Differential Equations
Math 2270-004
Spring 2018
Lecture Page

2270-004 home page
Department of Mathematics
College of Science
University of Utah

Lecture notes for each week should be posted by Thursday at 3:00 p.m. on the preceding week. Printing for Math classes is free in the Rushing Student Center, in the basement of LCB. It is recommended that you use these notes in conjunction with attending class. 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
    week1.pdf Notes that include outline for entire week
    The daily post-notes from this week are below:
      jan8.pdf syllabus, 1.1. linear systems of equations
      jan9.pdf 1.2 Gaussian elimination
      jan10.pdf 1.2 reduced row echelon form, consistent and inconsistent systems.
      jan12.pdf 1.2, intro to 1.3. reduced row echelon form, intro to vectors.
     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 vector equations
      jan17.pdf 1.4 vector equations and matrix equations are systems of linear equations.
      jan19.pdf 1.5 solution sets of linear systems
     week2_post.pdf all material we covered in week 2

Week 3: January 22-26 Sections 1.6-1.8
    week3.pdf Notes that include outline for entire week
      jan22.pdf review of 1.1-1.5 concepts and conclusions
      jan23.pdf 1.6 applications, and introduction to 1.7 linear dependence/independence
      jan24.pdf 1.7 linear dependencies correspond to solutions to homogeneous matrix equations; rref of a matrix encodes column dependencies.
      jan26.pdf 1.8 Matrix transformations are linear transformations, examples.
     week3_post.pdf all material we covered in week 3

Week 4: January 29 - February 2 Sections 1.8-1.9, 2.1-2.2
    week4.pdf Notes that include outline for entire week
      jan29.pdf 1.9 linear transformations from R2 to R2
      jan30.pdf 1.9 continued
      jan31.pdf 1.9, 2.1 matrix multiplication arises from composition of linear transformations.
      feb2.pdf 2.1 matrix algebra
     week4_post.pdf all material we covered in week 4

Week 5: February 5-9 Sections 2.1-2.3
    week5.pdf Notes that include outline for entire week
      feb5.pdf 2.1-2.2 matrix algebra and introduction to matrix inverses
      feb6.pdf 2.2-2.3 matrix inverses
      feb7.pdf 2.3 big theorem relating key concepts, and giving a long list of conditions equivalent to a matrix having an inverse.
     week5_post.pdf all material we covered in week 5

Week 6: Feb 12-16 Sections 2.3, 3.1-3.3
    week6.pdf Notes that include outline for entire week
      feb12.pdf 2.3 matrix inverses via products of elementary matrices
      feb13.pdf 3.1 determinants
      feb14.pdf 3.2 determinant properties
      feb16.pdf 3.3 formula for inverse matrices, Friday fft.
     week6_post.pdf all material we covered in week 6

Week 7: Feb 20-23 Sections 4.1-4.3
    week7.pdf Notes that include outline for entire week
      feb20.pdf 4.1 vector spaces and subspaces
      feb21.pdf 4.1-4.2 Linear combinations, span, linear dependence/independence in vector spaces. Subspaces as spans of collections of vectors.
      feb23.pdf 4.2-4.3 nullspace, column space, basis.
     week7_post.pdf all material we covered in week 7

Week 8: Feb 26 - Mar 2 Sections 4.2-4.6
    week8.pdf Notes that include outline for entire week
      feb26.pdf 4.2-4.3 good bases for subspaces of Rn.
      feb27.pdf 4.2 general linear transformation between vector spaces, kernel and range subspaces.
      feb28.pdf 4.4-4.5 bases for vector spaces yield coordinate systems.
      mar2.pdf 4.4-4.5 vector space isomorphisms and coordinates, change of coordinates matrix introduction.
     week8_post.pdf all material we covered in week 8

Week 9: Mar 5-9 Sections 4.5-4.6, 5.1-5.2
    week9.pdf Notes that include outline for entire week
      mar5.pdf 4.5-4.6 vector space theorems; 4 subspaces associated with matrices.
      mar6.pdf 4.5-4.6 completed
      mar7.pdf 4.7 transition matrices to change coordinates in a vector space.
      mar9.pdf 5.1-5.2 introduction to eigenvectors and eigenvalues
     week9_post.pdf all material we covered in week 9

Week 10: Mar 12-14 Sections 5.2-5.4
    week10.pdf Notes that include outline for entire week    
      mar12.pdf 5.2 using the characteristic equation to find eigenvalues and eigenspace bases.
      mar13.pdf 5.3 diagonalizable and non-diagonalizable matrices
      mar14.pdf 5.4 Matrix of a linear transformation T:V->W, given bases for V and W.
     week10_post.pdf all material we covered in week 10

Week 11: Mar 26-30 Sections 5.4-5.6
    week11.pdf Notes that include outline for entire week
      mar26.pdf 5.4 Matrix of a linear transformation T:V->W: "big picture" idea that encompasses our work on coordinates, change of coordinates, diagonalization, and more.
      mar27.pdf 5.5 complex eigenvalues and eigenvectors
      mar28.pdf 5.6 introduction to discrete dynamical systems, and understanding them via eigenvectors and eigenvalues.
      mar30.pdf 5.6 google page rank
     week11_post.pdf all material we covered in week 11

Week 12: Apr 2-6 Sections 6.1-6.4
    week12.pdf Notes that include outline for entire week
      apr2.pdf 6.1-6.2 algebra and geometry of dot product; orthogonality and projection onto a line.
      apr3.pdf 6.2-6.3 angles between vectors in Rn; orthogonal complements to subspaces, four fundamental subspaces of a matrix revisited, geometrically.
      apr4.pdf 6.3-6.4 orthogonal and orthonormal bases for subspaces W, and projection onto W.
      apr6.pdf 6.4 The Gram-Schmidt algorithm for creating orthonormal bases.
     week12_post.pdf all material we covered in week 12

Week 13: Apr 9-13 Sections 6.4-6.8
    week13.pdf Notes that include outline for entire week
      apr9.pdf 6.4 A=QR decomposition
      apr10.pdf 6.5 Least squares solutions
      apr11.pdf 6.6 best data fits for appropriate models, via least squares
      apr13.pdf 6.7-6.8 inner product spaces and Fourier series
     week13_post.pdf all material we covered in week 13

Week 14: Apr 16-20 Sections 6.8, 7.1-7.2
    week14.pdf Notes that include outline for M-W...Friday notes to be added.
      apr16.pdf 6.8 Fourier series example worked out; "show and tell" about .jpg image compression (more pages available in hard copy).
      apr17.pdf 7.1-7.2 Spectral theorem and quadratic forms
      apr18.pdf 7.1-7.2 diagonalizing quadratic forms; matrix multiplication via "outer product"; spectral decomposition theorem for symmetric matrices.
     week14_post.pdf all material we covered in week 14, except for Prof. Alberts' lecture on statistics applications of principal component analysis.

Week 15: Apr 23-24 Section 7.2 and review
    week15.pdf Notes for Monday; review notes to be added later.
      apr23.pdf 7.2 multivariable second derivative test, revisited.
      apr24.pdf course review notes