Publisher:

Chapman & Hall/CRC

Number of Pages:

547

Price:

89.95

ISBN:

9781584888062

Date Received:

Friday, March 5, 2010

Reviewable:

No

Series:

Pure and Applied Mathematics 294

Publication Date:

2010

Format:

Hardcover

Audience:

Category:

Textbook

**The Spaces R, R ^{k}, and C**

The Real Numbers R

The Real Spaces R^{k}

The Complex Numbers C

**Point-Set Topology**

Bounded Sets

Classification of Points

Open and Closed Sets

Nested Intervals and the Bolzano–Weierstrass Theorem

Compactness and Connectedness

**Limits and Convergence**

Definitions and First Properties

Convergence Results for Sequences

Topological Results for Sequences

Properties of Infinite Series

Manipulations of Series in R

**Functions: Definitions and Limits**

Definitions

Functions as Mappings

Some Elementary Complex Functions

Limits of Functions

**Functions: Continuity and Convergence**

Continuity

Uniform Continuity

Sequences and Series of Functions

**The Derivative**

The Derivative for *f*: *D*^{1} ? R

The Derivative for *f*: *D ^{k}* ? R

The Derivative for *f*: *D ^{k}* ? R

The Derivative for *f*: *D* ? C

The Inverse and Implicit Function Theorems

**Real Integration**

The Integral of *f*: [*a*, *b*] ? R

Properties of the Riemann Integral

Further Development of Integration Theory

Vector-Valued and Line Integrals

**Complex Integration**

Introduction to Complex Integrals

Further Development of Complex Line Integrals

Cauchy’s Integral Theorem and Its Consequences

Cauchy’s Integral Formula

Further Properties of Complex Differentiable Functions

Appendices: Winding Numbers Revisited

**Taylor Series, Laurent Series, and the Residue Calculus**

Power Series

Taylor Series

Analytic Functions

Laurent’s Theorem for Complex Functions

Singularities

The Residue Calculus

**Complex Functions as Mappings**

The Extended Complex Plane

Lineal Fractional Transformations

Conformal Mappings

**Bibliography**

**Index**

Publish Book:

Modify Date:

Friday, March 5, 2010

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