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12 Sachen
Advanced Calculus I (MATH521)
This package provides the full course class notes, homework answers, and exam questions for the course MATH521 (advanced calculus I) at UNC Chapel hill.
- Paket-deal
- • 11 Sachen •
- Introduction to Advanced Calculus 1 (The Real Numbers) • Notizen
- Axiom of Completeness and Consequences • Notizen
- Consequences of Axiom of Completeness • Notizen
- Consequences from Axiom of Completeness Continued. • Notizen
- Sequences • Notizen
- Und mehr ….
This package provides the full course class notes, homework answers, and exam questions for the course MATH521 (advanced calculus I) at UNC Chapel hill.
Compact Sets
Introduce and provide proof for compact sets, that is a set that is both bounded and closed, hence the Heine-Borel theorem. Then introduce the perfect set, the connected/disconnected sets, and lastly the canter set, write proofs for all three.
- Book & Paket-Deal
- Notizen
- • 4 Seiten •
Introduce and provide proof for compact sets, that is a set that is both bounded and closed, hence the Heine-Borel theorem. Then introduce the perfect set, the connected/disconnected sets, and lastly the canter set, write proofs for all three.
Topology of R
Continue introducing the different parts to the topology of R, from the epsilon neighborhood of a, to open subsets of R, isolated points and limit points of A, then closed sets. Proof these different fundamentals of topology.
- Paket-Deal
- Notizen
- • 2 Seiten •
Continue introducing the different parts to the topology of R, from the epsilon neighborhood of a, to open subsets of R, isolated points and limit points of A, then closed sets. Proof these different fundamentals of topology.
Sequences and Topology of R
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.
- Book & Paket-Deal
- Notizen
- • 4 Seiten •
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.
Sequences
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.
- Book & Paket-Deal
- Notizen
- • 3 Seiten •
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.
Limit of 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.
- Book & Paket-Deal
- Notizen
- • 2 Seiten •
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.
Algebraic Limit Theorem and Order Limit 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.
- Book & Paket-Deal
- Notizen
- • 3 Seiten •
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.
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.
- Book & Paket-Deal
- Notizen
- • 2 Seiten •
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.
Consequences from Axiom of Completeness Continued.
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.
- Book & Paket-Deal
- Notizen
- • 3 Seiten •
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.
Introduction to Advanced Calculus 1 (The Real Numbers)
Prove the irrationality of square root of two; Give some preliminary introduction to this course, including sets, functions, logics and proofs, induction.
- Book & Paket-Deal
- Notizen
- • 2 Seiten •
Prove the irrationality of square root of two; Give some preliminary introduction to this course, including sets, functions, logics and proofs, induction.