of Rn.
mar1.pdf 4.2-4.4: continued, and introduction to 5.1, function spaces as "vector" spaces. Rn.
mar3.pdf 4.4, intro to 5.1 column dependencies and reduced row echelon form; testing independence for functions.
feb27-mar3.pdf filled in notes from week 8
week8.note 4.2-4.4, 5.1 Notability note - includes audio from class.
Week 9: March 6-10 Sections 5.2-5.4
week9.pdf Notes that include outline for entire week
mar6.pdf 5.1-5.2 linear differential equations
mar7.pdf 5.1-5.3 solving linear constant coefficient homogeneous linear differential equations, and the roles of the Wronskian matrix.
mar8.pdf 5.3 algorithm for finding basis functions for solutions to L(y)=0, via the characteristic polynomial.
mar10.pdf 5.3 Euler's formula and complex roots; brief overview of 5.4 mechanical oscillations.
mar6-10.pdf filled in notes from week 9
week9.note 5.1-5.3 Notability note - includes audio from class.
Week 10: March 20-24 Sections 5.4-5.6
week10.pdf Notes that include outline for entire week
mar20.pdf 5.4 unforced mass-spring configuration, damped and undamped.
mar21.pdf 5.5: particular solutions to L(y)=f, intro to method of undetermined coefficients
mar22.pdf 5.5 continued, overview of 5.6: forced oscillation phenomena
mar24.pdf 5.6 forced oscillation phenomena when no damping: superposition, beating, resonance
mar20-24.pdf filled in notes from week 10
week10.note 5.4-5.6 Notability note - includes audio from class.
Week 11: March 27-29 Sections 5.6, 10.1-10.2, exam 2 review questions
week11.pdf Notes that include outline for entire week
mar27.pdf 5.6 forced oscillation phenomena when damping: steady periodic solutions and practical resonance
mar28.pdf 5.4 pendulum and mass-spring experiments; 5.6 practical resonance in RLC circuits (5.6, EP 3.7)
mar29.pdf 10.1-10.2 introduction to Laplace transforms (plus filled-in review sheet for second midterm).
mar27-29.pdf filled in notes from week 11
week11.note 5.6, EP 3.7, 10.1-10.2 Notability note - includes audio from class. Audio is from time 0:00-1:41 (M,T), and 3:52-4:44 (W); I accidentally forgot to turn the sound off until a couple hours after class on Tuesday ... oops. :-)
Week 12: April 3-7 Sections 10.2-10.5, EP 7.6
week12.pdf Notes that include outline for entire week
apr3.pdf 10.1-10.3 Laplace transforms and IVP's continued.
apr4.pdf continued; partial fractions and IVP's.
apr5.pdf 10.2-10.3 partial fractions; unit step functions.
apr7.pdf 10.4, EP7.6 turning forcing on and off; impulse forcing.
apr3-7.pdf filled in notes from week 12
week12.note 5.6, EP 7.6, 10.1-10.2 Notability note - includes audio from class.
Week 13: April 10-14 Sections 6.1-6.2, 7.1-7.2
week13.pdf Notes that include outline for entire week
apr10.pdf 10.4, EP7.6 convolutions and integral formulas for solutions to IVPs
apr11.pdf 6.1 eigenvalues and eigenvectors
apr12.pdf 6.1-6.2 eigendata and diagonalization
apr14.pdf 7.1-7.3 intro to Chapter 7 and what systems of differential equations have to do with eigendata
apr10-14.pdf filled in notes from week 13
week13.note EP 7.6, 6.1-6.2, 7.1-7.3 intro; Notability note - includes audio from class.
Week 14: April 17-21 Sections 7.1-7.4
week14.pdf Notes that include outline for entire week
apr17.pdf 7.1-7.3 focus on why nth order DE's are equivalent to special first order systems of DE's, 7.1.
apr18.pdf 7.1-7.3, continued.
apr19.pdf 7.3, first order systems with complex eigendata; nonhomogeneous problems.
apr21.pdf 7.4 mass-spring systems
apr17-21.pdf filled in notes from week 14
week14.note 7.1-7.4 Notability note - includes audio from class.
Week 15: April 24-25 Section 7.4
week15.pdf contains Monday's notes and review notes for Tuesday.
apr24.pdf 7.4 mass-spring systems and forced oscillations
apr25.pdf 7.4 shake table experiment and review notes
apr24-25.pdf filled in notes from week 15
week15.note 7.4 and course review Notability note - includes audio from class.