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Differential Equations
2250-4 home page
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Lecture notes will be posted by 4:00 p.m. the day before class, and it will be your responsibility to bring a copy to class. Most people find it useful to have the notes handy so as to minimize copying directly from the blackboard, thus leaving time in class to work on and write down example details and key explanations.
Week 1: Jan 10-14
jan10.pdf 1.1: introduction to differential equations
jan11.pdf 1.2-1.3: integral solutions and slope fields.
jan12.pdf 1.2-1.3: applications of integral solutions (1.2), and the existence-uniqueness theorem for initial value problems (1.3).
jan14.pdf 1.3-1.4: separation of variables to illustrate and understand the local IVP existence and uniqueness theorem.
Week 2: Jan 18-21
jan18.pdf 1.4-1.5 Toricelli model/experiment and then introduction to linear DEs.
jan18.mw Don't print this out - it's gibberish unless you open it with Maple.
jan19.pdf 1.5 linear differential equations
jan21.pdf 2.1 improved population models
Week 3: Jan 24-28
jan24.pdf 2.1-2.2 equibria and stability for autonomous first order differential equations
jan21.mw Maple document for U.S. population data and logistic equation
jan25.pdf 2.1-2.2 continued.
jan26.pdf 2.3: improved velocity models.
jan28.pdf 1.5 project: Newtons law of cooling with time-periodic ambient temperature and a stable steady periodic solution.
Week 4: Jan 31 - Feb 4
jan31.pdf 2.4-2.6 numerical solutions to initial value problems for first order differential equations.
numerical1.mw file to open from Maple (output removed).
feb1.pdf Euler, improved Euler, Runge-Kutta templates. (We'll mainly use Monday's notes.)
feb2.pdf 3.1-3.2: introduction to linear systems and matrices
feb4.pdf 3.1-3.3: Gaussian elimination and reduced row echelon form for linear systems and matrices.
Week 5: Feb7 - Feb 11
feb7.pdf 3.3 reduced row echelon form of a matrix and solutions to linear systems
feb7.mw Maple worksheet for February 7 notes.
feb8.pdf 3.3-3.4 rref continued, matrix equations, fundamental relationship between solutions to homogeneous problems and inhomogeneous problems.
feb9.pdf 3.4 - 3.5 matrix algebra and inverse matrices
feb11.pdf 3.5 matrix inverses and determinants
Week 6: Feb 14 - Feb 18
feb14.pdf 3.6 determinants
feb15.pdf 3.6 continued - adjoint formula for inverses, and Cramer's rule.
feb16.pdf Introduction to Chapter 4
feb18.pdf 4.1-4.3
Week 7: Feb 22 - Feb 25
feb22.pdf 4.1-4.3 continued: linear dependence and independence, vector spaces and subspaces.
feb23.pdf 4.1-4.3 continued: linear dependence and independence, span, vector spaces and subspaces.
feb25.pdf 4.4 bases and dimension for vector spaces (and subspaces).
Week 8: Feb 28 - Mar 4
feb28.pdf 4.4-4.5 finding bases for subspaces associated to matrices.
mar1.pdf 4.7 general vector space examples, and connection to differential equations.
mar2.pdf 5.1 second order linear differential equations.
mar4.pdf 5.2-5.3 finding all solutions to nth order, constant coefficient linear homogeneous differential equations.
Week 9: Mar 7 - Mar 11
mar7.pdf 5.2-5.3 repeated and complex roots
mar8.pdf 5.3-5.4 complex roots; begin mass-spring differential equation.
mar9.pdf 5.4 mechanical vibrations.
mar11.pdf 5.4 and EP 3.7: mass-spring, pendulum experiments; RLC circuits lead to same DE's as mass-spring and pendulum models.
EP3.7.pdf supplemental section for electrical circuits
Week 10: Mar 14 - Mar 18
mar14.pdf 5.5 finding particular solutions for non-homogeneous linear differential equations.
mar15.pdf 5.6 applications to forced oscillation problems.
mar16.pdf 5.6 damped forced oscillation problems.
mar18.pdf 10.1-10.2 Laplace transforms for solving differential equation initial value problems.
Week 11: Mar 28 - Apr 1
mar28.pdf 10.2-10.3 Laplace transform methods, continued.
mar29.pdf exam review notes, and a copy of the Laplace transform table you'll be given on exam (from front cover of our text)...mostly we'll finish the Laplace table entries and examples from Monday's notes.
mar30.pdf two extended problems to review with - see how many topics from Tuesday's review notes you can highlight during the discussion - bring the review notes to class.
apr1.pdf 10.4-10.5 unit step function to turn functions and and off, and Laplace convolution.
Week 12: Apr 4 - Apr 8
apr4.pdf 10.4-10.5, EP 7.6: applications of the convolution formula to forced oscillation problems.
apr5.pdf 6.1 introduction to eigenvalues and eigenvectors
apr6.pdf 6.1-6.2 eigenspaces, eigenbases and diagonalization for matrices.
apr8.pdf 7.1 (and references to 7.2, 7.3), systems of differential equations.
Week 13: Apr 11 - Apr 15
apr11.pdf 7.2-7.3 linear systems of first order differential equations.
apr12.pdf 7.2-7.3 applications of first order systems of DE's.
apr13.pdf 7.4 multi mass-spring systems.
apr15.pdf 7.4 forced multi mass-spring systems and detecting practical resonance without solving the actual damped problem.
apr15maple.mw Maple document - commands and ideas might help with earthquake project.
Week 14: Apr 18 - Apr 22
apr18.pdf 7.5 defective eigenspaces
apr19.pdf 9.1-9.2 introduction to nonlinear systems of differential equations
apr20.pdf 9.1-9.3 linearization of autonomous systems of differential equations near equilibria.
apr22.pdf 9.2-9.3 classification of equilibrium solutions; predator-prey from 9.3. We'll also play with pplane.
Week 14: Apr 25 - Apr 27
apr25.pdf 9.3 population models.
apr26.pdf 9.4 mechanical systems.
apr27.pdf review sheet!