Differential Equations
Math 2250-4
Spring 2013
Lecture Page

2250-4 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: January 7-11
    jan7.pdf   jan7.mw  Introduction to course and Chapter 1.
    jan8.pdf   jan8.mw  1.1-1.2 solving first order differential equations by direct and indirect antidiffererntiation techniques.
    jan9.pdf   jan9.mw  1.2 continued, introduction to 1.3 slope fields and the graphs to solutions of first order initial value problems.
    jan11.pdf   jan11.mw  1.3-1.4 slope fields and the local existence of unique solutions to IVP's, illustrated with separable DEs.

Week 2: January 14-18
    jan14.pdf   jan14.mw  1.3-1.4 continued.
    jan15.pdf   jan15.mw  1.4-1.5 applications of separable DE's; introduction to linear DE's.
    jan16.pdf   jan16.mw  1.5 linear differential equations and input-output modeling
    jan18.pdf   jan18.mw  E.P. 3.7 linear DE's from electrical circuits; begin 2.1 improved population models.

Week 3: January 22-25
    jan22.pdf   jan22.mw  2.2 autonomous differential equations, equilibria, stability.
    jan23.pdf   jan23.mw  2.2 continued
    jan25.pdf   jan25.mw  2.3 improved velocity models.

Week 4: January 28 - February 1
    jan28.pdf   jan28.mw  2.3 continued.
    jan29.pdf   jan29.mw   2.4-2.6 numerical methods for approximate solutions to first order differential equations.
      numericaltemplate.pdf algorithms for Euler, improved Euler, Runge Kutta.
    jan30.pdf   jan30.mw   conclude Chapter 2, then begin 3.1-3.2.
    feb1.pdf   feb1.mw   3.1-3.3 Gaussian elimination and reduced row echelon form, for the solution set to systems of linear algebraic equations.
      feb1workedexamples.pdf   feb1workedexamples.mw   details from the three worked exercises involving three linear equations in three unknowns.

Week 5: February 4 - February 8
    feb4.pdf   feb4.mw  3.2-3.3 Gaussian elimination, row echelon, and reduced row echelon form.
    feb5.pdf   feb5.mw  3.3 using the reduced row echelon forms of augmented and coefficient matrices to deduce the possible solution spaces for associated systems of linear equations.
    feb6.pdf   feb6.mw  3.4 matrix algebra.
    feb8.pdf   feb8.mw  3.5 matrix inverses.

Week 6: February 11 - February 15
    feb11.pdf   feb11.mw  3.5-3.6 matrix inverses and determinants
    feb12.pdf   feb12.mw  3.6 continued
    exam1review.pdf   exam1review.mw  review questions for exam 1, for Wednesday discussion.
    feb15.pdf   feb15.mw  4.1-4.3 linear combination concepts for vectors: span

Week 7: February 19 - February 22
    feb19.pdf   feb19.mw  4.1-4.3 linear combination concepts: linear independence and dependence.
    feb20.pdf   feb20.mw  4.1-4.3 linear combination concepts: vector space, subspace, basis.
    feb22.pdf   feb22.mw  4.2-4.4 linear combination concepts: explicit and implicit definitions of subspaces, basis, dimension.

Week 8: February 25 - March 1
    feb25.pdf   feb25.mw  4.4 and key facts from 4.1-4.4.
    feb26.pdf   feb26.mw  5.1 second order linear differential equations.
    feb27.pdf   feb27.mw  5.2 key facts for nth order linear differential equations.
    mar1.pdf   mar1.mw  5.2: linear independence tests for functions. 5.3: how to use the characteristic polynomial to find the solution space for homogeneous constant coefficient linear DE's; the algorithms for distinct and repeated real roots.

Week 9: March 4 - March 8
    mar4.pdf   mar4.mw  5.3 How to find yH(x) for constant coefficient linear homogeneous differential equations.
    mar5.pdf   mar5.mw  5.4 Mechanical oscillation problems.
    mar6.pdf   mar6.mw  5.4 Pendulum model; experiment set-ups.
    mar8.pdf   mar8.mw  5.5 Finding yP for L(y)=f.

Week 10: March 18 - March 22
    mar18.pdf   mar18.mw  5.5 continued: undetermined coefficients and variation of parameters, for finding yP.
    mar19.pdf   mar19.mw  5.6 undamped forced oscillations.
    mar20.pdf   mar20.mw  5.6 damped forced oscillations; also, using conservation of energy for undamped problems to find natural frequencies.
    mar22.pdf   mar22.mw  10.1-10.2 introduction to the Laplace transform and how it can be used to solve initial value problems for linear differential equations.

Week 11: March 25 - March 29
    mar25.pdf   mar25.mw  10.1-10.3 Laplace transforms and initial value problems.
    mar26.pdf   mar26.mw  10.2-10.3 Laplace transforms and Chapter 5 initial value problems continued; partial fractions review.
    exam2review.pdf   exam2review.mw  review questions for exam 2, for Wednesday discussion.
    mar29.pdf   mar29.mw  10.4-10.5 Laplace transforms for unit step functions and convolutions, plus applications.

Week 12: April 1 - April 5
    apr1.pdf   apr1.mw  10.4-10.5, EP7.7 impulse functions, convolutions, and applications.
    apr2.pdf   apr2.mw  6.1-6.2 eigenvalues and eigenvectors
    apr3.pdf   apr3.mw  6.1-6.2 eigenspace bases and diagonalizability
    apr5.pdf   apr5.mw  7.1 systems of differential equations.

Week 13: April 8 - April 12
    apr8.pdf   apr8.mw  7.2 linear and non-linear systems of differential equations. Homogeneous and non-homogeneous linear systems of DE's, and x=xP+xH
    apr9.pdf   apr9.mw  7.3 the eigenvalue-eigenvector method for solving first order homogeneous sytems of DE's when the matrix A is constant.
    apr10.pdf   apr10.mw  7.3 applications of first order systems of DE's.
    apr12.pdf   apr12.mw  7.4 multi-component mechanical oscillations

Week 14: April 15 - April 19
    apr15.pdf   apr15.mw  7.4 unforced conservative mass-spring systems
    apr16.pdf   apr16.mw  7.4 forced mass-spring systems and practical resonance
    apr17.pdf   apr17.mw  9.1-9.2 autonomous first order systems of differential equations
    apr19.pdf   apr19.mw  9.2-9.3 classification of of equilbria and populations applications, for autonomous systems of DE's.

Week 15: April 22 - April 24
    apr22.pdf   apr22.mw  9.2-9.4 classification of equilbrium points for autonomous systems of two first order differential equations.
    apr23.pdf   apr23.mw  9.4 nonlinear autonomous mass-spring problems, interpreted as first order systems.
    Math_2250_review.pdf  Review notes for Wednesday