Abhijit Champanerkar

We covered Chapters 7-11 of Rudin's Principles of Mathematical Analysis (1976). Topics include sequences and series of functions, differentiation and integration of functions of several variables, special functions, the integration of differential forms, and Lebesgue integration/measure theory.

Proof based review of single variable calculus as well as sequences and series of functions.

many things, basic topology, sequence, functions, continuity, differentiation, integration and so on

i learned how to slice bread in many many different ways

Calculus with more rigid foundation. Or simply the first 7 chapters of baby rudin...

Calculus with proofs. Literally finishing the baby rudin.

sets (compact sets, closed sets, etc.), functions, sequences and series, continuity, differentiability, integrability (essentially following the outline of chapters in Rudin, all from an abstract perspective); we also, thanks to Prof. Champarnerkar's efforts, picked up some important analysis proof methods that we would return to frequently (using approximations, drawing a picture to understand the problem first, etc.)

We covered the content in Chapters 7, 8, 9, 10, and 11 of Rudin's Principles of Mathematical Analysis ("baby Rudin"), building on last semester's Modern Analysis I, which had covered chapters 1-6 (to finish out Rudin) -- topics included multivariable differentiation (total derivative, Jacobian matrix, etc.), Reimann-Stieglitz integral, Stokes' Theorem (general case for Rn -> Rm), Lebesgue integration theory, etc.; supplemented with other readings, mostly drawn from Spivak's Calculus on Manifolds, which helped develop a deeper understanding of the mathematical concepts involved; Prof. Champarnerkar also made connections to other areas of mathematics such as topology, Fourier Analysis, complex analysis (even if these were not the main focus of this class-- and one definitely did not need to have studied them all previously to take Modern Analysis II).

First half of Baby Rudin. Basically rigorous proofs covering calc1.

In this course we picked up where we left off last semester with Sequences and Series of Functions (Chapter 7 of Rudin) and went all the way through to Lebesgue Theory (Chapter 11) with a few very helpful side ventures into Spivak's Calculus on Manifolds.