University Of North Carolina - Chapel Hill

Finish the lecture on sequences and the convergence of Cauchy. Then introduce the topology of R and in it the epsilon neighborhood of a in R. Define open sets, limit points, isolated points, and closed subsets.

Introduce sequences and its epsilon proof. Then explain sequences with the algebraic limit theorem and the order limit theorem. Write proof for the theorem that a sequence converges if and only if that sequence is a Cauchy sequence.

Give an epsilon proof for the limit of a sequence, where in more detail the partial sum of a series and its convergence is explained and tested with the p-series test. Then, introduce the Cauchy sequence and the monotone convergence theorem.

Explain and provide proof for the algebraic limit theorem and the order limit theorem. Use proof by contradiction for the assumption and conclusion of the two sequences.

Introduce sequences and its epsilon proof. Define the convergence of an to a and how to prove it with a backwards proof by first identifying the candidate for the limit and prove that that is the candidate, then prove convergence. Then introduce some theorems about sequences, namely the algebraic limit theorem and the order limit theorem.

Explain and prove more consequences from the axiom of completeness. First, the density of rational numbers in real numbers using Archimedean principle 1 and axiom of completeness. Then prove the existence of the square root of 2 with contradiction. Lastly, the sequences argument with the algebraic limit theorem and order limit theorem.

Explain the proof for the nested interval property, and also the proofs for the Archimedean Property, which is split into two parts.

Introduce Axiom of Completeness, the bed rock of advanced calculus, where every nonempty bounded above subset of R has a lower upper bound (supremum), and every nonempty bounded below subset of R has a greatest lower bound (infimum). Introduce the consequences of the Axiom of Completeness, with the Nested Interval Property and the Archimedean Property.

Prove the irrationality of square root of two; Give some preliminary introduction to this course, including sets, functions, logics and proofs, induction.

Busi 408 at UNC Chapel Hill's Kenan-Flagler Business School is taught by professor Chip Snively and Melissa Hart. This study guide contains the FULL PACKAGE for everything you need to know, including all class notes, midterm preparation (x2), final exam preparation, and notes from the textbook. It is crucial you do well in this course at it is the prerequisite for most other courses in the Business School, and corporate finance is the basic building block for your future career. Companies and b...