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Differential Equations
2250-004 home page
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Lecture notes for each week should be posted over the preceding weekend, and I will bring copies to class on Mondays. 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 8-12 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:
jan8.pdf syllabus, 1.1. differential equations, solutions to DE's and to IVP's for DE's.
jan9.pdf 1.1-1.2 differential equations of the form y'(x)=f(x).
jan10.pdf 1.2 continued: position-velocity-acceleration problems
jan12.pdf 1.3-1.4 slope fields and solution graphs, introduction to separable DE's.
week1_post.pdf all material we covered in week 1
Week 2: January 16-19 Sections 1.3-1.5
week2.pdf Notes that include outline for entire week
jan16.pdf 1.3-1.4 existence-uniqueness theorem, with separable DE examples
jan17.pdf 1.4-1.5 separable DE application; introduction to linear differential equations.
jan19.pdf 1.5 linear DE's continued; input-output modeling
week2_post.pdf all material we covered in week 2
Week 3: January 22-26 Sections 1.5, EP 3.7, 2.1-2.3
week3.pdf Notes that include outline for entire week
jan22.pdf 1.5, EP 3.7: input-output modeling example, and RLC circuits application
jan23.pdf 2.1 improved population model: logistic DE.
jan24.pdf 2.2 equilibrium solutions and phase diagrams for autonomous first order differential equations.
jan26.pdf 2.2 phase diagram analysis; many solutions from one; harvesting logistic, and doomsday-extinction model.
week3_post.pdf all material we covered in week 3
Week 4: January 29 - Feb 2 Sections 2.3-2.6, 3.1-3.2
week4.pdf Notes that include outline for entire week
jan29.pdf 2.3 improved acceleration models.
jan30.pdf 2.4 Euler's method for numerical approximation of solutions to first order differential equations.
jan31.pdf 2.5-2.6 Improved Euler and Runge-Kutta numerical methods for first order DE's. Also, handout with Matlab functions and scripts.
feb2.pdf 3.1-3.2
week4_post.pdf all material we covered in week 4
Week 5: Feb 5-9 Sections 3.1-3.5
week5.pdf Notes that include outline for entire week
feb5.pdf 3.1-3.3 reduced row echelon form and solving systems of linear equations
feb6.pdf 3.3 reduced row echelon form of a matrix A and how it relates to possible solutions for associated linear systems
feb7.pdf 3.3 continued
feb9.pdf 3.4 matrix algebra; introduction to 3.5 matrix inverses
week5_post.pdf all material we covered in week 5
Week 6: Feb 12-14 Sections 3.5-3.6
week6.pdf Notes that include outline for entire week
feb12.pdf 3.5 matrix inverses
feb13.pdf 3.6 definition of determinants
feb14.pdf 3.6 determinant properties, and review notes for exam on Friday.
week6_post.pdf all material covered in week 6
Week 7: Feb 20-23 Sections 3.6, 4.1-4.3
week7.pdf Notes that include outline for entire week
feb20.pdf 3.6 adjoint formula for inverse matrices; Cramer's rule.
feb21.pdf 4.1 visualizing linear combinations, vector equations, and "span" in R2 and R3.
feb23.pdf 4.1-4.3 linear independence and span
week7_post.pdf all material covered in week 7
Week 8: Feb 26 - Mar 2 Sections 4.2-4.4, 5.1
week8.pdf Notes that include outline for entire week
feb26.pdf 4.2-4.4 linear independence, span, basis, dimension, for subspaces of Rn.
feb27.pdf 4.2-4.4 vector spaces and subspaces.
feb28.pdf 4.3-4.4 sub(vector)spaces in Rn, and how concepts like linear independence and span are interpreted for function "vectors".
mar2.pdf 4.4 finding bases for subspaces of Rn, and how reduced row echelon form of a matrix encodes the matrix column dependencies.
week8_post.pdf all material covered in week 8
Week 9: Mar 5-9 Sections 5.1-5.3
week9.pdf Notes that include outline for entire week
mar5.pdf 5.1-5.2 second (and higher order) linear differential equations
mar6.pdf 5.1-5.2 continued, introduction to 5.3
mar7.pdf 5.3 part 1: solutions to homogeneous linear differential equations with constant coefficients; real roots to characteristic equation
mar9.pdf 5.3 part 2: complex roots to characteristic equation
week9_post.pdf all material covered in week 9
Week 10: Mar 12-16 Sections 5.4-5.6
week10.pdf Notes that include outline for entire week
mar12.pdf 5.4 part 1: unforced oscillation problems without damping.
mar13.pdf 5.4 part 2: unforced oscillation problems without damping.
mar14.pdf 5.5 Finding particular solutions for nonhomogeneous linear differential equations, L(y)=f
mar16.pdf 5.5, intro to 5.6 forced oscillations
week10_post.pdf all material covered in week 10
Week 11: Mar 26-28 Sections 5.6,10.1-10.2
week11.pdf Notes that include outline for entire week
mar26.pdf 5.6: forced oscillations without damping: superposition, beating, resonance.
mar27.pdf 5.6: forced oscillations with damping: solutions as superposition of steady periodic and transient solutions; practical resonance.
mar28.pdf 10.1-10.3 introduction to Laplace transforms
week11_post.pdf all material covered in week 11
Week 12: Apr 2-6 Sections 10.2-10.5, EP7.6
week12.pdf Notes that include outline for entire week
apr2.pdf 10.1-10.3 Laplace transform table entries, IVP's.
apr3.pdf 10.2-10.3 continued; the linearized pendulum DE and an experiment.
apr4.pdf 10.2-10.4 partial fractions, resonance table entries, step functions.
apr6.pdf 10.5, EP7.6 piecewise and impulse forcing.
week12_post.pdf all material covered in week 12
Week 13: Apr 9-13 Sections 10.5, EP7.6, 6.1-6.2
week13.pdf Notes that include outline for entire week
apr9.pdf 10.5, EP7.6 convolutions
apr10.pdf 6.1-6.2 eigenvalues and eigenvectors
apr11.pdf 6.1-6.2 eigenspaces and diagonalizability
apr13.pdf 7.1-7.3 introduction to systems of differential equations
week13_post.pdf all material covered in week 13
Week 14: Apr 16-20 Sections 7.1-7.4
week14.pdf Notes that include outline for entire week
apr16.pdf 7.1-7.2: systems of differential equations and calculus review, for differentiation rules in the matrix-vector setting.
apr17.pdf 7.2-7.3: using eigendata and exponential functions to solve homogeneous first order systems of DEs.
apr18.pdf 7.3: handling complex eigendata...includes finished G-H example.
apr20.pdf 7.4: unforced mass-spring systems
week14_post.pdf all material covered in week 14
Week 15: Apr 23-24 7.4 and review
week15.pdf includes 7.4 forced oscillations; review notes will be posted later.
apr23.pdf 7.4: mass-spring systems
apr24.pdf filled-in review notes