Continues 18.100. Roughly half the subject devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals.

Analysis I in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.

This is the first of two collections of lecture notes used to teach first year calculus at San Jacinto College (Houston TX). The notes are formatted as presentation slides and were typeset using Beamer (LaTeX). All the main topics of a first semester course in calculus are addressed. In this sense, the notes are self-contained. However, if one deems it necessary to supplement the notes with a full textbook, I recommend one or more of these open-source textbooks:Hoffman, Dale, Contemporary Calculus. 2013Strang, Gilbert and Edwin Herman, Calculus Volume 2. 2016Guichard, David, Community Calculus. 2022