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

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Complex Analysis eBooks . We hope mathematician or person who’s interested in mathematics like these books.

A First Course in Complex Analysis with Applications by Dennis G. Zill and Patrick D. Shanahan ,Loyola Marymount University . This is an other great free downloadable mathematics book cover the following topics of complex number.

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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