Complex Analysis: A First Course with Applications 3rd edition

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• Chapter 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
  • 1: Review Quiz
  
  
• Chapter 2: Complex Functions and Mappings
  • 2.1: Complex Functions
  • 2.2: Complex Functions as Mappings
  • 2.3: Linear Mappings
  • 2.4: Special Power Functions
  • 2.5: Reciprocal Function
  • 2.6: Applications
  • 2: Review Quiz
  
  
• Chapter 3: Analytic Functions
  • 3.1: Limits and Continuity
  • 3.2: Differentiability and Analyticity
  • 3.3: Cauchy-Riemann Equations
  • 3.4: Harmonic Functions
  • 3.5: Applications
  • 3: Review Quiz
  
  
• Chapter 4: Elementary Functions
  • 4.1: Exponential and Logarithmic Functions
  • 4.2: Complex Powers
  • 4.3: Trigonometric and Hyperbolic Functions
  • 4.4: Inverse Trigonometric and Hyperbolic Functions
  • 4.5: Applications
  • 4: Review Quiz
  
  
• Chapter 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
  • 5.6: Applications
  • 5: Review Quiz
  
  
• Chapter 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
  • 6.7: Applications
  • 6: Review Quiz
  
  
• Chapter 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: Review Quiz