ABSTRACT

Presents Real & Complex Analysis Together Using a Unified ApproachA two-semester course in analysis at the advanced undergraduate or first-year graduate levelUnlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together. It takes a unified, elegant approach to the theory that is consistent with

chapter 1|21 pages

3 Intervals inR

PACES

chapter |2 pages

z Re + R

chapter |8 pages

uuuu1

chapter 2|1 pages

POINT-SET TOPOLOGY

chapter 2|2 pages

Point-Set Topology

OUNDED

chapter 1|9 pages

2 Bounded Sets inR

chapter 2|3 pages

2 Limit Points and Isolated Points

chapter 3|2 pages

OPEN AND CLOSED SETS

chapter 3|25 pages

2 Closed Sets

chapter 3|1 pages

LIMITS CONVERGENCE

chapter 3|51 pages

Limits and Convergence

EFINITIONS AND ROPERTIES

chapter 4|1 pages

FUNCTIONS: DEFINITIONS LIMITS

chapter 1|20 pages

1 Notation andDefinitions

chapter |12 pages

IMITS OF

UNCTIONS

chapter 1|9 pages

tanθ sinθ θ

chapter 5|21 pages

FUNCTIONS: CONTINUITY CONVERGENCE

chapter |12 pages

2UC

NIFORM ONTINUITY

chapter 3|23 pages

2 UniformConvergence

chapter 6|22 pages

THE DERIVATIVE

chapter 3|14 pages

2 SomeUseful Results

chapter 4|13 pages

3 The Cauchy-RiemannEquations

chapter 5|22 pages

2 The Inverse Function Theorem

chapter 7|10 pages

REAL INTEGRATION

chapter |15 pages

PPP

chapter 2|27 pages

3 The Fundamental Theorem of Calculus

chapter 8|14 pages

COMPLEX INTEGRATION

chapter 2|1 pages

3 Antiderivatives and Path-Independence

chapter |7 pages

zCCz

chapter 3|27 pages

3 Deformation of Contours

chapter |5 pages

7SE

UPPLEMENTARY XERCISES

chapter |1 pages

AURENT ’ STCF

HEOREM FOR OMPLEX UNCTIONS

chapter 4|1 pages

LAURENT’S THEOREM FOR COMPLEX FUNCTIONS

chapter |16 pages

rzr

chapter |1 pages

N (z) rCzC

chapter C|9 pages

(α) $ α θ

chapter 10|19 pages

COMPLEX FUNCTIONS MAPPINGS

XTENDED OMPLEX

chapter |3 pages

4SE

UPPLEMENTARY XERCISES