(eBook PDF) Complex Analysis: A First Course with Applications 3rd Edition – Digital Ebook – Instant Delivery Download
Product details:
- ISBN-10 : 1449694616
- ISBN-13 : 978-1449694616
- Author: Dennis G. Zill (Author), Patrick D. Shanahan (Author)
Complex Analysis: A First Course with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex analysis, this text discusses the theory of the most relevant mathematical topics in a student-friendly manner. With a clear and straightforward writing style, concepts are introduced through numerous examples, illustrations, and applications. Each section of the text contains an extensive exercise set containing a range of computational, conceptual, and geometric problems. In the text and exercises, students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity.
Table contents:
Chapter 1: Complex Numbers and the Complex Plane
- 1.1: Complex Numbers and Their Properties (7)
- 1.2: Complex Plane (7)
- 1.3: Polar Form of Complex Numbers (5)
- 1.4: Powers and Roots (5)
- 1.5: Sets of Points in the Complex Plane (6)
- 1.6: Applications (3)
- 1: Review Quiz (6)
Chapter 2: Complex Functions and Mappings
- 2.1: Complex Functions (8)
- 2.2: Complex Functions as Mappings (6)
- 2.3: Linear Mappings (7)
- 2.4: Special Power Functions (5)
- 2.5: Reciprocal Function (4)
- 2.6: Applications (3)
- 2: Review Quiz (3)
Chapter 3: Analytic Functions
- 3.1: Limits and Continuity (8)
- 3.2: Differentiability and Analyticity (6)
- 3.3: Cauchy-Riemann Equations (4)
- 3.4: Harmonic Functions (4)
- 3.5: Applications (2)
- 3: Review Quiz (4)
Chapter 4: Elementary Functions
- 4.1: Exponential and Logarithmic Functions (8)
- 4.2: Complex Powers (4)
- 4.3: Trigonometric and Hyperbolic Functions (8)
- 4.4: Inverse Trigonometric and Hyperbolic Functions (6)
- 4.5: Applications
- 4: Review Quiz (7)
Chapter 5: Integration in the Complex Plane
- 5.1: Real Integrals (6)
- 5.2: Complex Integrals (5)
- 5.3: Cauchy-Goursat Theorem (4)
- 5.4: Independence of Path (5)
- 5.5: Cauchy’s Integral Formulas and Their Consequences (5)
- 5.6: Applications (5)
- 5: Review Quiz (11)
Chapter 6: Series and Residues
- 6.1: Sequences and Series (4)
- 6.2: Taylor Series (6)
- 6.3: Laurent Series (5)
- 6.4: Zeros and Poles (4)
- 6.5: Residues and Residue Theorem (5)
- 6.6: Some Consequences of the Residue Theorem (10)
- 6.7: Applications (3)
- 6: Review Quiz (3)
Chapter 7: Conformal Mappings
7.1: Conformal Mapping (3)
7.2: Linear Fractional Transformations (5)
7.3: Schwarz-Christoffel Transformations (4)
7.4: Poisson Integral Formulas (2)
7.5: Applications (2)
7: Review Quiz (2)
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