Differential Equations
Math 2250-1
Fall 2012
Lecture Page

2250-1 home page
Department of Mathematics
College of Science
University of Utah

Lecture notes will be posted by 4:00 p.m. the day before class. I strongly recommend bringing a copy of these notes to class, so we can go through the concepts and fill in the details together.

Week 1: August 20-24
    aug20.pdf   aug20.mw  Introduction to course and Chapter 1.
    aug21.pdf   aug21.mw  1.2: differential equations of the form y'(x)=f(x)
    aug22.pdf   aug22.mw  1.2-1.3: also begin slope fields and geometric interpretation of first order DE IVPs.
    aug24.pdf   aug24.mw  1.3-1.4: slope fields and first order DE's; examples using separable differential equations.

Week 2: August 27-31
    aug27.pdf   aug27.mw  More separable DE's
    aug28.pdf   aug28.mw  and 1.5 linear differential equations
    aug29.pdf   aug29.mw  1.5 linear differential equations
    aug31.pdf   aug31.mw  1.5 applications, including EP 3.7; begin 2.1 improved population models * updated with derivation of formula for solutions to logistic differential equation IVPs that we did in class on Tuesday Sept. 4

Week 3: September 4-7
    sept4.pdf   sept4.mw  2.1-2.2 autonomous first order DEs
    sept5.pdf   sept5.mw  2.2 autonomous first order DEs and applications
    sept7.pdf   sept7.mw  2.3 improved velocity models

Week 4: September 10-14
    sept10.pdf   sept10.mw  2.3 continued, including escape velocity.
    sept11.pdf   sept11.mw  2.4-2.6 numerical methods for first order DE IVPs
      numericaltemplate.pdf  numerical algorithms template
    sept12.pdf   sept12.mw  2.2; 3.1-3.2: populations; simultaneous linear algebraic equations and how to find the solution sets.
    sept14.pdf   sept14.mw  3.1-3.3: Gaussian elimination and reduced row echelon form, for the solution set to systems of linear algebraic equations.
      sept14workedexamples.pdf   sept14workedexamples.mw 

Week 5: September 17-21
    sept17.pdf   sept17.mw  3.2-3.3 Reduced row echelon form for solving linear systems of equations.
    sept18.pdf   sept18.mw  3.3 How the shape of the reduced row echelon form determines the structure of the solution set to linear systems of equations.   sept18filledin.pdf   sept18filledin.mw 
    sept19.pdf   sept19.mw  3.4 Matrix algebra
    sept21.pdf   sept21.mw  3.5 Matrix inverses

Week 6: September 24-28
    sept24.pdf   sept24.mw  3.6 Determinants
    sept25.pdf   sept25.mw  3.6 Determinants
    exam1review.pdf   exam1review.mw  review topics, for 1.1-1.5, 2.1-2.4, 3.1-3.6.
    sept28.pdf   sept28.mw  4.1-4.3 linear combinations of vectors

Week 7: October 1-5
    oct1.pdf   oct1.mw  4.1-4.3 linear combinations, span, linear independence, and how to study these questions in Rm via reduced row echelon form matrices.
    oct2.pdf   oct2.mw  4.1-4.3 continued
    oct3.pdf   oct3.mw  4.2-4.4 vector spaces, subspaces, bases, dimension.    oct3filledin.pdf   oct3filledin.mw  lecture discussion notes filled in.
    oct5.pdf   oct5.mw  4.4 bases and dimension, and review.

Week 8: October 15-19
    oct15.pdf   oct15.mw  5.1-5.2 second order differential equations
    oct16.pdf   oct16.mw  5.1-5.2 second order and nth order linear differential equations
    oct17.pdf   oct17.mw  5.2-5.3 second order and nth order linear differential equations, with a focus on ways to test functions for linear independence.
    oct19.pdf   oct19.mw  5.3 algorithms for finding solution space bases, for constant coefficient homogeneous linear differential equations.

Week 9: October 22-26
    oct22.pdf   oct22.mw  5.4 mechanical vibrations.
    oct23.pdf   oct23.mw  5.4 mechanical vibrations continued
    oct24.pdf   oct24.mw  5.4 pendulum and mass-spring experiments. Also begin 5.5, particular solutions yP(x) for non-homogeneous linear DEs.
    oct26.pdf   oct26.mw  5.5 particular solutions to non-homogeneous linear differential equations

Week 10: October 29-November 2
    oct29.pdf   oct29.mw  5.5 particular solutions to linear DEs; 5.6 overview of forced oscillation problems, details for forced undamped oscillators
    oct30.pdf   oct30.mw  5.6 forced damped oscillators and applications
    oct31.pdf   oct31.mw  5.6 conservation of energy to find the natural frequencies for undamped mechanical and electrical configurations.
    nov2.pdf   nov2.mw  10.1-10.2 The Laplace transform, and why it is an amazing tool for solving linear differential equation IVPs.

Week 11: November 5-9
    nov5.pdf   nov5.mw  10.1-10.3 Laplace transform and initial value problems
    nov6.pdf   nov6.mw  10.2-10.3 Laplace transform table entries, partial fractions, and initial value problems.
    exam2review.pdf   exam2review.mw  review outline for exam 2   exam2reviewfilledin.pdf filled-in version
    nov9.pdf   nov9.mw  10.4-10.5 the unit step function - to turn forcing on and off; convolution to invert products of Laplace transforms.

Week 12: November 12-16
    nov12.pdf   nov12.mw  10.5, EP 7.6 - periodic and impulse functions; convolution applications.
    nov13.pdf   nov13.mw  6.1-6.2 eigenvalues and eigenvectors
    nov14.pdf   nov14.mw  6.2 eigenvalues and eigenvectors, and matrix diagonalizability.
    nov16.pdf   nov16.mw  7.1 systems of differential equations

Week 13: November 19-21
    nov19.pdf   nov19.mw  7.2-7.3 first order linear systems of differential equations
    nov20.pdf   nov20.mw  7.3 the eigenvalue-eigenvector method for solving constant coefficient homogeneous linear systems of DE's with diagonalizable matrices; real and complex eigendata.
    nov21.pdf   nov21.mw  7.3 applications of first order linear systems of differential equations.

Week 14: November 26-30
    nov26.pdf   nov26.mw  7.4 second order linear systems of DE's for undamped mechanical systems.
    nov27.pdf   nov27.mw  7.4 unforced undamped mechanical systems - examples and experiment; begin forced systems.
    nov28.pdf   nov28.mw  7.4 forced undamped mechanical systems; earthquake shaking and (im)practical resonance.
    nov30.pdf   nov30.mw  9.1-9.2 autonomous first order systems of differential equations, and linearization.

Week 15: December 3-7
    dec3.pdf   dec3.mw  9.2-9.3 Classification of equilibria for autonomous systems via eigenvalues of the linearized system. Examples from interacting population models
    dec4.pdf   dec4.mw  9.2-9.4 Classification of equilibria for autonomous systems, continued. Examples from interacting population models and non-linear mechanical oscillation models.
    dec5.pdf   dec5.mw  9.4 non-linear autonomous mechanical oscillation models, interepreted as first order systems.
    Math2250review.pdf   notes for Friday