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MATH2023 Analysis

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

By: Fergus O' Sullivan
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Decks in this class (13)

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.
23  cards
6 - Power series
Radius of convergence. Ratio test, root test. Cauchy product formula for power series.
23  cards
7 - Functions
Limits of functions, characterisation of limits via sequences. Continuity and differentiability of real and complex functions. Harmonic functions.
27  cards
8 - Sequences of Functions
Pointwise and uniform convergence. Cauchy sequence of functions. Continuity of the limit function. Differentiability of real and complex functions.
12  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.
19  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
13 - Revision and Misc
0  cards

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MATH2023 Analysis

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