複變函數

To study elementary theory of functions of a complex variable and its applications to science and engineering

Calculus

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Homework 20% Exam #1 20% Exam #2 30% Final Exam 30%

• Elementary functions

  exponential and logarithmic functions, and trigonometric and hyperbolic functions

  講授：

  3

• Integrals

  contour integrals, upper bounds for moduli of contour integrals, antiderivatives, Cauchy-Goursat theroem, Cauchy integral formula, Liouville's theorem and fundamental theorem of algebra, and maximum modulus principle.

  講授：

  12

• Series representaions of functions

  Taylor series, Laurent series, and power series

  講授：

  6

• Theory of residues and its applications

  isolated singular points, Cauchy's residue theorem, residue at poles, zeros of analytic functions, argument principle, Rouche's theorem, and inverse Laplace transform

  講授：

  10

• Mapping by elementary functions

  Linear transformations, linear fractional transformations, mappings by 1/z, z^2,and z^(1/2), etc.

  講授：

  3

• Conformal mapping

  Preservation of angles, scale factors, local inverse, harmonic conjugates, transformation of harmonic functions, and transformation of boundry conditions

  講授：

  3

• Mapping by elementary functions

  Linear transformations, linear fractional transformations, mappings by 1/z, z^2,and z^(1/2), etc.

  講授：

  3

• Functions of a complex variable

  limits, continuity, derivatives, Cauchy-Riemann equations, analytic functions, harmonic functions

  講授：

  9

Complex variables and Its Applications by J. W. Brown and R. V. Churchill, 9th edition, McGraw Hill 2014.

地點

EE754

時間

Office hours: 2-4 pm Tuesday

聯絡方式

#54317 cmyang@cn.nctu.edu.tw