Applied Complex Variables and Asymptotic Methods

Complex Numbers and Elementary Functions Holomorphic Functions and Cauchy-Riemann Equations Harmonic Functions and Poisson Integral Formula Cauchy Integral Formula and Integral Theorems Laurent Series and Annuli Isolated Singularities and Residues Branch Points, Branch Cuts, and Logarithms Entire Functions and Liouville's Theorem Meromorphic Functions and the Argument Principle Rouche's Theorem and Zero Counting Fundamental Theorem of Algebra Contour Integration and Residue Calculus Jordan's Lemma and Arc Estimates Keyhole and Sector Contours Principal Value Integrals Real Integral Evaluation by Complex Methods Conformal Mapping and Bilinear Transformations Complex Potential Flow and Blasius Formula Watson's Lemma and Laplace's Method Stationary Phase and Steepest Descent Maximum Modulus Principle