9781107614185

A Course in Mathematical Analysis: Volume 1, Foundations and Elementary Real Analysis

1st

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both studen

22.1

Integration along a path

Exercises

p.680

22.2

Approximating path integrals

Exercises

p.683

22.3

Cauchy’s theorem

Exercises

p.688

22.4

The Cauchy kernel

Exercises

p.690

22.6

Cauchy’s integral formula for circular and square paths

Exercises

p.697

22.7

Simply connected domains

Exercises

p.699

22.8

Liouville’s theorem

Exercises

p.700

22.12

The Schwarz reflection principle

Exercises

p.706

23.1

Zeros

Exercises

p.710

23.2

Laurent series

Exercises

p.713

23.3

Isolated singularities

Exercises

p.717

23.4

Meromorphic functions and the complex sphere

Exercises

p.720

23.5

The residue theorem

Exercises

p.724

23.6

The principle of the argument

Exercises

p.727

23.7

Locating zeros

Exercises

p.732

25.2

Univalent functions on C

Exercises

p.750

25.3

Univalent functions on the punctured plane C∗

Exercises

p.751

25.4

The Mobius group

Exercises

p.757

25.5

The conformal automorphisms of D

Exercises

p.759

25.6

Some more conformal transformations

Exercises

p.762

25.7

The space H(U) of holomorphic functions on a domain U

Exercises

p.765

26.3

The functions πcosec πz

Exercises

p.775

26.5

*Euler’s product formula*

Exercises

p.781

26.6

Weierstrass products

Exercises

p.790

26.7

The gamma function revisited

Exercises

p.793

26.8

Bernoulli numbers, and the evaluation of ζ(2k)

Exercises

p.796

26.9

The Riemann zeta function revisited

Exercises

p.800

29.1

Integrating non-negative functions

Exercises

p.839

29.2

Integrable functions

Exercises

p.844

29.4

Convergence in measure

Exercises

p.853

29.5

The spaces L1 R(X, Σ, μ) and L1 C(X, Σ, μ)

Exercises

p.856

29.6

The spaces Lp R(X, Σ, μ) and Lp C(X, Σ, μ), for 0

Exercises

p.862

29.7

The spaces L∞R (X, Σ, μ) and L∞C (X, Σ, μ)

Exercises

p.864