Graduate Calculus

Partner: Udemy
Affiliate Name:
Area:
Description: This course provides you with the rigorous mathematics that underlies calculus. You will see proofs of results you have seen in undergraduate calculus and be introduced to much deeper notions, such as compact sets, uniform continuity, Lipschitz continuity, limit supremum, etc.,  all in the generality of metric spaces as well. By working on difficult homework questions, chosen from actual exams, you will be ready to take Qualifying, a.k.a. Prelim, exams in graduate schools. This course can also help with GRE in math subject.You will learn how to write accurate and rigorous proofs. I will show you how to approach a problem and how to bring together scattered observation to formulate a proof. Then, via examples that I do myself, I show you how to present your solutions in a coherent and rigorous way that will meet the standard expected of graduate students (in qualifying exams).In this part 1, we coversequences, and their limits (in metric spaces)limit supremum and limit infimumcontinuity and semi-continuityseries, convergence teststopological definition of continuitycontinuous functions on compact setscontinuous functions on connected setslocal propertiesmodulus of continuityuniformly continuous functions, Lipschitz and Hölder maps, absolutely continuous functionsA possible future course will cover single-variable differential and integral calculus: uniform convergence of sequences and series of functions, equi-continuity, power series, analytic functions and Taylor series. A whole separate course (or even two) is needed to cover multivariable calculus -- but that is far into future.Here is how material is organized:Video Lectures. Each section (7 total) begins with lectures that cover definitions, provide key examples  and counter-examples, and present the most imp
Category: Teaching & Academics > Math > Calculus
Partner ID:
Price: 24.99
Commission:
Source: Impact
Go to Course