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Differential Equations
2250-010 home page
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Lecture notes for Wednesday will be posted by 5:00 p.m. on the preceding Monday. Lecture notes for Friday and Monday will be posted by the preceding Wednesday at 5:00 p.m. I strongly recommend bringing a copy of these notes to class, so we can go through the concepts and fill in the details together. Printing for Math classes is free in the Rushing Student Center, in the basement of LCB.
Week 1: January 6-10
jan6.pdf jan6.mw Introduction to course and Chapter 1.
jan8.pdf jan8.mw 1.2: antidifferentiation to solve differential equations of the form y'(x)=f(x), and applications.
jan10.pdf jan10.mw 1.3: slope fields; existence and uniqueness for initial value problems, illustrated with separable differential equations.
Week 2: January 13-17
jan13.pdf jan13.mw 1.4 separable differential equations and applications (We will finish Friday's notes first, starting at Exercise 3.)
jan15.pdf jan15.mw 1.5 linear differential equations
jan17.pdf jan17.mw 1.5, EP3.7 linear differential equations applications; begin 2.1 improved population models.
Week 3: January 22-24
jan22.pdf jan22.mw 2.1-2.2 applications of logistic DE; general autonomous first order differential equations.
jan24.pdf jan24.mw 2.2 autonomous differential equations, and applications
Week 4: January 27-31
jan27.pdf jan27.mw 2.3 improved velocity-acceleration models
jan29.pdf jan29.mw 2.4-2.6 numerical methods
Jan29_exercise4sols.pdf
jan31.pdf jan31.mw 3.1-3.2 Gaussian elimination to solve linear systems of equations
Week 5: Feb 3-7
feb3.pdf feb3.mw 3.3 row echelon form and reduced row echelon form for understanding the solution space to linear systems of equations
feb5.pdf feb5.mw 3.4 matrix algebra
feb7.pdf feb7.mw 3.5 matrix inverses
Week 6: Feb 10-14
feb10.pdf feb10.mw 3.6 determinants and connections to matrix inverses
February 12: We will use Monday's notes to finish our discussion of determinants. We will also work related homework problems, from the set due at 5:00.
Week 7: Feb 19-21
feb19.pdf feb19.mw 4.1-4.3 vector subspaces and linear combination concepts for Rn.
feb21.pdf feb21.mw 4.1-4.4 subspaces, bases, dimension.
Week 8: Feb 24-28
feb24.pdf feb24.mw 4.1-4.4 completed
feb26.pdf feb26.mw 5.1-5.2 second order linear differential equations
feb28.pdf feb28.mw 5.2-5.3 overview of nth order linear differential equations
Week 9: Mar 3-7
mar3.pdf mar3.mw 5.3 algorithms for finding bases for the solution spaces to nth order constant coefficient homogeneous linear differential equations, based on their characteristic polynomials.
mar5.pdf mar5.mw 5.4 applications to mechanical oscillations
mar7.pdf mar7.mw 5.4 pendulum model DE via conservation of energy and linearization; pendulum and mass-spring experiments.
Week 10: Mar 17-21
mar17.pdf mar17.mw 5.5 Finding particular solutions to linear differential equations.
mar19.pdf mar19.mw 5.6 applications to forced oscillation problems, and resulting physical phenomena
mar21.pdf mar21.mw 10.1-10.2 Laplace transform method of solving initial value problems
Week 11: Mar 24-28
mar24.pdf mar24.mw 10.1-10.3 Laplace transform table entries, and using these entries to solve constant coefficient linear differential equations.
mar26.pdf mar26.mw 10.1-10.3 Laplace transform continued. Also, using total energy to find natural angular frequencies, and practical resonance in forced RLC circuits.
Week 12: Mar 31- Apr 4
mar31.pdf mar31.mw 6.1-6.2 eigenvalues and eigenvectors
apr2.pdf apr2.mw 10.4-10.5 unit step functions and convolutions
apr4.pdf apr4.mw 10.4-10.5, EP7.6 unit step functions and convolutions continued, and delta function forcing.
EP7.6.pdf supplemental Edwards-Penney section on convolution solutions and impulse function forcing.
Week 13: Apr 7-11
apr7.pdf apr7.mw forced RLC circuits, EP 3.7, EP7.6
EP3.7.pdf RLC circuits
apr9.pdf apr9.mw 7.1-7.3 first order systems of differential equations, applications, and connections to single higher order differential equations.
apr11.pdf apr11.mw 7.3 complex eigendata in linear first order systems of DE's; applications.
Week 14: Apr 14-18
apr14.pdf apr14.mw 7.4 undamped unforced spring system oscillations
apr16.pdf apr16.mw 7.4 undamped forced spring system oscillations
apr18.pdf apr18.mw 9.1-9.2 nonlinear autonomous systems of first order differential equations
Week 15: Apr 21-24
apr21.pdf apr21.mw 9.1-9.4 nonlinear autonomous systems continued
Math_2250_review.pdf Math_2250_review.docx Course review - we'll spend the first 25 minutes of class on 9.1-9.4, then use these review notes.