# MATH2023 Analysis

This class was created by Brainscape user Fergus O' Sullivan. Visit their profile to learn more about the creator.

Flashcard maker: Fergus O' Sullivan
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## Decks in this class (12)

1 - Numbers
Foundation of natural numbers, integers, rational, real, and complex numbers. Incompleteness of rationals and completeness of reals. Infimum, supremum.
57  cards
2 - Sequences and Convergence
Limit laws, squeeze law, monotone convergence theorem, convergence tests. Euler number, n-th root.
26  cards
3 - Sequences and Convergence 2.0
Limit superior and limit inferior, subsequences, accumulation points, Cauchy sequences.
20  cards
4 - Number series
Convergence. Geometric, harmonic, telescoping series and their convergence or divergence. Series of positive numbers, comparison test.
22  cards
5 - Number Series 2.0
Alternating series, convergence test. Conditional and absolute convergence. Ratio and root tests, rearrangement, Cauchy product formula.
0  cards
6 - Power series
Radius of convergence. Ratio test, root test. Cauchy product formula for power series.
0  cards
7 - Functions
Limits of functions, characterisation of limits via sequences. Continuity and differentiability of real and complex functions. Harmonic functions.
0  cards
8 - Sequences of Functions
Pointwise and uniform convergence. Cauchy sequence of functions. Continuity of the limit function. Differentiability of real and complex functions.
0  cards
9 - Power Series 2.0
Uniform convergence of power series, Weierstrass test. Continuity, differentiation and integration using uniform convergence and application to power series. Uniqueness of power series, analytic functions.
0  cards
10 - Contour Integration
Curves in the plane. Integral along piecewise smooth curves. Fundamental theorem of calculus, primitives and path independence.
0  cards
11 - Contour Integration 2.0
Existence of primitive. Cauchy’s integral theorem and Cauchy’s integral formula.
0  cards
12 - Residue and Singularities
Isolated singularities and classification. Residues, residue theorem. Application to calculation of real integrals.
0  cards

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