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**A First Course in Complex Analysis with Applications ** written by
** Dennis G. Zill, Patrick D. Shanahan **.

This text grew out of chapters 17-20 in Advanced Engineering Mathematics, Second Edition (Jones and Bartlett Publishers), by Dennis G. Zill and the late Michael R. Cullen. This present work represents an expansion and revision of that original material and is intended for use in either a one-semester or a one-quarter course. Its aim is to introduce the basic principles and applications of complex analysis to undergraduates who have no prior knowledge of this subject.

The motivation to adapt the material from Advanced Engineering Mathematics into a stand-alone text sprang from our dissatisfaction with the succession of textbooks that we have used over the years in our departmental undergraduate course offering in complex analysis. It has been our experience that books claiming to be accessible to undergraduates were often written at a level that was too advanced for our audience. The “audience” for our juniorlevel course consists of some majors in mathematics, some majors in physics, but mostly majors from electrical engineering and computer science. At our institution, a typical student majoring in science or engineering does not take theory-oriented mathematics courses in methods of proof, linear algebra, abstract algebra, advanced calculus, or introductory real analysis.

(Dennis G. Zill)

**Book Detail :- **
** Title: ** A First Course in Complex Analysis with Applications
** Edition: **
** Author(s): ** Dennis G. Zill, Patrick D. Shanahan
** Publisher: ** Jones and Bartlett
** Series: **
** Year: ** 2003
** Pages: ** 517
** Type: ** PDF
** Language: ** English
** ISBN: ** 0763714372,9780763714376,9780585462769
** Country: ** US

** Download from Amazon : **

**About Author :- **

Author ** Dennis G. Zill ** is Professor of Mathematics from Loyola Marymount University, Los Angeles, CA, United States

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**A First Course in Complex Analysis with Applications ** written by
** Dennis G. Zill, Patrick D. Shanahan **
cover the following topics.
**1. Complex Numbers and the Complex Plane **

1.1 Complex Numbers and Their Properties

1.2 Complex Plane

1.3 Polar Form of Complex Numbers

1.4 Powers and Roots

1.5 Sets of Points in the Complex Plane

1.6 Applications

Review Quiz
**2. Complex Functions and Mappings**

2.1 Complex Functions

2.2 Complex Functions as Mappings

2.3 Linear Mappings

2.4 Special Power Functions

2.4.1 The Power Function zn

2.4.2 The Power Function z1/n

2.5 Reciprocal Function

2.6 Limits and Continuity

2.6.1 Limits

2.6.2 Continuity

2.7 Applications

Review Quiz
**3. Analytic Functions**

3.1 Differentiability and Analyticity

3.2 Cauchy-Riemann Equations

3.3 Harmonic Functions

3.4 Applications

Review Quiz
**4. Elementary Functions**

4.1 Exponential and Logarithmic Functions

4.1.1 Complex Exponential Function

4.1.2 Complex Logarithmic Function

4.2 Complex Powers

4.3 Trigonometric and Hyperbolic Functions

4.3.1 Complex Trigonometric Functions

4.3.2 Complex Hyperbolic Functions

4.4 Inverse Trigonometric and Hyperbolic Functions

4.5 Applications

Review Quiz
**5. Integration in the Complex Plane**

5.1 Real Integrals

5.2 Complex Integrals

5.3 Cauchy-Goursat Theorem

5.4 Independence of Path

5.5 Cauchy’s Integral Formulas and Their Consequences

5.5.1 Cauchy’s Two Integral Formulas

5.5.2 Some Consequences of the Integral Formulas

5.6 Applications

Review Quiz
**6. Series and Residues **

6.1 Sequences and Series

6.2 Taylor Series

6.3 Laurent Series

6.4 Zeros and Poles

6.5 Residues and Residue Theorem

6.6 Some Consequences of the Residue Theorem

6.6.1 Evaluation of Real Trigonometric Integrals

6.6.2 Evaluation of Real Improper Integrals

6.6.3 Integration along a Branch Cut

6.6.4 The Argument Principle and Rouch´e’s Theorem

6.6.5 Summing Infinite Series

6.7 Applications

Review Quiz
**7. Conformal Mappings**

7.1 Conformal Mapping

7.2 Linear Fractional Transformations

7.3 Schwarz-Christoffel Transformations

7.4 Poisson Integral Formulas

7.5 Applications

7.5.1 Boundary-Value Problems

7.5.2 Fluid Flow

Review Quiz
**Appendixes **

I Proof of Theorem 2.1 APP-2

II Proof of the Cauchy-Goursat Theorem APP-4

III Table of Conformal Mappings APP-9

Answers for Selected Odd-Numbered Problems ANS-1

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