複變函數論   (89年度 上學期)

(1) CHAPTER 1 From Complex Numbers to Cauchy's Theorem * Complex Numbers * Functions * Power Series * Some Elementary Functions * Curves and Integrals * Cauchy's Theorem (2) CHAPTER 2 Applications of Cauchy's Theorem * Cauchy's Integral Formula * Isolated Singular Points * Evaluation of Definite Integrals * Logarithms and General Powers * Additional Definite Integrals * Zeros of Analytic Functions * Univalence and Inverses * Laurent Series * Combinations of Power Series and Laurent Series * The Maximum Principle (3) CHAPTER 3 Harmonic functions; Conformal Mapping * Harmonic Functions * Harmonic Functions in a Disk * Harmonic Functions and Fourier in a Disk * Conformal Mapping * Some Applications of Conformal Mapping to Physics * Some Special Flows * Mobius Transformations * Further Examples of Transformations and Flows * Dirichlet Problems in General * The Riemann Mapping Theorem * Intuitive Riemann Surfaces

(1) (期中考+期末考) * 75 % (2) 作業成績 25%