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, January 20th (intro to the semester, Riemann sums)

Lecture 2, Friday, January 22nd (definition of volume, basic properties)

Lecture 3, Monday, January 25th (whirlwind tour of probability)

Lecture 4, Wednesday, January 27th (integrability of continuous functions)

Lecture 5, Friday, January 29th (measure 0 and integrability)

Lecture 6, Monday, February 1st (Fubini's theorem in two dimensions)

Lecture 7, Wednesday, February 3rd (Fubini's theorem in general)

Lecture 8, Friday, February 5th (numeric integration in one variable)

Lecture 9, Monday, February 8th (numeric integration, Monte Carlo methods)

Lecture 10, Wednesday, February 10th (other pavings, start of determinants)

Lecture 11, Friday, February 12th (algebraic properties of determinants)

Lecture 12, Monday, February 15th (eigenvalues, geometric properties of determinants)

Lecture 13, Wednesday, February 17th (classical changes of variable)

Lecture 14, Friday, February 19th (general changes of variable)

Lecture 15, Monday, February 22nd (exam review)

Lecture 16, Friday, February 26th (integration under limits)

Lecture 17, Monday, February 29th (Lebesgue integration)

Lecture 18, Wednesday, March 2nd (Properties of Lebesgue integration)

Lecture 19, Friday, March 4th (Fourier transform, volumes of k-//ograms)

Lecture 20, Monday, March 7th (the volume integral on manifolds)

Lecture 21, Wednesday, March 9th (relaxed parametrizations, 0-volume)

Lecture 22, Friday, March 11th (independence of parametrization)

Lecture 23, Monday, March 21st (areas of disks on surfaces, curvature)

Lecture 24, Wednesday, March 23rd (Gauss curvature and best coordinates)

Lecture 25, Friday, March 25th (Gauss' Theorem Egregium)

Lecture 26, Monday, March 28th (Review for Exam II)

MIDTERM 2, Wednesday, March 30th (key for midterm solutions)

Lecture 27, Friday, April 1st (differential forms)

Lecture 28, Monday, April 4th (elementary forms, wedge product)

Lecture 29, Wednesday, April 6th (integrating on parameterized manifolds)

Lecture 30, Friday, April 8th (orientation on manifolds)

Lecture 31, Monday, April 11th (orientation-preserving parametrizations)

Lecture 32, Wednesday, April 13th (examples of oriented integrations)

Lecture 33, Friday, April 15th (physical intuition in 3-space)

Lecture 34, Monday, April 18th (boundaries of compact subsets)

Lecture 35, Wednesday, April 20th (orienting boundaries of compact subsets)

Lecture 36, Friday, April 22nd (the exterior derivative)

Lecture 37, Monday, April 25th (computing the exterior d, div, grad, curl)

Lecture 38, Wednesday, April 27th (examples of Stokes' theorem)

Lecture 39, Friday, April 29th (proof sketch of Stokes' theorem)

Lecture 40, Monday, May 2nd (review (part I), Green's theorem)

Lecture 41, Wednesday, May 4th (review (part II), divergence theorem)

Lecture 42, Friday, May 6th (review (part III), proof example)