Lecture Notes

Here are scanned copies of my lecture notes from each class day, to be posted shortly after class. Often, what appears on the board in class will be different according to student questions and comments.

Lecture 1, Wednesday, September 9th (introduction to vector operations, subspaces)

Lecture 2, Friday, September 11th (linear transformations)

Lecture 3, Monday, September 14th (composing, inverting linear transformations)

Lecture 4, Wednesday, September 16th (inner product spaces)

Lecture 5, Friday, September 18th (limits of sequences)

Lecture 6, Monday, September 21st (limits of functions)

Lecture 7, Wednesday, September 23rd (continuity, part I of MVT)

Lecture 8, Friday, September 25th (Bolzano-Weierstrass theorem)

Lecture 9, Monday, September 28th (end of MVT proof, start of differentiation)

Lecture 10, Wednesday, September 30th (derivatives as jacobians)

Lecture 11, Friday, October 2nd (properties of derivatives)

Lecture 12, Monday, October 5th (continuous partials imply differentiable)

Lecture 13, Wednesday, October 7th (exam review)

Lecture 14, Monday, October 12th (echelon form)

Lecture 15, Wednesday, October 14th (size of solutions to linear equations)

Lecture 16, Friday, October 16th (elementary matrices)

Lecture 17, Monday, October 19th (computing matrix inverses)

Lecture 18, Wednesday, October 21st (bases, dimension of subspace)

Lecture 19, Friday, October 23rd (subspaces of linear transformations)

Lecture 20, Monday, October 26th (polynomial interpolation)

Lecture 21, Wednesday, October 28th (vector spaces and bases)

Lecture 22, Friday, October 30th (Newton's method)

Lecture 23, Monday, November 2nd (Lipschitz ratio and Kantorovich's theorem)

Lecture 24, Wednesday, November 4th (pf sketch of Kontorovich's theorem, final improvements)

Lecture 25, Friday, November 6th (inverse function theorem)

Lecture 26, Monday, November 9th (implicit function theorem)

Lecture 27, Wednesday, November 11th (exam review)

Lecture 28, Monday, November 16th (definition of manifold)

Lecture 29, Wednesday, November 18th (manifolds are zero loci)

Lecture 30, Friday, November 20th (tangent spaces to manifolds)

Lecture 31, Monday, November 23rd (Taylor polynomials)

Lecture 32, Wednesday, November 25th (little o notation, computing Taylor polynomials)

Lecture 33, Monday, November 30th (Taylor's theorem with remainder)

Lecture 34, Wednesday, December 2nd (local max/min, quadratic forms)

Lecture 35, Friday, December 4th (tests for local extrema)

Lecture 36, Monday, December 7th (constrained extrema)

Lecture 37, Wednesday, December 9th (Lagrange multipliers)

Lecture 38, Friday, December 11th (examples of Lagrange multipliers, spectral theorem)

Lecture 39, Monday, December 14th (exam review, part I)

Solution to problem 3 on review