Math 2270-1
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Professor Korevaar
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Lectures are listed in reverse chronological order.
Week 16
finalreview.pdf review sheet for final exam
dec6.pdf 8.3: singular value decomposition
dec5.pdf 8.2: spectral theorem!!
Week 15
dec2.pdf 8.2: conics and quadric surfaces
dec2maple.pdf 8.1-8.2: Maple worksheet for browser viewing
dec2maple.mws 8.1-8.2: worksheet to open from Maple.
nov30.pdf 7.5, 8.1-8.2: Google's secret; introduction to chapter 8
nov29.pdf 7.6: stability of x=0 for matrix power discrete dynamical systems
nov28.pdf 7.5: powers of complex numbers
Week 14
nov23.pdf 7.5: complex numbers; understanding the glucose-insulin model with complex eigenvalues and eigenvectors.
nov22.pdf 7.4-7.5: powers and similar matrices. Glucose-insulin discrete dynamical system.
nov21.pdf 7.4: When are matrices diagonalizable?
Week 13
nov18.pdf 7.3: 3 by 3 orthogonal matrices with det = 1 are rotations: an example which reviews much!
nov16.pdf 7.3: similar matrices have identical eigenvalue-eigenvector structure.
nov15.pdf 7.2-7.3: finding eigenvalues and eigenspace bases for square matrices
Week 12
nov11.pdf 7.1: Coyotes and roadrunners: discrete dynamical systems
nov9.pdf extra: determinants in multivariable integration formulas: length/area/volume expansion factors.
nov8.pdf 6.3: geometric meaning of determinants, for volumes and orientation.
nov7.pdf 6.2-6.3: determinants of products and transposes; Adjoint inverse formula and Cramer's rule
Week 11
review2.pdf review sheet for exam 2
practice2.pdf practice second exam
nov1.pdf 6.1-6.2: determinant properties
oct31.pdf 6.1: math induction and n by n determinants
Week 10
oct28.pdf 6.1: 3 by 3 determinants
oct26.pdf 5.4: orthogonal complements and the 4 subspaces associated to any Euclidean space linear transformation
oct25.pdf 5.5: inner product spaces
Week 9
oct21.pdf 5.4: applying least squares to data fitting problems
oct19.pdf 5.3-5.4: orthogonal transformations, projection matrices, least-squares solutions to inconsistent systems.
oct18.pdf 5.3: orthogonal transformations
oct17.pdf 5.2: Gram-Schmidt creation of orthonormal bases
Week 8
oct14.pdf 5.1: R^n Pythagorean Theorem, Cauchy Schwarz inequality, and angles
oct12.pdf 5.1: orthonormal bases and projection
oct11.pdf 4.3: how change of basis affects the matrix of a linear transformation
oct10.pdf 4.3: matrix of a linear transformation, examples.
Week 7
oct5.pdf 4.3: matrix of a linear transformation.
oct4.pdf 4.1-4.2: linear transformations, kernel, image, isomorphisms, rank + nullity theorem.
oct3.pdf 4.1-4.2: linear spaces, subspaces, bases, coordinates
Week 6
sept30.pdf 4.1: Linear (combination) spaces, aka vector spaces
sept28.pdf 3.4: matrix of a linear transformation with respect to arbitrary bases
sept26.pdf 3.4: vector coordinates with respect to a given basis
Week 5
sept23.pdf 3.3: interesting theorems about dimension and bases
sept21.pdf 3.2-3.3: using rref to examine column dependencies and to understand important dimension theorems
sept20.pdf 3.2-3.3: for a given subspace a "good" collection of vectors spans it and is linearly independent, i.e. a basis!
sept16.pdf 3.1: finish Friday's notes
Week 4
sept16.pdf 3.1: kernal, image, subspaces
twigexample.pdf an example for what Maple B.2 could look like - lecture finished fractals.pdf
sept13.pdf 2.4+: matrix algeba; understanding fractal algorithm by analogy to Newton iteration for root finding.
2270hw.html sept. 12 lab play with matrix algebra and fractals, in LCB 115
Week 3
sept9.pdf 2.3: inverse transformations and matrices, continued
fractals.pdf extra: notes on fractals
sept7.pdf 2.2-2.4: composition of matrix functions and the matrix product; inverse transformations and the inverse matrix
sept6.pdf 2.2,2.4: geometry and algebra of linear and affine transformations; composition and the matrix product
Week 2
sept2.pdf 2.1: geometry of matrix (linear) and affine transformations.
aug31.pdf Appendix A and 2.1: review of dot product and Euclidean space geometry, begin matrix transformations
aug30.pdf 1.3 properties of rref(A|b) and solution multiplicity. The linear combination interpretation of linear systems.
aug29.pdf 1.2 using reduced row echelon form and backsolving to solve linear systems
Week 1
aug26.pdf 1.1 introduction to applications of linear systems (Professor Alfeld's notes)
aug24.pdf 1.1 introduction to linear algebra and linear geometry