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Math 2270-3
2270-3 home page
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Lecture notes will (usually) be posted by 4:00 p.m. the day before class, and it will be your responsibility to bring a copy to class.
Week 1: Aug 24-28
aug24.pdf 1.1: introduction to linear systems of equations.
aug25.pdf 1.1-1.2: and using Gaussian elimination to compute reduced row echelon form.
aug26.pdf 1.2-1.3: reduced row echelon form and the vector linear combination form for explicit solutions.
aug28.pdf 1.3: what rref tells us about the solution space to linear systems of equations. The second geometric interpretation of a linear system, as a linear combination problem. (The first interpretation was as an intersecting hyperplane problem. )
Week 2: Aug 31-Sept 4
aug31.pdf Appendix A: The dot product, lengths and angles, in Euclidean space.
sept1.pdf Appendix A and 2.1 - matrix transformation properties and example.
sept2.pdf 2.1-2.2: general matrix transformations, and the case of transforming the plane to itself.
2270MapleIntro.mw Maple 13 worksheet introductin Maple.
2270MapleIntro.pdf Browser-readable version, which Maple wouldn't know what to do with.
sept4.pdf 2.2: and affine transformations.
Week 3: Sept 8 - Sept 11
sept8.pdf 2.3: composition of matrix transformations, and matrix multiplication.
sept9.pdf 2.4: inverse transformations and inverse matrices.
September 11: We meet in the computer classroom, LCB 115. You'll need to log in to the Math Department system, see directions in the 2270MapleIntro.pdf file posted above, for September 2. We'll also look at the fractal lecture notes in the directory http://www.math.utah.edu/~korevaar/fractals. The Maple 13 file we'll use to make fractals is also in that directory. Your first computer projectis to recreate on the fractals shown in the lecture notes or in the "art gallery", and then to create a new original fractal of your own design.
Week 4: Sept 14 - Sept 18
Sept 14: we'll use the Sept 9 notes!
sept15.pdf 3.1: Image and kernel.
sept16.pdf 3.1-3.2: Image, kernel, and subspace concepts.
sept16maple.mw Maple 13 worksheet which created pages 3-5 of today's notes.
sept16maple.pdf .pdf version
sept18.pdf 3.1-3.3 odds and ends, plus a list of maple matrix commands.
matrixoperations.mw Maple matrix commands
matrixoperations.pdf .pdf version
sept18maple.mw Sept 16 example, with NullSpace and ColumnSpace commands
sept18maple.pdf .pdf version
Week 5: Sept 21 - Sept 25
sept21.pdf Definitions for linear independence and span - to accompany discussion of Friday example.
sept22.pdf 3.3: bases and dimension for subspaces.
sept 23: we'll finish Tuesday's notes, and go over the review sheet for the first exam, posted on our exam page 2270exams.html
Week 6: Sept 28 - Oct 2
sept28.pdf 3.4: vector coordinates with respect to a given basis. Introduction to the matrix of a linear transformation with respect to a given basis.
sept29.pdf 3.4: similar matrices
sept30.pdf 4.1: Linear Spaces (aka vector spaces)
oct2.pdf 4.1: Linear Spaces, subspaces, and examples.
Week 7: Oct 5 - Oct 9
oct5.pdf 4.1-4.2: finish talking about bases and how to find them in general examples; begin talking about linear transformations.
oct6: We'll use Monday's notes.
oct7.pdf 4.2: Linear transformations, kernel, image, isomorphisms.
oct9.pdf 4.2-4.3: Isomorphism theorem details; the matrix of a linear transformation with respect to a basis.
Week 8: Oct 19 - Oct 23
oct19.pdf 5.1: orthonormal bases and projection.
oct19b.pdf change of basis details.
oct20: use Monday's notes.
oct21.pdf 5.1: projection as a linear transformation, and the orthogonal complement to subspaces; Cauchy-Schwarz and triangle inequalities; correlation coefficients and high-dimension angles.
oct23.pdf 5.2: Gram-Schmidt construction of orthonormal bases, and the A=QR decomposition.
Week 9: Oct 26 - Oct 30
oct26.pdf 5.3: orthogonal transformations
oct27.pdf 5.3: transpose algebra; matrices for projection; introduction to least squares solutions (5.4).
oct28.pdf 5.4: general projection formula, and applications of least squares approximate solutions for linear systems.
oct29.pdf 5.4: example of using ln-ln data and linear regression to find power law relationships...relevant to hw, and to Monday Maple project. (First we'll finish Wednesday's notes.)
powerlaws.mw the Maple 13-importable version
Week 10: Nov 2 - Nov 6
project 2 We're in the computer lab on November 1!
nov3.pdf 5.5: inner product spaces, as a way to review chapter 5 concepts. Also bring the Friday notes to class, about using ln-ln linear regression to find power laws. I've also posted a review sheet and review material for Exam 2 on Friday, in our 2270exams directory.
nov4.pdf intro to chapter 6: determinants for 3 by 3 matrices; the other half of the lecture will be for going over the exam 2 review sheet.
Week 11: Nov 9 - Nov 13
nov9.pdf 6.1-6.2 definition of determinant and some of its algebraic properties.
nov10.pdf 6.2 more determinant algebra
nov11.pdf 6.2 (almost) the rest of determinant algebra
nov13.pdf 6.2-6.3 determinant algebra and start of determinant geometry
Week 12: Nov 16 - Nov 20
nov16.pdf 6.3 geometric meaning of determinants.
nov17.pdf 7.1 good bases to analyze discrete dynamical systems.
nov18.pdf 7.2-7.3 how to find eigenvalues and eigenvectors.
nov20.pdf 7.2-7.4 the geometry and algebra of matrix eigenvalues and eigenspaces.
Week 13: Nov 23 - Nov 25
nov23.pdf 7.2-7.4
nov24.pdf 7.3-7.4 odds and ends
nov25.pdf 7.5: introduction to complex eigenvalues and eigenvectors; review/introduction to complex number algebra and geometry.
nov25maple.pdf Maple output for glucose-insulin model.
Week 14: Nov 30 - Dec 4
nov30.pdf 7.5 Glucose-insulin example worked with complex eigenvalues and eigenvectors.
dec1.pdf 7.5-7.6: rotation-dilations to handle complex eigenvalue situation; introduction to 7.6.
dec 2: we'll go over Tuesday notes, other hw questions, and then discuss the google page rank algorithm dynamical system:
page rank notes.pdf
google.pdf Maple computations to accompany the first set of notes.
dec4.pdf Introduction to Chapter 8
Week 16: Dec 7 - Dec 11
dec7.pdf 8.1-8.2 Diagonalizing symmetric matrices and quadratic forms
dec8.pdf 8.1-8.2 applications to quartic surfaces and second derivative test at critical points of multivariable functions. Also, proof of spectral theorem.
dec9.pdf 8.2 positive definite matrices and the second derivative test
finalreview.pdf Friday December 11 is course review day; if you think before class about what we've covered during this semester, you may have some good questions to bring up during our discussion.